%% PVS Version 5.0 - Allegro CL Enterprise Edition 8.2 [64-bit Mac OS X (Intel)] (Nov 3, 2011 16:18) %% 8.2 [64-bit Mac OS X (Intel)] (Nov 3, 2011 16:18) $$$pvs-strategies (defstep s-rest () (then (skosimp) (expand "step") (assert) (hide-all-but ( 1 ) +) (branch (split) ((grind))) ) "help string" "skosimp, expand step, assert, hide, split, grind" ) (defstep replaceh (arg) (replace arg :hide? t) "help string" "replace arg :hide? t" ) (defstep s-ensures () (then (skosimp) (use ensures_leto) (assert) (hide 2) (expand "ensures") (expand "co") (expand "transient") (expand "<=" +) (expand "wp") (expand "cap") (expand "cup") (expand "neg") (expand "at") ) "help-string" "using ensures, and expanding; the argument is the responsible thread" ) $$$ownpred.pvs % Wim H. Hesselink, October 2012 ownpred[t: TYPE]: THEORY % to avoid the function member % about predicates, relations, and mu-calculus BEGIN p, q, r, s: VAR pred[t] x, y: VAR t k, n: VAR nat pseq: VAR [nat -> pred[t]] rel: VAR pred[[t, t]] neg(p)(x): bool = NOT p(x) neg_involutive: LEMMA neg(neg(p)) = p cup(p, q)(x): bool = p(x) OR q (x) cap(p, q)(x): bool = p(x) AND q (x) bigcup(pseq)(x): bool = EXISTS k: pseq(k)(x) bigcup(n, pseq)(x): bool = EXISTS k: k < n AND pseq(k)(x) wp(rel)(q)(x): bool = FORALL y: rel(x, y) IMPLIES q(y) END ownpred $$$ownpred.prf (ownpred (neg_involutive 0 (neg_involutive-1 nil 3358782077 ("" (skolem!) (("" (apply-extensionality :hide? t) (("" (expand "neg") (("" (propax) nil nil)) nil)) nil)) nil) ((t formal-type-decl nil ownpred nil) (boolean nonempty-type-decl nil booleans nil) (neg const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (bool nonempty-type-eq-decl nil booleans nil)) shostak))) $$$bdUnity.pvs % Bounded Unity by Wim H. Hesselink, September-October 2013 bdUnity[ t: TYPE ]: THEORY BEGIN IMPORTING ownpred, maxfinset % used in run_round below p, q, pq, pa, pm: VAR pred[t] x, y: VAR t i, j, k, m, n: VAR nat xs, ys: VAR [nat -> t] pset: VAR pred[pred[t]] specification: TYPE = [# inv: pred[t], % the global invariant step: pred[[t, t]], % the step relation fwd: [nat -> pred[[t, t]]] % weak fairness relations #] s: VAR specification enabled(s)(k)(x): bool = EXISTS y: s`fwd(k)(x, y) good(s): bool = reflexive?(s`step) % AND (s`inv <= wp(s`step)(s`inv)) % AND (FORALL k: s`fwd(k) <= s`step) % all used in machine closed AND (FORALL x: s`inv(x) IMPLIES % locally finite(s) is_finite({k | enabled(s)(k)(x)}) ) % nuspec: (good) = (# inv := fullset, step := fullset, fwd := (LAMBDA i: emptyset) #) co(s)(p, q): bool = cap(p, s`inv) <= wp(s`step)(q) unless(s)(p, q): bool = cap(cap(p, neg(q)), s`inv) <= wp(s`step)(cup(p, q)) unless_co: LEMMA unless(s)(p, q) = co(s)(cap(p, neg(q)), cup(p, q)) co_unless: LEMMA pm = difference(q, p) AND p <= pa AND pa <= q IMPLIES co(s)(p, q) = unless(s)(pa, pm) stable(s)(p): bool = co(s)(p, p) cobar(s)(p, q): bool = EXISTS k: p <= enabled(s)(k) AND FORALL x, y: p(x) AND s`fwd(k)(x, y) IMPLIES q(y) transient(s)(p): bool = EXISTS k: cap(p, s`inv) <= enabled(s)(k) AND FORALL x, y: p(x) AND s`fwd(k)(x, y) AND s`inv(x) IMPLIES NOT p(y) ensuresA(s)(p, q): bool = co(s)(cap(p, neg(q)), cup(p, q)) AND cobar(s)(cap(cap(p, neg(q)), s`inv), q) ensures(s)(p, q): bool = co(s)(cap(p, neg(q)), cup(p, q)) AND transient(s)(cap(p, neg(q))) ensuresA_ensures: LEMMA good(s) IMPLIES ensuresA(s)(p, q) = ensures(s)(p, q) fw(s)(k)(x, y): bool = s`fwd(k)(x, y) OR NOT enabled(s)(k)(x) subset_ensures: LEMMA % cap(p, s`inv) <= q IMPLIES ensures(s)(p, q) stable_unless: LEMMA unless(s)(p, q) AND stable(s)(pq) IMPLIES unless(s)(cap(p, pq), q) stable_ensures: LEMMA % ensures(s)(p, q) AND stable(s)(pq) IMPLIES ensures(s)(cap(p, pq), q) % Formal semantics of bounded unity % An operational interpretation exec(s)(xs): bool = FORALL n: s`step(xs(n), xs(n+1)) AND s`inv(xs(n)) weakfair(s)(k)(xs): bool = FORALL n: EXISTS i: fw(s)(k)(xs(n+i), xs(n+i+1)) run(s)(xs): bool = exec(s)(xs) AND FORALL k: weakfair(s)(k)(xs) sched(n): nat = min({i | EXISTS k: k * k + i = n}) sched_schedules: LEMMA i <= j IMPLIES sched(j * j + i) = i choice(s, k, x): pred[t] = { y | s`fwd(k)(x, y)} chosen(s, k, x): t = IF empty?(choice(s, k, x)) THEN x ELSE epsilon(choice(s, k, x)) ENDIF runfrom(s, x)(n): RECURSIVE t = IF n = 0 THEN x ELSE chosen(s, sched(n - 1), runfrom(s, x)(n - 1)) ENDIF MEASURE n runfrom_run: LEMMA s`inv(x) AND good(s) IMPLIES run(s)(runfrom(s, x)) run_exists: LEMMA s`inv(x) AND good(s) IMPLIES EXISTS xs: run(s)(xs) AND xs(0) = x machine_closed: LEMMA exec(s)(xs) AND good(s) IMPLIES EXISTS ys: run(s)(ys) AND (FORALL i: i <= n IMPLIES ys(i) = xs(i)) drop(n)(xs)(i): t = xs(n + i) drop_run: LEMMA run(s)(xs) IMPLIES run(s)(drop(n)(xs)) round(s)(n, xs): bool = FORALL k: EXISTS i: i < n AND fw(s)(k)(xs(i), xs(i+1)) run_round: LEMMA % locally finite run(s)(xs) AND good(s) IMPLIES EXISTS n: round(s)(n, xs) rounds(s)(i)(n, xs): RECURSIVE bool = IF i = 0 THEN true ELSE EXISTS j: j <= n AND round(s)(j, xs) AND rounds(s)(i-1)(n-j, drop(j)(xs)) ENDIF MEASURE i run_rounds: LEMMA run(s)(xs) AND good(s) IMPLIES EXISTS n: rounds(s)(i)(n, xs) rounds_split: LEMMA rounds(s)(j+m)(n, xs) IMPLIES EXISTS i: i <= n AND rounds(s)(j)(i, xs) AND rounds(s)(m)(n-i, drop(i)(xs)) rounds_down: LEMMA i <= j AND rounds(s)(j)(n, xs) IMPLIES rounds(s)(i)(n, xs) rounds_furtheron: LEMMA rounds(s)(j)(n, drop(i)(xs)) IMPLIES rounds(s)(j)(n + i, xs) leto(s)(j, p, q): bool = % bounded leads-to FORALL xs: exec(s)(xs) AND p(xs(0)) IMPLIES FORALL n: rounds(s)(j)(n, xs) IMPLIES EXISTS i: i <= n AND q(xs(i)) leadsto(s)(p, q): bool = FORALL xs: run(s)(xs) AND p(xs(0)) IMPLIES EXISTS i: q(xs(i)) leto_leadsto: LEMMA leto(s)(j, p, q) AND good(s) IMPLIES leadsto(s)(p, q) % Fundamental rules for leto subset_leto: LEMMA % cap(p, s`inv) <= q IMPLIES leto(s)(j, p, q) ensures_leto: LEMMA % ensures(s)(p, q) IMPLIES leto(s)(1, p, q) leto_union: LEMMA (FORALL p: pset(p) IMPLIES leto(s)(n, p, q)) IMPLIES leto(s)(n, Union(pset), q) leto_transitive: LEMMA leto(s)(m, p, pq) AND leto(s)(n, pq, q) IMPLIES leto(s)(m + n, p, q) PSP_leto: LEMMA % leto(s)(n, p, q) AND unless(s)(pa, pm) IMPLIES leto(s)(n, cap(p, pa), cup(cap(q, pa), pm)) PSP0_leto: LEMMA % unless(s)(p, q) AND leto(s)(n, fullset, neg(pa)) AND p <= pa IMPLIES leto(s)(n, p, q) leto_completion: LEMMA (FORALL q: pset(q) IMPLIES leto(s)(n, p, q) AND unless(s)(q, pm) ) IMPLIES leto(s)(n, p, cup(Intersection(pset), pm)) % Derived rules stable_conjunction: LEMMA leto(s)(n, p, q) AND stable(s)(pa) IMPLIES leto(s) (n, cap(p, pa), cap(q, pa)) cup_leto: LEMMA leto(s)(m, p, q) AND leto(s)(m, pq, q) IMPLIES leto(s)(m, cup(p, pq), q) leto_transitive_2: LEMMA leto(s)(m, p, cup(pq, pa)) AND leto(s)(n, pq, cup(q, pa)) IMPLIES leto(s)(m + n, p, cup(q, pa)) leto_transitive_1: LEMMA leto(s)(m, p, cup(pq, q)) AND leto(s)(n, pq, q) IMPLIES leto(s)(m + n, p, q) leto_up: LEMMA % leto(s)(i, p, q) AND i <= j IMPLIES leto(s)(j, p, q) sub_leto: LEMMA cap(p, s`inv) <= pq AND leto(s)(n, pq, q) IMPLIES leto(s)(n, p, q) leto_sub: LEMMA cap(pq, s`inv) <= q AND leto(s)(n, p, pq) IMPLIES leto(s)(n, p, q) shunting_leto: LEMMA leto(s)(n, cap(p, neg(pq)), q) IMPLIES leto(s)(n, p, cup(q, pq)) leto_inv: LEMMA leto(s)(j, cap(p, s`inv), q) = leto(s)(j, p, q) %%%%%%%% Measure z: VAR int vf, svf: VAR [t -> int] vena: VAR [nat -> pred[t]] r: VAR posnat fac, del: VAR posnat % factor, delay delay, offset: VAR nat cov: VAR [nat -> pred[t]] we: VAR [posnat -> posnat] mwe: VAR posnat alt, exc: VAR pred[t] leq(z, vf)(x): bool = z <= vf(x) disgrowth(s, vf, we, cov): bool = (FORALL z, r: leto(s)(we(r), cap(leq(z, vf), cov(r)), leq(z + we(r), vf) )) distributed_progress: THEOREM % disgrowth(s, vf, we, cov) AND (FORALL r: we(r) <= mwe) AND (FORALL x: s`inv(x) IMPLIES EXISTS i: cov(i)(x)) IMPLIES leto(s)(n + mwe - 1, leq(z, vf), cup(leq(z + n, vf), cov(0))) proportional_progress: THEOREM (FORALL k, z: leto(s)(k + offset, leq(z, vf), cup(leq(z + k, vf), alt))) AND (FORALL x: s`inv(x) IMPLIES fac * svf(x) <= vf(x)) AND (FORALL x: s`inv(x) IMPLIES vf(x) <= fac * svf(x) + delay OR exc(x)) IMPLIES leto(s)(fac * i + delay + offset, leq(z, svf), cup(leq(z + i, svf), cup(alt, exc)) ) fwd_measure(vf, vena, s): bool = (FORALL x, y: s`step(x, y) AND s`inv(x) IMPLIES vf(x) <= vf(y)) % 1 AND (FORALL k: cap(vena(k), s`inv) <= enabled(s)(k)) % 2 AND (FORALL k, x, y: s`fwd(k)(x, y) AND vena(k)(x) AND s`inv(x) % 3 IMPLIES vf(x) < vf(y) ) AND (FORALL k, x, y: s`step(x, y) AND vena(k)(x) AND s`inv(x) % 4 IMPLIES vena(k)(y) OR vf(x) < vf(y) ) fwd_measure_ensures: LEMMA %% using %1, %4, %2, %3, using ensures fwd_measure(vf, vena, s) IMPLIES leto(s)(1, cap(leq(z, vf), vena(k)), leq(z + 1, vf)) none(vena, s)(x): bool = FORALL k: NOT vena(k)(x) fwd_measure_leadsto: LEMMA fwd_measure(vf, vena, s) IMPLIES leto(s)(1, leq(z, vf), cup(leq(z + 1, vf), none(vena, s))) fwd_measure_leadsto_more: LEMMA fwd_measure(vf, vena, s) IMPLIES leto(s)(n, leq(z, vf), cup(leq(z + n, vf), none(vena, s))) proportional(vf, svf, fac, del)(x): bool = fac * svf(x) <= vf(x) AND vf(x) < fac * svf(x) + del proportional_measure_leadsto: THEOREM fwd_measure(vf, vena, s) AND subset?(s`inv, proportional(vf, svf, fac, del)) AND fac * (i - 1) + del <= n IMPLIES leto(s)(n, leq(z, svf), cup(leq(z + i, svf), none(vena, s))) proportionA(vf, svf, fac)(x): bool = fac * svf(x) <= vf(x) proportionB(vf, svf, fac, del)(x): bool = vf(x) < fac * svf(x) + del proportional_measure_leadsto1: THEOREM fwd_measure(vf, vena, s) AND subset?(s`inv, proportionA(vf, svf, fac)) AND subset?(cap(s`inv, p), proportionB(vf, svf, fac, del)) AND fac * (i - 1) + del <= n IMPLIES leto(s)(n, leq(z, svf), cup(neg(p), cup(leq(z + i, svf), none(vena, s))) ) %%%% now the same for leadsto subset_leadsto: LEMMA % cap(p, s`inv) <= q IMPLIES leadsto(s)(p, q) ensures_leadsto: LEMMA % ensures(s)(p, q) IMPLIES leadsto(s)(p, q) leadsto_union: LEMMA (FORALL p: pset(p) IMPLIES leadsto(s)(p, q)) IMPLIES leadsto(s)(Union(pset), q) leadsto_transitive: LEMMA leadsto(s)(p, pq) AND leadsto(s)(pq, q) IMPLIES leadsto(s)(p, q) PSP_leadsto: LEMMA % leadsto(s)(p, q) AND unless(s)(pa, pm) IMPLIES leadsto(s)(cap(p, pa), cup(cap(q, pa), pm)) % leadsto_completion: LEMMA % This can be proved if pset is finite. % (FORALL q: pset(q) % IMPLIES leadsto(s)(n, p, q) AND unless(s)(q, pm) ) % IMPLIES leadsto(s)(n, p, cup(Intersection(pset), pm)) % Derived rules cup_leadsto: LEMMA % can be derived from leadsto_union leadsto(s)(p, q) AND leadsto(s)(pq, q) IMPLIES leadsto(s)(cup(p, pq), q) leadsto_transitive_2: LEMMA leadsto(s)(p, cup(pq, pa)) AND leadsto(s)(pq, cup(q, pa)) IMPLIES leadsto(s)(p, cup(q, pa)) leadsto_transitive_1: LEMMA leadsto(s)(p, cup(pq, q)) AND leadsto(s)(pq, q) IMPLIES leadsto(s)(p, q) sub_leadsto: LEMMA cap(p, s`inv) <= pq AND leadsto(s)(pq, q) IMPLIES leadsto(s)(p, q) leadsto_sub: LEMMA cap(pq, s`inv) <= q AND leadsto(s)(p, pq) IMPLIES leadsto(s)(p, q) shunting_leadsto: LEMMA leadsto(s)(cap(p, neg(pq)), q) IMPLIES leadsto(s)(p, cup(q, pq)) leadsto_inv: LEMMA leadsto(s)(cap(p, s`inv), q) = leadsto(s)(p, q) bounding_leadsto: LEMMA leadsto(s)(p, q) AND leto(s)(n, p, cup(q, pa)) AND stable(s)(pa) AND empty?(cap(q, pa)) AND good(s) IMPLIES leto(s)(n, p, q) END bdUnity $$$bdUnity.prf (bdUnity (nuspec_TCC1 0 (nuspec_TCC1-1 nil 3591000903 ("" (expand "good") (("" (split) (("1" (grind) nil nil) ("2" (grind) nil nil) ("3" (grind) nil nil) ("4" (skosimp) (("4" (expand "is_finite") (("4" (inst + 1 id) (("1" (grind) nil nil) ("2" (skosimp) (("2" (expand "id") (("2" (expand "fullset") (("2" (typepred x1!1) (("2" (expand "enabled") (("2" (expand "emptyset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((fullset const-decl "set" sets nil) (reflexive? const-decl 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(("" (inst - pa!1 emptyset) (("" (assert) (("" (split) (("1" (case "cup(cap(q!1, pa!1), emptyset) =cap(q!1, pa!1)") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (expand "emptyset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1 2) (("2" (expand "unless") (("2" (expand "stable") (("2" (expand "co") (("2" (expand "<=") (("2" (expand "wp") (("2" (expand "cup") (("2" (expand "cap") (("2" (expand "neg") (("2" (expand "emptyset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((PSP_leto formula-decl nil bdUnity nil) (emptyset const-decl "set" sets nil) (set type-eq-decl nil sets nil) (cap const-decl "bool" ownpred nil) (cup const-decl "bool" ownpred nil) (= const-decl "[T, T -> boolean]" equalities nil) (unless const-decl "bool" bdUnity nil) (co const-decl "bool" bdUnity nil) (wp const-decl "bool" ownpred nil) (neg const-decl "bool" ownpred nil) (<= const-decl "bool" mucalculus nil) (stable const-decl "bool" bdUnity nil) (finite_emptyset name-judgement "finite_set" finite_sets nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (t formal-type-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) nil) (stable_conjunction-1 nil 3617510892 ("" (skosimp) (("" (lemma PSP_leadold) (("" (inst?) (("" (inst - pa!1 emptyset) (("" (assert) (("" (split) (("1" (case "cup(cap(q!1, pa!1), emptyset) =cap(q!1, pa!1)") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (expand "emptyset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1 2) (("2" (expand "unless") (("2" (expand "stable") (("2" (expand "co") (("2" (expand "<=") (("2" (expand "wp") (("2" (expand "cup") (("2" (expand "cap") (("2" (expand "neg") (("2" (expand "emptyset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((emptyset const-decl "set" sets nil) (set type-eq-decl nil sets nil) (cap const-decl "bool" ownpred nil) (cup const-decl "bool" ownpred nil) (= const-decl "[T, T -> boolean]" equalities nil) (unless const-decl "bool" bdUnity nil) (co const-decl "bool" bdUnity nil) (wp const-decl "bool" ownpred nil) (neg const-decl "bool" ownpred nil) (<= const-decl "bool" mucalculus nil) (stable const-decl "bool" bdUnity nil) (finite_emptyset name-judgement "finite_set" finite_sets nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (t formal-type-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) shostak)) (cup_leto 0 (cup_leto-1 nil 3624287140 ("" (skosimp) (("" (lemma leto_union) (("" (name ppset "{p:pred[t] | p = p!1 OR p = pq!1}") (("" (inst - m!1 ppset q!1 s!1) (("" (case "Union(ppset) = cup(p!1, pq!1)") (("1" (replaceh -1) (("1" (assert) (("1" (skosimp) (("1" (expand "ppset") (("1" (split) (("1" (assert) nil nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (prop) (("1" (expand "Union") (("1" (expand "cup") (("1" (flatten) (("1" (skolem!) (("1" (typepred a!1) (("1" (expand "ppset") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "Union") (("2" (expand "cup") (("2" (split) (("1" (inst?) (("1" (expand "ppset") (("1" (propax) nil nil)) nil)) nil) ("2" (inst?) (("2" (assert) (("2" (expand "ppset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((leto_union formula-decl nil bdUnity nil) (number nonempty-type-decl nil numbers nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (specification type-eq-decl nil bdUnity nil) (p!1 skolem-const-decl "pred[t]" bdUnity nil) (pq!1 skolem-const-decl "pred[t]" bdUnity nil) (NOT const-decl "[bool -> bool]" booleans nil) (Union_surjective name-judgement "(surjective?[setofsets[T], set[T]])" sets_lemmas nil) (ppset skolem-const-decl "[pred[t] -> boolean]" bdUnity nil) (cup const-decl "bool" ownpred nil) (Union const-decl "set" sets nil) (setofsets type-eq-decl nil sets nil) (setof type-eq-decl nil defined_types nil) (set type-eq-decl nil sets nil) (t formal-type-decl nil bdUnity nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (pred type-eq-decl nil defined_types nil) (= const-decl "[T, T -> boolean]" equalities nil) (OR const-decl "[bool, bool -> bool]" booleans nil)) shostak)) (leto_transitive_2 0 (leto_transitive_2-1 nil 3624287477 ("" (skosimp) (("" (lemma leto_transitive) (("" (inst - m!1 n!1 p!1 "cup(pq!1, pa!1)" "cup(q!1, pa!1)" s!1) (("" (assert) (("" (hide -1 2) (("" (use cup_leto) (("" (assert) (("" (hide - 2) (("" (use subset_leto) (("" (assert) (("" (hide 2) (("" (expand "<=") (("" (expand "cup") (("" (expand "cap") (("" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((leto_transitive formula-decl nil bdUnity nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (cup_leto formula-decl nil bdUnity nil) (<= const-decl "bool" mucalculus nil) (cap const-decl "bool" ownpred nil) (subset_leto formula-decl nil bdUnity nil) (specification type-eq-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (t formal-type-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) shostak)) (leto_transitive_1 0 (leto_transitive_1-1 nil 3624287959 ("" (skosimp) (("" (lemma leto_transitive_2) (("" (inst - m!1 n!1 p!1 q!1 pq!1 q!1 s!1) (("" (assert) (("" (case "cup(q!1, q!1)=q!1") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (expand "cup") (("2" (iff) (("2" (prop) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((leto_transitive_2 formula-decl nil bdUnity nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (cup const-decl "bool" ownpred nil) (= const-decl "[T, T -> boolean]" equalities nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (t formal-type-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) shostak)) (leto_up 0 (leto_up-1 nil 3624288190 ("" (skosimp) (("" (lemma leto_transitive) (("" (inst - i!1 "j!1-i!1" p!1 q!1 q!1 s!1) (("1" (assert) (("1" (hide -1 2) (("1" (use subset_leto) (("1" (assert) (("1" (hide -1 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ((leto_transitive formula-decl nil bdUnity nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (subset_leto formula-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (<= const-decl "bool" mucalculus nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (t formal-type-decl nil bdUnity nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (j!1 skolem-const-decl "nat" bdUnity nil) (i!1 skolem-const-decl "nat" bdUnity nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil)) shostak)) (sub_leto 0 (sub_leto-1 nil 3624288385 ("" (skosimp) (("" (lemma leto_transitive) (("" (inst - 0 n!1 p!1 pq!1 q!1 s!1) (("" (assert) (("" (hide -2 2) (("" (use subset_leto) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((leto_transitive formula-decl nil bdUnity nil) (subset_leto formula-decl nil bdUnity nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (t formal-type-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) shostak)) (leto_sub 0 (leto_sub-1 nil 3624288461 ("" (skosimp) (("" (lemma leto_transitive) (("" (inst - n!1 0 p!1 pq!1 q!1 s!1) (("" (assert) (("" (hide -2 2) (("" (use subset_leto) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((leto_transitive formula-decl nil bdUnity nil) (subset_leto formula-decl nil bdUnity nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (t formal-type-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) shostak)) (shunting_leto 0 (shunting_leto-1 nil 3624288527 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - n!1 p!1 "cup(cap(p!1, neg(pq!1)), pq!1)" "cup(q!1, pq!1)" s!1) (("" (assert) (("" (hide 2) (("" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "neg") (("1" (skosimp) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (lemma leto_sub) (("1" (inst - n!1 "cap(p!1, neg(pq!1))" q!1 "cup(q!1, pq!1)" s!1) (("1" (assert) (("1" (hide - 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -) (("2" (use subset_leto) (("2" (assert) (("2" (hide 2) (("2" (expand "<=") (("2" (expand "cap") (("2" (expand "cup") (("2" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((sub_leto formula-decl nil bdUnity nil) (<= const-decl "bool" mucalculus nil) (leto_sub formula-decl nil bdUnity nil) (subset_leto formula-decl nil bdUnity nil) (cup_leto formula-decl nil bdUnity nil) (specification type-eq-decl nil bdUnity nil) (neg const-decl "bool" ownpred nil) (cap const-decl "bool" ownpred nil) (cup const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (t formal-type-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) shostak)) (leto_inv 0 (leto_inv-1 nil 3624288950 ("" (skosimp) (("" (iff) (("" (lemma sub_leto) (("" (inst - j!1 _ _ q!1 s!1) (("" (prop) (("1" (inst - p!1 "cap(p!1, s!1`inv)") (("1" (assert) (("1" (hide - 1) (("1" (expand "<=") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil) ("2" (inst - "cap(p!1, s!1`inv)" p!1) (("2" (assert) (("2" (hide - 1) (("2" (expand "<=") (("2" (expand "cap") (("2" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (t formal-type-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (specification type-eq-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (<= const-decl "bool" mucalculus nil) (sub_leto formula-decl nil bdUnity nil)) shostak)) (distributed_progress_TCC1 0 (distributed_progress_TCC1-1 nil 3670922272 ("" (subtype-tcc) nil nil) ((exec const-decl "bool" bdUnity nil) (leq const-decl "bool" bdUnity nil) (cap const-decl "bool" ownpred nil) (leto const-decl "bool" bdUnity nil) (disgrowth const-decl "bool" bdUnity nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil)) nil)) (distributed_progress 0 (distributed_progress-2 nil 3670927228 ("" (skosimp) (("" (case "FORALL n: FORALL z, k: k < n IMPLIES leto(s!1) (k + mwe!1 - 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(("" (assert) (("" (replace 1) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (t formal-type-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (leadsto const-decl "bool" bdUnity nil)) shostak)) (leadsto_transitive_2 0 (leadsto_transitive_2-1 nil 3624292491 ("" (skosimp) (("" (lemma leadsto_transitive) (("" (inst - p!1 "cup(pq!1, pa!1)" "cup(q!1, pa!1)" s!1) (("" (assert) (("" (hide -1 2) (("" (use cup_leadsto) (("" (assert) (("" (hide - 2) (("" (use subset_leadsto) (("" (assert) (("" (hide 2) (("" (expand "<=") (("" (expand "cap") (("" (expand "cup") (("" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((leadsto_transitive formula-decl nil bdUnity nil) (cup_leadsto formula-decl nil bdUnity nil) (<= const-decl "bool" mucalculus nil) (cap const-decl "bool" ownpred nil) (subset_leadsto formula-decl nil bdUnity nil) (specification type-eq-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (cup const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (t formal-type-decl nil bdUnity nil)) shostak)) (leadsto_transitive_1 0 (leadsto_transitive_1-1 nil 3624292624 ("" (skosimp) (("" (lemma leadsto_transitive_2) (("" (inst - p!1 q!1 pq!1 q!1 s!1) (("" (assert) (("" (case "cup(q!1, q!1) = q!1") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (expand "cup") (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (prop) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((leadsto_transitive_2 formula-decl nil bdUnity nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (cup const-decl "bool" ownpred nil) (= const-decl "[T, T -> boolean]" equalities nil) (specification type-eq-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (pred type-eq-decl nil defined_types nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (t formal-type-decl nil bdUnity nil)) shostak)) (sub_leadsto 0 (sub_leadsto-1 nil 3624292734 ("" (skosimp) (("" (lemma leadsto_transitive) (("" (inst - p!1 pq!1 q!1 s!1) (("" (assert) (("" (hide -2 2) (("" (use subset_leadsto) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((leadsto_transitive formula-decl nil bdUnity nil) (subset_leadsto formula-decl nil bdUnity nil) (specification type-eq-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (pred type-eq-decl nil defined_types nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (t formal-type-decl nil bdUnity nil)) shostak)) (leadsto_sub 0 (leadsto_sub-1 nil 3624292814 ("" (skosimp) (("" (lemma leadsto_transitive) (("" (inst - p!1 pq!1 q!1 s!1) (("" (assert) (("" (hide -2 2) (("" (use subset_leadsto) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((leadsto_transitive formula-decl nil bdUnity nil) (subset_leadsto formula-decl nil bdUnity nil) (specification type-eq-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (pred type-eq-decl nil defined_types nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (t formal-type-decl nil bdUnity nil)) shostak)) (shunting_leadsto 0 (shunting_leadsto-1 nil 3624292902 ("" (skosimp) (("" (lemma sub_leadsto) (("" (inst - p!1 "cup(cap(p!1, neg(pq!1)), pq!1)" "cup(q!1, pq!1)" s!1) (("" (assert) (("" (hide 2) (("" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "neg") (("1" (skosimp) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leadsto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (lemma leadsto_sub) (("1" (inst - "cap(p!1, neg(pq!1))" q!1 "cup(q!1, pq!1)" s!1) (("1" (assert) (("1" (hide - 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -) (("2" (use subset_leadsto) (("2" (assert) (("2" (hide 2) (("2" (expand "<=") (("2" (expand "cap") (("2" (expand "cup") (("2" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((sub_leadsto formula-decl nil bdUnity nil) (<= const-decl "bool" mucalculus nil) (leadsto_sub formula-decl nil bdUnity nil) (subset_leadsto formula-decl nil bdUnity nil) (cup_leadsto formula-decl nil bdUnity nil) (specification type-eq-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (neg const-decl "bool" ownpred nil) (cap const-decl "bool" ownpred nil) (cup const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (t formal-type-decl nil bdUnity nil)) shostak)) (leadsto_inv 0 (leadsto_inv-1 nil 3624293310 ("" (skolem!) (("" (iff) (("" (lemma sub_leadsto) (("" (inst - _ _ q!1 s!1) (("" (prop) (("1" (inst - p!1 "cap(p!1, s!1`inv)") (("1" (assert) (("1" (hide 1 -) (("1" (expand "<=") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil) ("2" (inst - "cap(p!1, s!1`inv)" p!1) (("2" (assert) (("2" (hide 1 -) (("2" (expand "<=") (("2" (expand "cap") (("2" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((t formal-type-decl nil bdUnity nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (specification type-eq-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (<= const-decl "bool" mucalculus nil) (sub_leadsto formula-decl nil bdUnity nil)) shostak)) (bounding_leadsto 0 (bounding_leadsto-1 nil 3624293638 ("" (expand "leto") (("" (skosimp*) (("" (inst?) (("" (assert) (("" (inst?) (("" (assert) (("" (expand "cup") (("" (skosimp) (("" (split) (("1" (inst?) (("1" (assert) nil nil)) nil) ("2" (expand "leadsto") (("2" (lemma machine_closed) (("2" (inst - i!1 s!1 xs!1) (("2" (assert) (("2" (skosimp) (("2" (inst? -4) (("2" (assert) (("2" (split) (("1" (skolem!) (("1" (inst + i!2) (("1" (case "i!2 <= i!1") (("1" (inst - i!2) (("1" (assert) nil nil)) nil) ("2" (inst - i!1) (("2" (assert) (("2" (replace -3 * rl) (("2" (hide-all-but (-1 -2 -4 -6 -7 1)) (("2" (case "forall i: pa!1(ys!1(i!1 + i))") (("1" (inst - "i!2-i!1") (("1" (assert) (("1" (expand "empty?") (("1" (expand "member") (("1" (expand "cap") (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (induct i) (("1" (assert) nil nil) ("2" (skosimp) (("2" (expand "stable") (("2" (expand "co") (("2" (expand "<=" -) (("2" (expand "wp") (("2" (expand "cap") (("2" (expand "run") (("2" (flatten) (("2" (expand "exec") (("2" (inst?) (("2" (flatten) (("2" (assert) (("2" (inst? -7) (("2" (assert) (("2" (inst -7 "ys!1(1 + i!1 + j!1)") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (inst - 0) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((leadsto const-decl "bool" bdUnity nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (<= const-decl "bool" reals nil) (nat_induction formula-decl nil naturalnumbers nil) (stable const-decl "bool" bdUnity nil) (<= const-decl "bool" mucalculus nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (exec const-decl "bool" bdUnity nil) (run const-decl "bool" bdUnity nil) (wp const-decl "bool" ownpred nil) (co const-decl "bool" bdUnity nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (empty? const-decl "bool" sets nil) (cap const-decl "bool" ownpred nil) (member const-decl "bool" sets nil) (int_plus_int_is_int application-judgement "int" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (machine_closed formula-decl nil bdUnity nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (cup const-decl "bool" ownpred nil) (t formal-type-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (leto const-decl "bool" bdUnity nil)) shostak))) $$$intsum.pvs % Wim H. Hesselink, October 2013 intsum: THEORY BEGIN n, i, j: VAR nat f, g: VAR [nat -> int] w: VAR int p: VAR pred[nat] trunc(n, p): finite_set[nat] = {i | i < n AND p(i)} ; +(f, g): [nat -> int] = LAMBDA n: f(n) + g(n); *(w, f): [nat -> int] = LAMBDA n: w * f(n) sum(n, f): RECURSIVE int = IF n = 0 THEN 0 ELSE f(n-1) + sum(n-1, f) ENDIF MEASURE n sum_natural: LEMMA (FORALL i: 0 <= f(i)) IMPLIES 0 <= sum(n, f) sum_leq: LEMMA (FORALL i: f(i) <= 1) IMPLIES sum(n, f) <= n sum_leq_card: LEMMA (FORALL i: f(i) <= 1 AND (f(i) = 1 IMPLIES p(i))) IMPLIES sum(n, f) <= card(trunc(n, p)) delta(i, w)(n): int = IF n = i THEN w ELSE 0 ENDIF sum_delta: LEMMA sum(n, delta(i, w)) = IF i < n THEN w ELSE 0 ENDIF sum_homomorphic: LEMMA sum(n, f + g) = sum(n, f) + sum(n, g) sum_monotonic: LEMMA (FORALL i: i < n IMPLIES f(i) <= g(i)) IMPLIES sum(n, f) <= sum(n, g) sum_equal: LEMMA (FORALL i: i < n IMPLIES f(i) = g(i)) IMPLIES sum(n, f) = sum(n, g) sum_strict_monotonic: LEMMA (FORALL i: i < n IMPLIES f(i) <= g(i)) AND (EXISTS i: i < n AND f(i) < g(i)) IMPLIES sum(n, f) < sum(n, g) sum_monotonic_delta: LEMMA (FORALL i: i < n AND i /= j IMPLIES f(i) <= g(i)) AND j < n AND f(j) + w <= g(j) IMPLIES sum(n, f) + w <= sum(n, g) sum_distributive: LEMMA sum(n, w * f) = w * sum(n, f) char(p)(i): int = IF p(i) THEN 1 ELSE 0 ENDIF sum_char: LEMMA sum(n, char(p)) = card(trunc(n, p)) const(w)(n): int = w sum_const: LEMMA sum(n, const(w)) = w * n END intsum $$$intsum.prf (intsum (trunc_TCC1 0 (trunc_TCC1-1 nil 3590140721 ("" (skolem!) (("" (expand "is_finite") (("" (inst + n!1 id) (("" (grind) nil nil)) nil)) nil)) nil) ((is_finite const-decl "bool" finite_sets nil) (injective? const-decl "bool" functions nil) (NOT const-decl "[bool -> bool]" booleans nil) (id const-decl "(bijective?[T, T])" identity nil) (bijective? const-decl "bool" functions nil) (below type-eq-decl nil nat_types nil) (pred type-eq-decl nil defined_types nil) (< const-decl "bool" reals nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) nil)) (sum_TCC1 0 (sum_TCC1-1 nil 3590140721 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (>= const-decl "bool" reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (sum_TCC2 0 (sum_TCC2-1 nil 3590140721 ("" (termination-tcc) nil nil) nil nil)) (sum_natural 0 (sum_natural-1 nil 3590140722 ("" (induct n) (("1" (expand "sum") (("1" (propax) nil nil)) nil) ("2" (skosimp*) (("2" (expand sum +) (("2" (inst?) (("2" (split) (("1" (inst?) (("1" (assert) nil nil)) nil) ("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil) ((real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_plus_int_is_int application-judgement "int" integers nil) (nat_induction formula-decl nil naturalnumbers nil) (sum def-decl "int" intsum nil) (<= const-decl "bool" reals nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) shostak)) (sum_leq 0 (sum_leq-1 nil 3590666253 ("" (induct n) (("1" (expand "sum") (("1" (propax) nil nil)) nil) ("2" (skosimp*) (("2" (expand sum +) (("2" (inst?) (("2" (replace -2) (("2" (inst?) 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(("" (case "forall E, n: card(E) < n IMPLIES ( maximum(f!1, E) <= n!1 IFF (FORALL x: E(x) IMPLIES f!1(x) <= n!1))") (("1" (inst - E!1 "card(E!1)+ 1") (("1" (assert) nil nil)) nil) ("2" (hide 2) (("2" (induct n) (("1" (skosimp) (("1" (assert) nil nil)) nil) ("2" (skosimp*) (("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil) nil shostak)) (maximum_prop1 0 (maximum_prop1-1 nil 3589622403 ("" (skosimp) (("" (use maximum_prop (n "maximum(f!1, E!1)")) (("" (assert) (("" (inst?) (("" (assert) nil nil)) nil)) nil)) nil)) nil) ((maximum_prop formula-decl nil maxfinset nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (t formal-type-decl nil maxfinset nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (maximum def-decl "nat" maxfinset nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil)) shostak)) (arg_max 0 (arg_max-1 nil 3589621787 ("" (skosimp) (("" (expand "nonempty?") (("" (expand "empty?") (("" (skosimp) (("" (expand "member") (("" (inst-cp + x!1) (("" (assert) (("" (lemma maximum_prop) (("" (inst - E!1 f!1 _) (("" (inst-cp - "maximum(f!1, E!1)") (("" (assert) (("" (inst-cp -2 x!1) (("" (assert) (("" (inst - "maximum(f!1, E!1)-1") (("" (assert) (("" (skosimp) (("" (inst - x!2) (("" (inst + x!2) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((nonempty? const-decl "bool" sets nil) (t formal-type-decl nil maxfinset nil) (maximum_prop formula-decl nil maxfinset nil) (maximum def-decl "nat" maxfinset nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (member const-decl "bool" sets nil) (empty? const-decl "bool" sets nil)) shostak))) $$$ctrees.pvs % Wim H. Hesselink, August 2016 % Proofs for: Tournaments for mutual exclusion: % verification and concurrent complexity % Part 1. Specification of the tree ctrees [ degree: posnat, node: type+ ]: THEORY BEGIN IMPORTING maxfinset[node] digit: TYPE = below[degree] node_finite: AXIOM is_finite(fullset[node]) root: node % We first give the tree in terms of the functions parent and sibnr. % In this tree, we define depth, ancestors, and the root path. parent: [node -> node] sibnr: [node -> digit] n, n1: VAR node i, k: VAR nat z: VAR int anc(n, k): RECURSIVE node = IF k = 0 THEN n ELSE parent(anc(n, k-1)) ENDIF MEASURE k tree_axiom: AXIOM parent(root) = root AND nonempty?({ k | anc(n, k) = root }) anc_root: LEMMA anc(root, k) = root anc_additive: LEMMA anc(anc(n, i), k) = anc(n, i+k) c_depth(n): nat = min({k | anc(n, k) = root }) c_depth_root: LEMMA c_depth(root) = 0 anc_beyond_c_depth: LEMMA c_depth(n) <= k IMPLIES anc(n, k) = root c_depth_anc: LEMMA c_depth(anc(n, k)) = IF k < c_depth(n) THEN c_depth(n) - k ELSE 0 ENDIF c_depth_parent: LEMMA c_depth(parent(n)) = IF n = root THEN 0 ELSE c_depth(n) - 1 ENDIF c_path(n, z): node = IF 0 <= z AND z <= c_depth(n) THEN anc(n, c_depth(n) - z) ELSE n ENDIF c_depth_c_path: LEMMA c_depth(c_path(n, k)) = IF k <= c_depth(n) THEN k ELSE c_depth(n) ENDIF equal_c_paths: LEMMA c_path(n, i) = c_path(n1, k) AND i <= c_depth(n) AND k <= c_depth(n1) IMPLIES i = k nr_tree_axiom: AXIOM FORALL n, n1: parent(n) = parent(n1) AND sibnr(n) = sibnr(n1) IMPLIES n = n1 OR n = root OR n1 = root c_sib(n, z): digit = sibnr(c_path(n, z+1)) joining_c_paths: LEMMA k < c_depth(n) AND k < c_depth(n1) AND c_path(n, k) = c_path(n1, k) AND c_sib(n, k) = c_sib(n1, k) IMPLIES c_path(n, k+1) = c_path(n1, k+1) % We now introduce depth, path, sib, and depthnode axiomatically. % The axioms have been proved for the setting above. depth(n): nat path(n, z): node sib(n, z): digit depth_path: AXIOM depth(path(n, k)) = IF k <= depth(n) THEN k ELSE depth(n) ENDIF path_zero: AXIOM path(n, 0) = root path_depth: AXIOM path(n, depth(n)) = n equal_paths: LEMMA path(n, i) = path(n1, k) AND i <= depth(n) AND k <= depth(n1) IMPLIES i = k joining_paths: AXIOM k < depth(n) AND k < depth(n1) AND path(n, k) = path(n1, k) AND sib(n, k) = sib(n1, k) IMPLIES path(n, k+1) = path(n1, k+1) depthnode: nat = maximum(depth, fullset[node]) upb_depth: LEMMA depth(n) <= depthnode leaf: finite_set[node] = { n | FORALL k, n1: path(n1, k) = n AND k <= depth(n1) IMPLIES n1 = n } depth_maximal_leaf: LEMMA % depth(n) = depthnode IMPLIES leaf(n) exists_leaf: LEMMA EXISTS n: leaf(n) AND depth(n) = depthnode intNode(n): bool = NOT leaf(n) END ctrees $$$ctrees.prf (ctrees (sibnr_TCC1 0 (sibnr_TCC1-1 nil 3678527008 ("" (inst + "lambda (n:node) : 0") (("" (assert) nil nil)) nil) ((digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" ctrees nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil ctrees nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil)) nil)) (anc_TCC1 0 (anc_TCC1-1 nil 3678527008 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (>= const-decl "bool" reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (anc_TCC2 0 (anc_TCC2-1 nil 3678527008 ("" (termination-tcc) nil nil) nil nil)) (anc_root 0 (anc_root-1 nil 3678528666 ("" (induct k) (("1" (expand "anc") (("1" (propax) nil nil)) nil) ("2" (skosimp) (("2" (expand anc +) (("2" (assert) (("2" (use tree_axiom) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((tree_axiom formula-decl nil ctrees nil) (nat_induction formula-decl nil naturalnumbers nil) (root const-decl "node" ctrees nil) (anc def-decl "node" ctrees nil) (= const-decl "[T, T -> boolean]" equalities nil) (node formal-nonempty-type-decl nil ctrees nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) shostak)) (anc_additive 0 (anc_additive-1 nil 3678527522 ("" (induct k) (("1" (skolem!) (("1" (name-replace ank "anc(n!1, i!1)") (("1" (expand "anc") (("1" (propax) nil nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (inst?) 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(("" (use tree_axiom) (("" (assert) nil nil)) nil)) nil) ((tree_axiom formula-decl nil ctrees nil) (node formal-nonempty-type-decl nil ctrees nil)) nil)) (c_depth_root 0 (c_depth_root-1 nil 3678533385 ("" (expand "c_depth") (("" (name-replace mn "min({k | anc(root, k) = root})") (("1" (typepred mn) (("1" (inst - 0) (("1" (assert) (("1" (expand "anc") (("1" (propax) nil nil)) nil)) nil)) nil)) nil) ("2" (use tree_axiom) (("2" (assert) nil nil)) nil)) nil)) nil) ((number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (set type-eq-decl nil sets nil) (nonempty? const-decl "bool" sets nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}" min_nat nil) (node formal-nonempty-type-decl nil ctrees nil) (anc def-decl "node" ctrees nil) (root const-decl "node" ctrees nil) (NOT const-decl "[bool -> bool]" booleans nil) (tree_axiom formula-decl nil ctrees nil) (c_depth const-decl "nat" ctrees nil)) shostak)) (anc_beyond_c_depth 0 (anc_beyond_c_depth-1 nil 3678528717 ("" (skosimp) (("" (expand "c_depth") (("" (name-replace mn "min({k | anc(n!1, k) = root})") (("1" (typepred mn) (("1" (hide -2) (("1" (lemma anc_additive) (("1" (inst - mn "k!1-mn" n!1) (("1" (replaceh -2) (("1" (assert) (("1" (lemma anc_root) (("1" (inst - "k!1-mn") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (use tree_axiom) (("2" (assert) nil nil)) nil)) nil)) nil)) nil) ((c_depth const-decl "nat" ctrees nil) (tree_axiom formula-decl nil ctrees nil) (NOT const-decl "[bool -> bool]" booleans nil) (anc_additive formula-decl nil ctrees nil) (anc_root formula-decl nil ctrees nil) (int_plus_int_is_int application-judgement "int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (mn skolem-const-decl "{a | anc(n!1, a) = root AND (FORALL (x: nat): anc(n!1, x) = root IMPLIES a <= x)}" ctrees nil) (n!1 skolem-const-decl "node" ctrees nil) (k!1 skolem-const-decl "nat" ctrees nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (root const-decl "node" ctrees nil) (anc def-decl "node" ctrees nil) (node formal-nonempty-type-decl nil ctrees nil) (min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}" min_nat nil) (<= const-decl "bool" reals nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (nonempty? const-decl "bool" sets nil) (set type-eq-decl nil sets nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) shostak)) (c_depth_anc 0 (c_depth_anc-1 nil 3678527070 ("" (skolem!) 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(minus_odd_is_odd application-judgement "odd_int" integers nil) (c_depth const-decl "nat" ctrees nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_plus_int_is_int application-judgement "int" integers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (anc_additive formula-decl nil ctrees nil) (NOT const-decl "[bool -> bool]" booleans nil) (tree_axiom formula-decl nil ctrees nil) (root const-decl "node" ctrees nil) (min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}" min_nat nil) (<= 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const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (c_depth_anc formula-decl nil ctrees nil) (tree_axiom formula-decl nil ctrees nil) (root const-decl "node" ctrees nil) (node formal-nonempty-type-decl nil ctrees nil) (c_depth_root formula-decl nil ctrees nil)) nil) (c_depth_parent-1 nil 3678550629 ("" (skosimp) (("" (lift-if) (("" (split) (("1" (flatten) (("1" (use c_depth_root) (("1" (use tree_axiom) (("1" (flatten) 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(("2" (inst - root) (("2" (expand "member") (("2" (expand "fullset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((node formal-nonempty-type-decl nil ctrees nil) (arg_max formula-decl nil maxfinset nil) (depth const-decl "nat" ctrees nil) (fullset const-decl "set" sets nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (empty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (root const-decl "node" ctrees nil) (nonempty? const-decl "bool" sets nil) (depth_maximal_leaf formula-decl nil ctrees nil) (depthnode const-decl "nat" ctrees nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) shostak))) $$$tournamentSafe0.pvs % Wim H. Hesselink, May-August 2016 % Proofs for: Tournaments for mutual exclusion: % verification and concurrent complexity % Part 2. The transition system for the case that MXd satisfies FCFS % Mutual exclusion and the invariants Iq* and Kq* tournamentSafe0[degree: posnat, node: TYPE+]: THEORY BEGIN IMPORTING ctrees[degree, node] thread: finite_set[node] = leaf N: posnat = % card(thread) K: posnat % upper bound of number of competing threads count_thread: (bijective?[(thread), below[N]]) % edigit: TYPE = ({z: int | -1 <= z AND z < degree}) enum_thread: (bijective?[below[N], (thread)]) = inverse(count_thread) % state: TYPE = [# mu: [node -> edigit], occ: [node -> (thread)], % ghost variable: the occupying thread bock: [node, digit -> (thread)], % ghost variable for lq2 competing: finite_set[node], % ghost cur: [node -> finite_set[digit]], prio: [node, digit -> finite_set[digit]], % private pc: [(thread) -> nat], level: [(thread) -> int], cnt: [(thread) -> nat] % ghost variable for progress #] x, y: VAR state p, q, r: VAR (thread) j, k, kk: VAR nat dig: VAR digit n: VAR node thread_depth: LEMMA % depth(q) <= depthnode % 11 NCS ; // level = p`length - 1 ; % 12 while level >= 0 do % 13 prio(curnode(p), curbranch(p)) := cur(curnode(p)) ; % 14 add sib(p, level) to cur(path(p, level)) ; % bock(curnode(p), curbranch(p)) := p ; % 15 await (empty?(prio(take(level, p), p(level))) % and mu(take(level, p)) = -1 % or mu(take(level, p)) = p(level) ; % mu(take(level, p)) := p(level) ; level -- ; % remove curbranch(p) from cur(curnode(p)); % for all j do remove curbranch(p) from prio(curnode(p), j) ; % occ(curnode(p)) := p ; % endwhile ; % 16 CS ; % 17 while level < p`length - 1 do % 18 level ++ ; % mu(curnode(p)) := -1 % endwhile ; % 19 { cnt ++ } goto 11 . % Thread q has reached the nodes take(k, q) with % level.q <= k <= q`length % It occupies the nodes take(k, q) with % level.q < k <= q`length goto(p, k, x): state = x WITH [ `pc(p) := k ] next11(p, x): state = x WITH [ `competing := add(p, x`competing), `pc(p) := 12 ] step11(p, x, y): bool = y = next11(p, x) AND x`pc(p) = 11 AND card(x`competing) /= K step12(p, x, y): bool = y = goto(p, IF x`level(p) < 0 THEN 16 ELSE 13 ENDIF, x) AND x`pc(p) = 12 curnode(p, x): node = path(p, x`level(p)) curbranch(p, x): digit = sib(p, x`level(p)) next13(p, x): state = x WITH [ `prio(curnode(p, x), curbranch(p, x)) := x`cur(curnode(p, x)), `pc(p) := 14 ] step13(p, x, y): bool = y = next13(p, x) AND x`pc(p) = 13 next14(p, x): state = x WITH [ `cur(curnode(p, x)) := add(curbranch(p, x), x`cur(curnode(p, x))), `bock(curnode(p, x), curbranch(p, x)) := p, `pc(p) := 15 ] step14(p, x, y): bool = y = next14(p, x) AND x`pc(p) = 14 next15(p, x): state = % x WITH [ `mu(curnode(p, x)) := curbranch(p, x), `occ(curnode(p, x)) := p, `cur(curnode(p, x)) := remove(curbranch(p, x), x`cur(curnode(p, x))), `prio := (LAMBDA n, dig: IF n = curnode(p, x) THEN remove(curbranch(p, x), x`prio(n, dig)) ELSE x`prio(n, dig) ENDIF ), `level(p) := x`level(p) - 1, `pc(p) := 12 ] step15F(p, x, y): bool = y = next15(p, x) AND x`pc(p) = 15 AND x`mu(curnode(p, x)) < 0 AND empty?(x`prio(curnode(p, x), curbranch(p, x))) step15G(p, x, y): bool = y = next15(p, x) AND x`pc(p) = 15 AND x`level(p) >= 0 AND x`mu(curnode(p, x)) = curbranch(p, x) step16(p, x, y): bool = % CS y = goto(p, 17, x) AND x`pc(p) = 16 step17(p, x, y): bool = y = goto(p, IF x`level(p) < depth(p) - 1 THEN 18 ELSE 19 ENDIF, x) AND x`pc(p) = 17 next18(p, x): state = % x WITH [ `mu(path(p, x`level(p) + 1)) := -1, `level(p) := x`level(p) + 1, `pc(p) := 17 ] step18(p, x, y): bool = y = next18(p, x) AND x`pc(p) = 18 next19(p, x): state = x WITH [ `cnt(p) := x`cnt(p) + 1, `competing := remove(p, x`competing), `pc(p) := 11 ] step19(p, x, y): bool = y = next19(p, x) AND x`pc(p) = 19 step(p, x, y): bool = step11(p, x, y) OR step12(p, x, y) OR step13(p, x, y) OR step14(p, x, y) OR step15F(p, x, y) OR step15G(p, x, y) OR step16(p, x, y) OR step17(p, x, y) OR step18(p, x, y) OR step19(p, x, y) iq0(q, x): bool = % -1 <= x`level(q) AND x`level(q) <= depth(q) - 1 iq1(q, x): bool = % 13 <= x`pc(q) AND x`pc(q) <= 15 IMPLIES 0 <= x`level(q) iq3(q, x): bool = % x`pc(q) = 18 IMPLIES x`level(q) < depth(q) - 1 iq0_rest: LEMMA % iq0(q, x) AND step(p, x, y) IMPLIES iq0(q, y) OR step15F(p, x, y) OR step18(p, x, y) iq0_15F: LEMMA iq0(q, x) AND step15F(p, x, y) AND iq1(q, x) IMPLIES iq0(q, y) iq0_18: LEMMA iq0(q, x) AND step18(p, x, y) AND iq3(q, x) IMPLIES iq0(q, y) iq0_step: LEMMA iq0(q, x) AND step(p, x, y) AND iq3(q, x) AND iq1(q, x) IMPLIES iq0(q, y) iq1_step: LEMMA % iq1(q, x) AND step(p, x, y) IMPLIES iq1(q, y) iq2(q, x): bool = % x`pc(q) = 16 IMPLIES x`level(q) = -1 iq2_rest: LEMMA % iq2(q, x) AND step(p, x, y) IMPLIES iq2(q, y) OR step12(p, x, y) iq2_12: LEMMA iq2(q, x) AND step12(p, x, y) AND iq0(q, x) IMPLIES iq2(q, y) iq2_step: LEMMA iq2(q, x) AND step(p, x, y) AND iq0(q, x) IMPLIES iq2(q, y) iq3_step: LEMMA % iq3(q, x) AND step(p, x, y) IMPLIES iq3(q, y) iq4(q, x): bool = % x`pc(q) = 11 OR x`pc(q) = 19 IMPLIES x`level(q) = depth(q) - 1 iq4_rest: LEMMA % iq4(q, x) AND step(p, x, y) IMPLIES iq4(q, y) OR step15F(p, x, y) OR step15G(p, x, y) OR step17(p, x, y) iq4_15F: LEMMA % iq4(q, x) AND step15F(p, x, y) IMPLIES iq4(q, y) iq4_15G: LEMMA % iq4(q, x) AND step15G(p, x, y) IMPLIES iq4(q, y) iq4_17: LEMMA % iq4(q, x) AND step17(p, x, y) AND iq0(q, x) IMPLIES iq4(q, y) iq4_step: LEMMA % iq4(q, x) AND step(p, x, y) AND iq0(q, x) IMPLIES iq4(q, y) iq5(q, j, x): bool = x`level(q) < j AND j < depth(q) IMPLIES x`mu(path(q, j)) = sib(q, j) mx(q, r, j, x): bool = x`level(q) < j AND j <= depth(q) AND x`level(r) < j AND j <= depth(r) AND path(q, j) = path(r, j) IMPLIES q = r iq5_rest: LEMMA % iq5(q, j, x) AND step(p, x, y) IMPLIES iq5(q, j, y) OR step15F(p, x, y) OR step15G(p, x, y) OR step18(p, x, y) iq5_15F: LEMMA % iq5(q, j, x) AND step15F(p, x, y) IMPLIES iq5(q, j, y) iq5_15G: LEMMA % iq5(q, j, x) AND step15G(p, x, y) IMPLIES iq5(q, j, y) iq5_18: LEMMA % iq5(q, j, x) AND step18(p, x, y) AND iq0(p, x) AND iq3(p, x) AND mx(p, q, j, x) IMPLIES iq5(q, j, y) iq5_step: LEMMA iq5(q, j, x) AND step(p, x, y) AND iq0(p, x) AND iq3(p, x) AND mx(p, q, j, x) IMPLIES iq5(q, j, y) mx_down: LEMMA % mx(q, r, j+1, x) AND iq5(q, j, x) AND iq5(r, j, x) IMPLIES mx(q, r, j, x) iqall(x): bool = (FORALL q: iq0(q, x) AND iq1(q, x) AND iq2(q, x) AND iq3(q, x) AND iq4(q, x) ) AND (FORALL q, j: iq5(q, j, x)) mx_j_implied: LEMMA % iqall(x) IMPLIES mx(q, r, j, x) init(x): bool = (FORALL q: x`pc(q) = 11 AND x`level(q) = depth(q) - 1) AND (FORALL (n: node): x`mu(n) = -1 AND empty?(x`cur(n)) AND FORALL dig: empty?(x`prio(n, dig)) ) AND x`competing = emptyset iqall_step: LEMMA iqall(x) AND step(p, x, y) IMPLIES iqall(y) init_iqall: LEMMA init(x) IMPLIES iqall(x) mx(q, r, x): bool = x`pc(q) = 16 AND x`pc(r) = 16 IMPLIES q = r mx_implied: LEMMA % iqall(x) IMPLIES mx(q, r, x) kq0(q, x): bool = 11 <= x`pc(q) AND x`pc(q) <= 19 kq0_step: LEMMA kq0(q, x) AND step(p, x, y) IMPLIES kq0(q, y) kq1(n, x): bool = x`mu(n) >= 0 IMPLIES x`level(x`occ(n)) < depth(n) AND n = path(x`occ(n), depth(n)) AND depth(n) < depth(x`occ(n)) kq1_11: LEMMA kq1(n, x) AND step11(p, x, y) IMPLIES kq1(n, y) kq1_12: LEMMA kq1(n, x) AND step12(p, x, y) IMPLIES kq1(n, y) kq1_14: LEMMA kq1(n, x) AND step14(p, x, y) IMPLIES kq1(n, y) kq1_13: LEMMA kq1(n, x) AND step13(p, x, y) IMPLIES kq1(n, y) kq1_15F: LEMMA % kq1(n, x) AND step15F(p, x, y) AND iq0(p, x) AND iq1(p, x) IMPLIES kq1(n, y) kq1_15G: LEMMA % % kq1(n, x) AND step15G(p, x, y) AND iq0(p, x) IMPLIES kq1(n, y) kq1_16: LEMMA kq1(n, x) AND step16(p, x, y) IMPLIES kq1(n, y) kq1_17: LEMMA kq1(n, x) AND step17(p, x, y) IMPLIES kq1(n, y) kq1_18: LEMMA % kq1(n, x) AND step18(p, x, y) IMPLIES kq1(n, y) kq1_19: LEMMA kq1(n, x) AND step19(p, x, y) IMPLIES kq1(n, y) kq1_step: LEMMA % kq1(n, x) AND step(p, x, y) AND iq0(p, x) AND iq1(p, x) IMPLIES kq1(n, y) kq4(x): bool = card(x`competing) <= K kq4_rest: LEMMA % kq4(x) AND step(p, x, y) IMPLIES kq4(y) OR step11(p, x, y) OR step19(p, x, y) kq4_11: LEMMA % kq4(x) AND step11(p, x, y) IMPLIES kq4(y) kq4_19: LEMMA % kq4(x) AND step19(p, x, y) IMPLIES kq4(y) kq4_step: LEMMA kq4(x) AND step(p, x, y) IMPLIES kq4(y) kq5(q, x): bool = x`competing(q) = (x`pc(q) /= 11) kq5_step: LEMMA % kq5(q, x) AND step(p, x, y) IMPLIES kq5(q, y) kqall(x): bool = (FORALL q: kq0(q, x) AND kq5(q, x)) AND (FORALL n: kq1(n, x)) AND kq4(x) kqall_step: LEMMA kqall(x) AND step(p, x, y) AND iqall(x) IMPLIES kqall(y) init_kqall: LEMMA % init(x) IMPLIES kqall(x) END tournamentSafe0 $$$tournamentSafe0.prf (tournamentSafe0 (N_TCC1 0 (N_TCC1-1 nil 3669471055 ("" (use empty_card[node]) (("" (assert) (("" (expand "empty?") (("" (expand "member") (("" (use exists_leaf) (("" (skosimp) (("" (inst?) (("" (expand "thread") (("" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (member const-decl "bool" sets nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (exists_leaf formula-decl nil ctrees nil) (empty? const-decl "bool" sets nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (empty_card formula-decl nil finite_sets nil)) nil)) (count_thread_TCC1 0 (count_thread_TCC1-2 nil 3678595162 ("" (lemma Card_bijection[node]) (("" (inst - thread N) (("" (flatten) (("" (hide -2) (("" (split) (("1" (skolem!) (("1" (inst?) nil nil)) nil) ("2" (expand "N") (("2" (hide 2) (("2" (typepred "card(thread)") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (number nonempty-type-decl nil numbers nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (N const-decl "posnat" tournamentSafe0 nil) (NOT const-decl "[bool -> bool]" booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (Card const-decl "nat" finite_sets nil) (card const-decl "{n: nat | n = Card(S)}" finite_sets nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (bijective? const-decl "bool" functions nil) nil (Card_bijection formula-decl nil finite_sets nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil)) nil) (count_thread_TCC1-1 nil 3669471603 ("" (lemma Card_bijection[digseq]) (("" (inst - thread N) (("" (flatten) (("" (hide -2) (("" (split) (("1" (skolem!) (("1" (inst?) nil nil)) nil) ("2" (expand "N") (("2" (hide 2) (("2" (typepred "card(thread)") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (N const-decl "posnat" tournamentSafe0 nil) (card const-decl "{n: nat | n = Card(S)}" finite_sets nil) (Card const-decl "nat" finite_sets nil) (= const-decl "[T, T -> boolean]" equalities nil) (NOT const-decl "[bool -> bool]" booleans nil) (bijective? const-decl "bool" functions nil) (Card_bijection formula-decl nil finite_sets nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentSafe0 nil)) nil)) (enum_thread_TCC1 0 (enum_thread_TCC1-2 nil 3678595219 ("" (use exists_leaf) (("" (skosimp) (("" (inst + n!1) (("" (expand "thread") (("" (propax) nil nil)) nil)) nil)) nil)) nil) (nil (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (exists_leaf formula-decl nil ctrees nil)) nil) (enum_thread_TCC1-1 nil 3670513754 ("" (use tree_has_leaves) (("" (inst - pp) (("" (split) (("1" (skosimp) (("1" (inst + bs!1) (("1" (expand "thread") (("1" (propax) nil nil)) nil)) nil)) nil) ("2" (typepred pp) (("2" (propax) nil nil)) nil)) nil)) nil)) nil) ((nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (< const-decl "bool" reals nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (NOT const-decl "[bool -> bool]" booleans nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) nil)) (thread_depth 0 (thread_depth-3 nil 3678594690 ("" (skolem!) (("" (use upb_depth) nil nil)) nil) ((set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (upb_depth formula-decl nil ctrees nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil)) nil) (thread_depth-2 nil 3678594612 ("" (skolem!) (("" (expand "depth") (("" (lemma maximum_prop1[node]) (("" (inst?) (("" (inst - q!1) (("" (expand "len") (("" (assert) (("" (typepred q!1) (("" (expand "thread") (("" (expand "leaves") (("" (propax) nil)))))))))))))))))))) nil) nil nil) (thread_depth-1 nil 3669522465 ("" (skolem!) (("" (expand "depth") (("" (lemma maximum_prop1[digseq]) (("" (inst?) (("" (inst - q!1) (("" (expand "len") (("" (assert) (("" (typepred q!1) (("" (expand "thread") (("" (expand "leaves") (("" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (NOT const-decl "[bool -> bool]" booleans nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (maximum_prop1 formula-decl nil maxfinset nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentSafe0 nil)) shostak)) (next15_TCC1 0 (next15_TCC1-1 nil 3670317107 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (digit type-eq-decl nil ctrees nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) nil nil (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (leaf const-decl "finite_set[node]" ctrees nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (curbranch const-decl "digit" tournamentSafe0 nil)) nil)) (next18_TCC1 0 (next18_TCC1-1 nil 3670050174 ("" (skolem!) (("" (ground) nil nil)) nil) ((real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (iq0_rest 0 (iq0_rest-1 nil 3669290464 ("" (skosimp) (("" (expand "step") (("" (assert) (("" (hide-all-but (1) +) (("" (split) (("1" (grind) nil nil) ("2" (grind) nil nil) ("3" (grind) nil nil) ("4" (grind) nil nil) ("5" (grind) nil nil) ("6" (grind) nil nil) ("7" (grind) nil nil) ("8" (grind) nil nil)) nil)) nil)) nil)) nil)) nil) ((step const-decl "bool" tournamentSafe0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (next19 const-decl "state" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (step17 const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (finite_remove application-judgement "finite_set" finite_sets nil) (next15 const-decl "state" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (goto const-decl "state" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (int_minus_int_is_int application-judgement "int" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (next11 const-decl "state" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (step11 const-decl "bool" tournamentSafe0 nil) (iq0 const-decl "bool" tournamentSafe0 nil)) shostak)) (iq0_15F 0 (iq0_15F-1 nil 3669290495 ("" (expand "step15F") (("" (expand "iq0") (("" (skosimp) (("" (expand "next15") (("" (case "q!1=p!1") (("1" (assert) (("1" (expand "iq1") (("1" (propax) nil nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((iq0 const-decl "bool" tournamentSafe0 nil) (next15 const-decl "state" tournamentSafe0 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (finite_remove application-judgement "finite_set" finite_sets nil) (int_minus_int_is_int application-judgement "int" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (iq1 const-decl "bool" tournamentSafe0 nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (boolean nonempty-type-decl nil booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (bool nonempty-type-eq-decl nil booleans nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (step15F const-decl "bool" tournamentSafe0 nil)) shostak)) (iq0_18 0 (iq0_18-1 nil 3669619720 ("" (expand "step18") (("" (expand "iq0") (("" (skosimp) (("" (replaceh -3) (("" (expand "next18") (("" (case "q!1=p!1") (("1" (assert) (("1" (expand "iq3") (("1" (propax) nil nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((iq0 const-decl "bool" tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (iq3 const-decl "bool" tournamentSafe0 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (next18 const-decl "state" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil)) shostak)) (iq0_step 0 (iq0_step-2 nil 3669619828 ("" (skosimp) (("" (use iq0_rest (y y!1)) (("" (use iq0_15F (y y!1)) (("" (use iq0_18 (y y!1)) (("" (assert) nil nil)) nil)) nil)) nil)) nil) ((iq0_rest formula-decl nil tournamentSafe0 nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (digit type-eq-decl nil ctrees nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (iq0_18 formula-decl nil tournamentSafe0 nil) (iq0_15F formula-decl nil tournamentSafe0 nil)) nil) (iq0_step-1 nil 3669290658 ("" (skosimp) (("" (use iq0_rest (y y!1)) (("" (use iq0_15F (y y!1)) (("" (assert) nil nil)) nil)) nil)) nil) ((iq0_rest formula-decl nil tournamentSafe0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (iq0_15F formula-decl nil tournamentSafe0 nil)) shostak)) (iq1_step 0 (iq1_step-1 nil 3669290751 ("" (skosimp) (("" (expand "step") (("" (assert) (("" (split) (("1" (grind) nil nil) ("2" (grind) nil nil) ("3" (grind) nil nil) ("4" (grind) nil nil) ("5" (grind) nil nil) ("6" (grind) nil nil) ("7" (grind) nil nil) ("8" (grind) nil nil) ("9" (grind) nil nil) ("10" (grind) nil nil)) nil)) nil)) nil)) nil) ((step const-decl "bool" tournamentSafe0 nil) (next11 const-decl "state" tournamentSafe0 nil) (/= 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"posint" integers nil) (step19 const-decl "bool" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil)) shostak)) (iq2_rest 0 (iq2_rest-1 nil 3669476856 ("" (skosimp) (("" (expand "step") (("" (assert) (("" (hide-all-but (1) +) (("" (split) (("1" (grind) nil nil) ("2" (grind) nil nil) ("3" (grind) nil nil) ("4" (grind) nil nil) ("5" (grind) nil nil) ("6" (grind) nil nil) ("7" (grind) nil nil) ("8" (grind) nil nil) ("9" (grind) nil nil)) nil)) nil)) nil)) nil)) nil) ((step const-decl "bool" tournamentSafe0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (next19 const-decl "state" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (step18 const-decl "bool" tournamentSafe0 nil) (next18 const-decl "state" tournamentSafe0 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nil 3669301181 ("" (skosimp) (("" (use iq2_rest (y y!1)) (("" (use iq2_12 (y y!1)) (("" (assert) nil nil)) nil)) nil)) nil) ((iq2_rest formula-decl nil tournamentSafe0 nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree 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(("2" (assert) (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((iqall const-decl "bool" tournamentSafe0 nil) (mx_j_implied formula-decl nil tournamentSafe0 nil) (iq5_step formula-decl nil tournamentSafe0 nil) (iq0_step formula-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (iq1_step formula-decl nil tournamentSafe0 nil) (iq2_step formula-decl nil tournamentSafe0 nil) (iq3_step formula-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil)) nil) (iqall_step-2 nil 3669292929 ("" (skosimp) (("" (expand iqall +) (("" (split) (("1" (skolem!) (("1" (expand "iqall") (("1" (flatten) (("1" (inst?) (("1" (use iq0_step (p p!1 x x!1 y y!1)) (("1" (use iq3_step (p p!1 x x!1 y y!1)) (("1" (use iq1_step (p p!1 x x!1 y y!1)) (("1" (assert) (("1" (flatten) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skolem!) (("2" (use iq5_step (p p!1 x x!1 y y!1)) (("2" (assert) (("2" (use mx_j_implied) (("2" (assert) (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (inst?) (("2" (assert) (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (pred type-eq-decl nil defined_types nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (iq3_step formula-decl nil tournamentSafe0 nil) (iq1_step formula-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (iq0_step formula-decl nil tournamentSafe0 nil) (iq5_step formula-decl nil tournamentSafe0 nil) (mx_j_implied formula-decl nil tournamentSafe0 nil) (iqall const-decl "bool" tournamentSafe0 nil)) nil) (iqall_step-1 nil 3669292787 ("" (skosimp) (("" (expand iqall +) (("" (split) (("1" (skolem!) (("1" (expand "iqall") (("1" (flatten) (("1" (inst?) (("1" (use iq0_step (p p!1 x x!1 y y!1)) (("1" (use iq3_step (p p!1 x x!1 y y!1)) (("1" (assert) (("1" (flatten) (("1" (assert) (("1" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (postpone) nil nil)) nil)) nil)) nil) nil shostak)) (init_iqall 0 (init_iqall-1 nil 3669299869 ("" (expand "iqall") (("" (expand "init") (("" (skosimp) (("" (split) (("1" (skolem!) (("1" (inst?) (("1" (flatten) (("1" (expand "iq0") (("1" (assert) (("1" (expand "iq3") (("1" (expand "iq1") (("1" (expand "iq2") (("1" (expand "iq4") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skolem!) (("2" (expand "iq5") (("2" (flatten) (("2" (assert) (("2" (inst?) (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((init const-decl "bool" tournamentSafe0 nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (iq0 const-decl "bool" tournamentSafe0 nil) (iq3 const-decl "bool" tournamentSafe0 nil) (iq2 const-decl "bool" tournamentSafe0 nil) (iq4 const-decl "bool" tournamentSafe0 nil) (iq1 const-decl "bool" tournamentSafe0 nil) (int_minus_int_is_int application-judgement "int" integers nil) (finite_emptyset name-judgement "finite_set" finite_sets nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (iq5 const-decl "bool" tournamentSafe0 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (iqall const-decl "bool" tournamentSafe0 nil)) shostak)) (mx_implied 0 (mx_implied-2 nil 3678602950 ("" (expand "mx") (("" (skosimp) (("" (lemma mx_j_implied) (("" (inst - 0 q!1 r!1 x!1) (("" (assert) (("" (expand "mx") (("" (case "path(q!1, 0) = path(r!1, 0)") (("1" (assert) (("1" (case "iq2(q!1, x!1) AND iq2(r!1, x!1)") (("1" (flatten) (("1" (expand "iq2") (("1" (assert) (("1" (typepred q!1) (("1" (typepred r!1) (("1" (expand "thread") (("1" (assert) (("1" (assert) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "iqall") (("2" (flatten) (("2" (hide-all-but (-2 1)) (("2" (split) (("1" (inst?) (("1" (assert) nil nil)) nil) ("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2 3) (("2" (lemma path_zero) (("2" (inst-cp - q!1) (("2" (replaceh -2) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (digit type-eq-decl nil ctrees nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (mx const-decl "bool" tournamentSafe0 nil) (path_zero formula-decl nil ctrees nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (iqall const-decl "bool" tournamentSafe0 nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (NOT const-decl "[bool -> bool]" booleans nil) (iq2 const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (path const-decl "node" ctrees nil) (= const-decl "[T, T -> boolean]" equalities nil) (mx_j_implied formula-decl nil tournamentSafe0 nil) (mx const-decl "bool" tournamentSafe0 nil)) nil) (mx_implied-1 nil 3669301291 ("" (expand "mx") (("" (skosimp) (("" (lemma mx_j_implied) (("" (inst - 0 q!1 r!1 x!1) (("" (assert) (("" (expand "mx") (("" (case "take(0, q!1) = take(0, r!1)") (("1" (assert) (("1" (case "iq2(q!1, x!1) AND iq2(r!1, x!1)") (("1" (flatten) (("1" (expand "iq2") (("1" (assert) (("1" (use leaves_separate) (("1" (typepred q!1) (("1" (typepred r!1) (("1" (expand "thread") (("1" (inst?) (("1" (assert) (("1" (flatten) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "iqall") (("2" (flatten) (("2" (hide-all-but (-2 1)) (("2" (split) (("1" (inst?) (("1" (assert) nil nil)) nil) ("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2 3) (("2" (expand "take") (("2" (split) (("1" (grind) nil nil) ("2" (apply-extensionality :hide? t) (("1" (typepred x!2) (("1" (grind) nil nil)) nil) ("2" (grind) nil nil) ("3" (grind) nil nil) ("4" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil) (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil) (nat_min application-judgement "{k: nat | k <= i AND k <= j}" real_defs nil) (nat_max application-judgement "{k: nat | i <= k AND j <= k}" real_defs nil) (int_max application-judgement "{k: int | i <= k AND j <= k}" real_defs nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (IFF const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (iqall const-decl "bool" tournamentSafe0 nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (NOT const-decl "[bool -> bool]" booleans nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (iq2 const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (mx_j_implied formula-decl nil tournamentSafe0 nil)) shostak)) (kq0_step 0 (kq0_step-1 nil 3669355216 ("" (grind) nil nil) ((thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (leaf const-decl "finite_set[node]" ctrees nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (finite_remove application-judgement "finite_set" finite_sets nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (digit type-eq-decl nil ctrees nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (x!1 skolem-const-decl "state" tournamentSafe0 nil) (p!1 skolem-const-decl "(thread)" tournamentSafe0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (kq0 const-decl "bool" tournamentSafe0 nil) (next11 const-decl "state" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (step11 const-decl "bool" tournamentSafe0 nil) (goto const-decl "state" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (next15 const-decl "state" tournamentSafe0 nil) (member const-decl "bool" sets nil) (empty? const-decl "bool" sets nil) (step15F const-decl "bool" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (next18 const-decl "state" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (step const-decl "bool" tournamentSafe0 nil)) shostak)) (kq1_11 0 (kq1_11-1 nil 3669360959 ("" (expand "step11") (("" (expand "kq1") (("" (skosimp) (("" (replaceh -2) (("" (assert) (("" (expand "next11") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((kq1 const-decl "bool" tournamentSafe0 nil) (next11 const-decl "state" tournamentSafe0 nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (step11 const-decl "bool" tournamentSafe0 nil)) shostak)) (kq1_12 0 (kq1_12-1 nil 3669361028 ("" (expand "step12") (("" (expand "kq1") (("" (skosimp) (("" (replaceh -2) (("" (expand "goto") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((kq1 const-decl "bool" tournamentSafe0 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (goto const-decl "state" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil)) shostak)) (kq1_14 0 (kq1_14-1 nil 3669820638 ("" (expand "step14") (("" (expand "kq1") (("" (skosimp) (("" (replaceh -2) (("" (expand "next14") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((kq1 const-decl "bool" tournamentSafe0 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (next14 const-decl "state" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil)) shostak)) (kq1_13 0 (kq1_13-1 nil 3669820677 ("" (expand "step13") (("" (expand "kq1") (("" (skosimp) (("" (replaceh -2) (("" (expand "next13") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((kq1 const-decl "bool" tournamentSafe0 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (next13 const-decl "state" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil)) shostak)) (kq1_15F 0 (kq1_15F-2 nil 3678605979 ("" (expand "step15F") (("" (expand "kq1") (("" (skosimp) (("" (replaceh -2) (("" (expand "next15") (("" (case "n!1 = curnode(p!1, x!1)") (("1" (assert) (("1" (expand "curnode") (("1" (case "depth(n!1) = x!1`level(p!1)") (("1" (assert) (("1" (expand "iq0") (("1" (propax) nil nil)) nil)) nil) ("2" (expand "iq1") (("2" (replaceh -1) (("2" (expand "iq0") (("2" (hide-all-but (-4 -5 1)) (("2" (flatten) (("2" (use depth_path) (("1" (assert) nil nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) (("2" (flatten) (("2" (assert) (("2" (case "x!1`occ(n!1)= p!1") (("1" (assert) nil nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((kq1 const-decl "bool" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentSafe0 nil) (iq1 const-decl "bool" tournamentSafe0 nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (x!1 skolem-const-decl "state" tournamentSafe0 nil) (p!1 skolem-const-decl "(thread)" tournamentSafe0 nil) (depth_path formula-decl nil ctrees nil) (iq0 const-decl "bool" tournamentSafe0 nil) (depth const-decl "nat" ctrees nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order 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nil)) nil) ((kq1 const-decl "bool" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (= const-decl "[T, T -> boolean]" equalities nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) 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application-judgement "int" integers nil) (next15 const-decl "state" tournamentSafe0 nil) (step15F const-decl "bool" tournamentSafe0 nil)) shostak)) (kq1_15G 0 (kq1_15G-2 nil 3678606158 ("" (expand "step15G") (("" (expand "kq1") (("" (skosimp) (("" (replaceh -2) (("" (expand "next15") (("" (case "n!1 = curnode(p!1, x!1)") (("1" (assert) (("1" (expand "curnode") (("1" (case "depth(n!1)= x!1`level(p!1)") (("1" (flatten) (("1" (assert) (("1" (expand "curbranch") (("1" (assert) (("1" (expand "iq0") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (expand "curbranch") (("2" (assert) (("2" (flatten) (("2" (assert) (("2" (lemma depth_path) (("2" (inst?) 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nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (= const-decl "[T, T -> boolean]" equalities nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" 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(("1" (inst?) (("1" (flatten) (("1" (expand "kq0") (("1" (assert) (("1" (expand "iq4") (("1" (assert) (("1" (expand "kq5") (("1" (replace -6) (("1" (expand "emptyset") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "kq1") (("2" (skosimp) (("2" (inst? -3) (("2" (assert) nil nil)) nil)) nil)) nil) ("3" (expand "kq4") (("3" (use card_emptyset[digseq]) (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((init const-decl "bool" tournamentSafe0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentSafe0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (kq0 const-decl "bool" tournamentSafe0 nil) (kq5 const-decl "bool" tournamentSafe0 nil) (emptyset const-decl "set" sets nil) (int_minus_int_is_int application-judgement "int" integers nil) (finite_emptyset name-judgement "finite_set" finite_sets nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (kq1 const-decl "bool" tournamentSafe0 nil) (card_emptyset formula-decl nil finite_sets nil) (kq4 const-decl "bool" tournamentSafe0 nil) (kqall const-decl "bool" tournamentSafe0 nil)) shostak))) $$$tournamentSafe1.pvs % Wim H. Hesselink, May-August 2016 % Proofs for: Tournaments for mutual exclusion: % verification and concurrent complexity. % Part 3. The invariants Lq* tournamentSafe1 [ degree: posnat, node: TYPE+ ] : THEORY BEGIN IMPORTING tournamentSafe0[degree, node] x, y: VAR state p, q, r: VAR (thread) j, k, kk: VAR nat n: VAR node dig: VAR digit no_step15G: LEMMA % x`mu(curnode(p, x)) = curbranch(p, x) AND iqall(x) AND kqall(x) IMPLIES x`level(p) < 0 mx_used: LEMMA 13 <= x`pc(q) AND x`pc(q) <= 15 AND 13 <= x`pc(r) AND x`pc(r) <= 15 AND path(q, x`level(q)) = path(r, x`level(r)) AND sib(q, x`level(q)) = sib(r, x`level(r)) AND iqall(x) IMPLIES q = r lq0(q, x): bool = 14 <= x`pc(q) AND x`pc(q) <= 15 IMPLIES NOT x`prio(curnode(q, x), curbranch(q, x))(curbranch(q, x)) lq2(n, dig, x): bool = x`cur(n)(dig) IMPLIES x`pc(x`bock(n, dig)) = 15 AND curnode(x`bock(n, dig), x) = n AND curbranch(x`bock(n, dig), x) = dig lq0_rest: LEMMA lq0(q, x) AND step(p, x, y) IMPLIES lq0(q, y) OR step13(p, x, y) lq0_13: LEMMA % lq0(q, x) AND step13(p, x, y) AND iqall(x) % use mx_used AND lq2(curnode(q, x), curbranch(q, x), x) IMPLIES lq0(q, y) lq0_step: LEMMA lq0(q, x) AND step(p, x, y) AND iqall(x) AND lq2(curnode(q, x), curbranch(q, x), x) IMPLIES lq0(q, y) lq1(q, x): bool = x`pc(q) = 15 IMPLIES x`cur(curnode(q, x))(curbranch(q, x)) lq1_rest: LEMMA % lq1(q, x) AND step(p, x, y) IMPLIES lq1(q, y) OR step15F(p, x, y) OR step15G(p, x, y) lq1_15F: LEMMA lq1(q, x) AND step15F(p, x, y) AND iqall(x) IMPLIES lq1(q, y) lq1_15G: LEMMA lq1(q, x) AND step15G(p, x, y) AND iqall(x) IMPLIES lq1(q, y) lq1_step: LEMMA lq1(q, x) AND step(p, x, y) AND iqall(x) IMPLIES lq1(q, y) lq2_step: LEMMA lq2(n, dig, x) AND step(p, x, y) IMPLIES lq2(n, dig, y) lqall(x): bool = (FORALL n, dig: lq2(n, dig, x)) AND (FORALL q: lq1(q, x) AND lq0(q, x)) lqall_step: LEMMA lqall(x) AND step(p, x, y) AND iqall(x) IMPLIES lqall(y) init_lqall: LEMMA init(x) IMPLIES lqall(x) globinv(x): bool = iqall(x) AND kqall(x) AND lqall(x) globinv_step: LEMMA globinv(x) AND step(p, x, y) IMPLIES globinv(y) init_globinv: LEMMA init(x) IMPLIES globinv(x) END tournamentSafe1 $$$tournamentSafe1.prf (tournamentSafe1 (no_step15G 0 (no_step15G-2 nil 3678801794 ("" (skosimp) (("" (expand "curbranch") (("" (expand "curnode") (("" (assert) (("" (case "iq0(p!1, x!1)") (("1" (expand "iq0") (("1" (assert) (("1" (name-replace nn "path(p!1, x!1`level(p!1))" nil) (("1" (case "kq1(nn, x!1)") (("1" (expand "kq1") (("1" (assert) (("1" (flatten) (("1" (name-replace jj "x!1`level(p!1)" nil) (("1" (case "depth(nn)=jj") (("1" (replace -1) (("1" (name-replace qq "x!1`occ(nn)") (("1" (case "iq5(qq, jj, x!1)") (("1" (expand "iq5") (("1" (assert) (("1" (replaceh -5) (("1" (replace -1) (("1" (assert) (("1" (case "mx(p!1, qq, jj + 1, x!1)") (("1" (expand "mx") (("1" (use joining_paths) (("1" (assert) nil nil)) nil)) nil) ("2" (use mx_j_implied) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "iqall") (("2" (flatten) (("2" (inst? -10) (("2" (assert) nil nil)) nil)) nil)) nil) ("3" (assert) nil nil)) nil)) nil)) nil) ("2" (hide-all-but (-5 -6) -) (("2" (replace -1 + rl) (("2" (use depth_path) (("1" (assert) nil nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "kqall") (("2" (flatten) (("2" (inst? -6) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "iqall") (("2" (flatten) (("2" (inst?) 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(edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (remove const-decl "set" sets nil) (member const-decl "bool" sets nil) (finite_remove application-judgement "finite_set" finite_sets nil) (int_minus_int_is_int application-judgement "int" integers nil) (curnode const-decl "node" tournamentSafe0 nil) (lq1 const-decl "bool" tournamentSafe1 nil)) nil) (lq1_15F-1 nil 3669885247 ("" (expand "step15F") (("" (expand "lq1") (("" (skosimp) (("" (replaceh -2) (("" (expand "next15") (("" (case "q!1=p!1") (("1" (assert) nil nil) ("2" (assert) (("2" (case "curnode(p!1, x!1)= take(x!1`level(q!1), q!1)") (("1" (assert) (("1" (expand "remove") (("1" (expand "member") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (= 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(("2" (expand "member") (("2" (inst?) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((lqall const-decl "bool" tournamentSafe1 nil) (lq2 const-decl "bool" tournamentSafe1 nil) (node formal-nonempty-type-decl nil tournamentSafe1 nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentSafe1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (empty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (lq1 const-decl "bool" tournamentSafe1 nil) (lq0 const-decl "bool" tournamentSafe1 nil) (int_minus_int_is_int application-judgement "int" integers nil) (finite_emptyset name-judgement "finite_set" finite_sets nil) (init const-decl "bool" tournamentSafe0 nil)) nil) (init_lqall-1 nil 3670127952 ("" (expand "init") (("" (expand "lqall") (("" (skosimp) (("" (split) (("1" (skolem!) 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Hesselink, May-August 2016 % Proofs for: Tournaments for mutual exclusion: % verification and concurrent complexity. % Part 4. Individual progress tournamentUnity0[ degree: posnat, node: TYPE+ ]: THEORY % BEGIN IMPORTING tournamentSafe1[degree, node], intsum, bdUnity[state] Thread: TYPE = (thread) p, q, r: VAR Thread x, y: VAR state degree_gt_1: AXIOM degree > 1 D: posnat % duration of doorway in MXd W: posnat % duration of waiting section in MXd exi: posnat % duration of exit in MXd cs: posnat % duration of critical section % positive for the sake of the covering theorem exi1: posnat = exi + 1 i, n, k, kk, m: VAR nat b: VAR bool se: VAR finite_set[Thread] z: VAR int nn: VAR node step(x, y): bool = x = y OR EXISTS p: step(p, x, y) sinc(x): int = % LET g = LAMBDA n: IF n < N THEN x`cnt(enum_thread(n)) ELSE 0 ENDIF IN sum(N, g) competing_leq(kk)(x): bool = % card(x`competing) <= kk allidle(x): bool = FORALL q: x`pc(q) = 11 %%%%%%% Individual progress %%%%%%% forward1(p)(x, y): bool = step12(p, x, y) OR step17(p, x, y) OR step19(p, x, y) enabled1(q)(x): bool = x`pc(q) = 12 OR x`pc(q) = 17 OR x`pc(q) = 19 enabled1_necessary: LEMMA forward1(q)(x, y) IMPLIES enabled1(q)(x) enabled1_sufficient: LEMMA % enabled1(q)(x) IMPLIES EXISTS y: forward1(q)(x, y) E1: specification[state] = (# inv := globinv, step := step, fwd := LAMBDA i: IF i < N THEN forward1(enum_thread(i)) ELSE emptyset ENDIF #) enabled_E1: LEMMA E1`inv(x) IMPLIES enabled(E1)(i)(x) = (i < N AND enabled1(enum_thread(i))(x)) good_E1: LEMMA good(E1) at(q, k)(x): bool = x`pc(q) = k between(q, i, k)(x): bool = i <= x`pc(q) AND x`pc(q) <= k out(q)(x): bool = x`pc(q) = 17 AND x`level(q) = depth(q) - 1 out_to19: LEMMA % ensures leto(E1)(1, out(q), at(q, 19)) from19to11: LEMMA % ensures leto(E1)(1, at(q, 19), at(q, 11)) out_to11: LEMMA leto(E1)(2, out(q), at(q, 11)) ass_exit: bool = FORALL q: leto(E1)(exi, fullset, neg(at(q, 18))) ass_cs: bool = FORALL q: leto(E1)(cs, fullset, neg(at(q, 16))) atlev(q, m, z)(x): bool = x`pc(q) = m AND x`level(q) = z leveq_betw(q, i, m, k)(x): bool = i <= x`pc(q) AND x`pc(q) <= m AND x`level(q) = k from17to18: LEMMA % z < depth(q) - 1 IMPLIES leto(E1)(1, atlev(q, 17, z), atlev(q, 18, z)) from18to17: LEMMA % ass_exit IMPLIES leto(E1)(exi, atlev(q, 18, z), atlev(q, 17, z + 1)) from17to17: LEMMA ass_exit AND z < depth(q) - 1 IMPLIES leto(E1)(exi1, atlev(q, 17, z), atlev(q, 17, z + 1)) levleq(q, k)(x): bool = % RENAME levless x`level(q) < k AND 12 <= x`pc(q) AND x`pc(q) <= 18 from12Eto16: LEMMA % leto(E1)(1, atlev(q, 12, -1), atlev(q, 16, -1)) from16to17: LEMMA % ass_cs IMPLIES leto(E1)(cs, atlev(q, 16, -1), atlev(q, 17, -1)) levleq_0_out: LEMMA % ass_exit AND ass_cs AND depth(q) > 0 IMPLIES leto(E1)(exi + cs + 2, levleq(q, 0), atlev(q, 17, 0)) levleq_to_out(k, m): bool = % induction hypothesis FORALL q: k < depth(q) IMPLIES leto(E1)(m, levleq(q, k), atlev(q, 17, k)) % NB needed for all threads q, for the sake of at15levri_down mubot(nn)(x): bool = x`mu(nn) = -1 occ(q, nn)(x): bool = x`level(q) < depth(nn) AND nn = path(q, depth(nn)) AND depth(nn) < depth(q) occ_unless_mubot: LEMMA unless(E1)(occ(q, nn), mubot(nn)) mu_to_bot: LEMMA % depth(nn) = k AND levleq_to_out(k, m) IMPLIES leto(E1)(m, fullset, mubot(nn)) inbranches(nn, x): finite_set[Thread] = % fan(nn) { q | x`level(q) <= depth(nn) AND depth(nn) < depth(q) AND path(q, depth(nn)) = nn } card_inbranches: LEMMA % uses MXN globinv(x) IMPLIES card(inbranches(nn, x)) <= degree cprio(q, x): finite_set[Thread] = { r | curnode(r, x) = curnode(q, x) AND NOT x`prio(curnode(r, x), curbranch(r, x))(curbranch(q, x)) AND 14 <= x`pc(r) AND x`pc(r) <= 15 } cprio_sub_inbranches: LEMMA % uses iq0 and iq1 x`pc(q) = 15 AND cprio(q, x)(r) AND globinv(x) IMPLIES inbranches(curnode(q, x), x)(r) level_cprio: LEMMA % cprio(q, x)(r) AND x`pc(q) = 15 AND globinv(x) IMPLIES x`level(r) = x`level(q) AND x`level(q) < depth(r) cprio_shrinks_at15: LEMMA % x`pc(q) = 15 AND cprio(q, y)(r) AND step(p, x, y) AND iqall(x) AND lq1(q, x) IMPLIES cprio(q, x)(r) OR q = p card_cprio_shrinks: LEMMA % x`pc(q) = 15 AND step(p, x, y) AND globinv(x) IMPLIES card(cprio(q, y)) <= card(cprio(q, x)) OR q = p card_cprio: LEMMA % uses card_inbranches, cprio_sub_inbranches x`pc(q) = 15 AND globinv(x) IMPLIES card(cprio(q, x)) <= degree card_cprio_mu: LEMMA % x`pc(q) = 15 AND x`mu(curnode(q, x)) >= 0 AND globinv(x) IMPLIES card(cprio(q, x)) < degree at15levpri(q, k, m)(x): bool = x`pc(q) = 15 AND x`level(q) = k AND card(cprio(q, x)) <= m ass_waiting: bool = % FORALL q, k: leto(E1)(W, atlev(q, 15, k), neg(mubot(path(q, k))) ) at15levpri_unless: LEMMA % use mx_used unless(E1)(cap(at15levpri(q, k, m+1), mubot(path(q, k))), cup(at15levpri(q, k, m), atlev(q, 12, k-1)) ) leadsto_at15levpri: LEMMA % ass_waiting IMPLIES leto(E1)(W, cap(at15levpri(q, k, m+1), mubot(path(q, k))), cup(at15levpri(q, k, m), atlev(q, 12, k-1)) ) unless_mubot: LEMMA unless(E1)(at15levpri(q, k, i+1), cap(at15levpri(q, k, i+1), mubot(path(q, k))) ) at15_mubot: LEMMA % levleq_to_out(k, m) IMPLIES leto(E1)(m, at15levpri(q, k, i+1), cap(at15levpri(q, k, i+1), mubot(path(q, k))) ) at15levpri_down: LEMMA % levleq_to_out(k, m) AND ass_waiting IMPLIES leto(E1)(m + W, at15levpri(q, k, i+1), cup(at15levpri(q, k, i), atlev(q, 12, k - 1)) ) at15levpri_induct: LEMMA % use lq0 for the base case levleq_to_out(k, m) AND ass_waiting IMPLIES leto(E1)(i * (m + W), at15levpri(q, k, i), atlev(q, 12, k - 1) ) degW(m): nat = % (degree - 1) * (W + m) at15levpri_degree: LEMMA % % use at15levpri_induct and leadsto_at15levpri levleq_to_out(k, m) AND ass_waiting IMPLIES leto(E1)(degW(m) + W, at15levpri(q, k, degree), atlev(q, 12, k - 1) ) atlev15_to12: LEMMA % levleq_to_out(k, m) AND ass_waiting IMPLIES leto(E1)(degW(m) + W, atlev(q, 15, k), atlev(q, 12, k - 1) ) ass_doorway: bool = FORALL q: leto(E1)(D, fullset, neg(between(q, 13, 14))) ass_doorway_extended: LEMMA % ass_doorway IMPLIES leto(E1)(D + 1, leveq_betw(q, 12, 15, k), atlev(q, 15, k)) level_step: LEMMA % levleq_to_out(k, m) AND ass_waiting AND ass_doorway IMPLIES leto(E1)((D + 1) + degree * (m + W), leveq_betw(q, 12, 15, k), atlev(q, 17, k) ) level_step_1: LEMMA % levleq_to_out(k, m) AND ass_waiting AND ass_doorway AND ass_exit AND k < depth(q) - 1 IMPLIES leto(E1)((D + 1) + degree * (m + W) + exi1, leveq_betw(q, 12, 18, k), atlev(q, 17, k + 1) ) level_step_2: LEMMA % levleq_to_out(k, m) AND ass_waiting AND ass_doorway AND ass_exit AND k = depth(q) - 1 IMPLIES leto(E1)((D + 1) + degree * (m + W), leveq_betw(q, 12, 18, k), atlev(q, 17, k) ) addend: posnat = D + 1 + degree * W + exi1 levleq_to_out_step: LEMMA % levleq_to_out(k, m) AND ass_waiting AND ass_doorway AND ass_exit IMPLIES levleq_to_out(k + 1, degree * m + addend) fun(k): RECURSIVE nat = % IF k = 0 THEN cs + exi + 2 ELSE degree * fun(k - 1) + addend ENDIF MEASURE k power(k, z): RECURSIVE int = IF k = 0 THEN 1 ELSE z * power(k-1, z) ENDIF MEASURE k fun_eq: LEMMA fun(k) = power(k, degree) * (cs + exi + 2 + addend / (degree-1)) - addend / (degree-1) levleq_to_out_all: LEMMA % ass_cs AND ass_waiting AND ass_doorway AND ass_exit IMPLIES levleq_to_out(k, fun(k)) from12_18to_out: LEMMA % ass_cs AND ass_waiting AND ass_doorway AND ass_exit AND k = depth(q) - 1 IMPLIES leto(E1)(degree * (fun(k) + W) + D + 1, between(q, 12, 18), atlev(q, 17, k)) fun1(k): nat = degree * (fun(k) + W) + D + 1 individual_progress: THEOREM % ass_cs AND ass_waiting AND ass_doorway AND ass_exit AND k = depth(q) - 1 IMPLIES leto(E1)(fun1(k) + 2, fullset, at(q, 11)) factor: real = cs + exi + 2 + addend / (degree-1) term0: real = degree * W + D + 1 - addend / (degree-1) * degree fun1_equals0: LEMMA % fun1(k) = power(k+1, degree) * factor + term0 constant0: real = (D + degree * (W + exi + 2)) / (degree -1) factor_equals: LEMMA factor = cs + constant0 term0_equals: LEMMA term0 = 1 - constant0 fun1_equals: LEMMA % fun1(k) = power(k+1, degree) * (cs + constant0) + 1 - constant0 END tournamentUnity0 $$$tournamentUnity0.prf (tournamentUnity0 (enabled1_necessary 0 (enabled1_necessary-1 nil 3670301093 ("" (grind) nil nil) ((Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (NOT const-decl "[bool -> bool]" booleans nil) (leaf const-decl "finite_set[node]" ctrees nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (goto const-decl "state" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (forward1 const-decl "bool" tournamentUnity0 nil) (enabled1 const-decl "bool" tournamentUnity0 nil)) shostak)) (enabled1_sufficient 0 (enabled1_sufficient-1 nil 3670301105 ("" (expand "enabled1") (("" (skosimp) (("" (case "x!1`pc(q!1) = 12") (("1" (expand "forward1") (("1" (expand "step12") (("1" (assert) (("1" (inst + "goto(q!1, IF x!1`level(q!1) < 0 THEN 16 ELSE 13 ENDIF, x!1)") nil nil)) nil)) nil)) nil) ("2" (expand "forward1") (("2" (case "x!1`pc(q!1) = 15") (("1" (assert) nil nil) ("2" (assert) (("2" (case "x!1`pc(q!1) = 16") (("1" (assert) nil nil) ("2" (case "x!1`pc(q!1) = 17") (("1" (expand "step17") (("1" (inst + "goto(q!1, IF x!1`level(q!1) < depth(q!1) - 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(("" (use out_to19) (("" (use from19to11) (("" (lemma leto_transitive) (("" (inst - 1 1 "out(q!1)" "at(q!1, 19)" "at(q!1, 11)" E1) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((out_to19 formula-decl nil tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (digit type-eq-decl nil ctrees nil) (leto_transitive formula-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (at const-decl "bool" tournamentUnity0 nil) (out const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (from19to11 formula-decl nil tournamentUnity0 nil)) shostak)) (from17to18 0 (from17to18-1 nil 3670653251 ("" (s-ensures) (("" (split) (("1" (skosimp*) (("1" (expand "E1") (("1" (expand "step") (("1" (assert) (("1" (skolem!) 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(("" (lemma PSP0_leto) (("" (inst - exi "atlev(q!1, 18, z!1)" "at(q!1, 18)" "atlev(q!1, 17, z!1 + 1)" E1) (("" (assert) (("" (hide - 2) (("" (split) (("1" (expand "unless") (("1" (expand "<=") (("1" (expand "wp") (("1" (expand "cap") (("1" (expand "atlev") (("1" (expand "cup") (("1" (expand "neg") (("1" (skosimp*) (("1" (expand "E1") (("1" (expand "step") (("1" (split -) (("1" (assert) nil nil) ("2" (skolem!) (("2" (hide 1) (("2" (case "q!1=p!1") (("1" (replaceh -1) (("1" (expand "step") (("1" (expand "step11") (("1" (assert) (("1" (expand "step12") (("1" (expand "step13") (("1" (expand "step14") (("1" (expand "step15F") (("1" (expand "step15G") (("1" (expand "step16") (("1" (expand "step17") (("1" (expand "step19") (("1" (expand "step18") (("1" (replaceh -1) (("1" (expand "next18") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 3 -4) (("2" (split) (("1" (hide -3) (("1" (grind) nil nil)) nil) ("2" (hide -2) (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "<=") (("2" (expand "atlev") (("2" (expand "at") (("2" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((ass_exit const-decl "bool" tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (digit type-eq-decl nil ctrees nil) (PSP0_leto formula-decl nil bdUnity nil) (<= const-decl "bool" mucalculus nil) (cap const-decl "bool" ownpred nil) (cup const-decl "bool" ownpred nil) (step const-decl "bool" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (step const-decl "bool" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (step15F const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (next18 const-decl "state" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (step11 const-decl "bool" tournamentSafe0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (finite_remove application-judgement "finite_set" finite_sets nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (next11 const-decl "state" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (goto const-decl "state" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (next15 const-decl "state" tournamentSafe0 nil) (member const-decl "bool" sets nil) (empty? const-decl "bool" sets nil) (next19 const-decl "state" tournamentSafe0 nil) (neg const-decl "bool" ownpred nil) (wp const-decl "bool" ownpred nil) (unless const-decl "bool" bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (at const-decl "bool" tournamentUnity0 nil) (atlev const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (exi const-decl "posnat" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil)) nil) (from18to17-1 nil 3670655806 ("" (skosimp) (("" (expand "ass_exit") (("" (inst?) (("" (lemma PSP_leto) (("" (inst?) 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const-decl "bool" functions nil) (enum_thread const-decl "(bijective?[below[N], (thread)])" tournamentSafe0 nil) (bijective? const-decl "bool" functions nil) (N const-decl "posnat" tournamentSafe0 nil) (NOT const-decl "[bool -> bool]" booleans nil) (neg const-decl "bool" ownpred nil) (cup const-decl "bool" ownpred nil) (cap const-decl "bool" ownpred nil) (wp const-decl "bool" ownpred nil) (<= const-decl "bool" mucalculus nil) (cobar const-decl "bool" bdUnity nil) (co const-decl "bool" bdUnity nil) (ensures const-decl "bool" bdUnity nil) (ensures_leto formula-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (at const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil)) shostak)) (from16to17 0 (from16to17-1 nil 3670312241 ("" (skosimp) (("" (lemma PSP0_leto) (("" (expand "ass_cs") (("" (inst?) (("" (assert) (("" (inst? -2) (("" (hide +) (("" (inst?) (("" (assert) (("" (hide -) (("" (split) (("1" (expand "unless") (("1" (expand "<=") (("1" (expand "wp") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "atlev") (("1" (expand "neg") (("1" (skosimp*) (("1" (expand "E1") (("1" (expand "step") (("1" (assert) (("1" (hide 1) (("1" (split) (("1" (assert) nil nil) ("2" (skolem!) (("2" (case "q!1=p!1") (("1" (replaceh -1) (("1" (expand "step") (("1" (expand "step11") (("1" (assert) (("1" (expand "step12") (("1" (expand "step13") (("1" (expand "step14") (("1" (expand "step15F") (("1" (expand "step15G") (("1" (expand "step17") (("1" (expand "step18") (("1" (expand "step19") (("1" (expand "step16") (("1" (replaceh -1) (("1" (expand "goto") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -4 3) (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "<=") (("2" (expand "atlev") (("2" (expand "at") (("2" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (PSP0_leto formula-decl nil bdUnity nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (cs const-decl "posnat" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (Thread type-eq-decl nil tournamentUnity0 nil) (atlev const-decl "bool" tournamentUnity0 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield -> numfield]" number_fields nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (at const-decl "bool" tournamentUnity0 nil) (unless const-decl "bool" bdUnity nil) (wp const-decl "bool" ownpred nil) (cup const-decl "bool" ownpred nil) (neg const-decl "bool" ownpred nil) (= const-decl "[T, T -> boolean]" equalities nil) (step const-decl "bool" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (step15F const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (goto const-decl "state" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (step11 const-decl "bool" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (next18 const-decl "state" tournamentSafe0 nil) (empty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (next15 const-decl "state" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (next11 const-decl "state" tournamentSafe0 nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (finite_remove application-judgement "finite_set" finite_sets nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_plus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (step const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (<= const-decl "bool" mucalculus nil) (ass_cs const-decl "bool" tournamentUnity0 nil)) shostak)) (levleq_0_out 0 (levleq_0_out-9 nil 3671639161 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "exi + cs + 2" "levleq(q!1, 0)" "cup(atlev(q!1, 18, -1), cup(atlev(q!1, 17, -1), cup(atlev(q!1, 16, -1), atlev(q!1, 12, -1))))" "atlev(q!1, 17, 0)" E1) (("" (assert) (("" (hide 2) (("" (split) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "levleq") (("1" (expand "atlev") (("1" (skosimp) (("1" (case "iq0(q!1, s!1) AND iq1(q!1, s!1)") (("1" (flatten) (("1" (expand "iq0") (("1" (flatten) (("1" (expand "iq1") (("1" (assert) (("1" (ground) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use from18to17) (("2" (assert) (("2" (lemma leto_up) (("2" (split) (("1" (inst - exi "2+cs+exi" _ _ _) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -2) (("2" (use from17to17) (("2" (assert) (("2" (split) (("1" (inst?) (("1" (assert) (("1" (expand "exi1") (("1" (assert) (("1" (inst - "1+exi") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (case "leto(E1)(cs + exi1, atlev(q!1, 16, -1), atlev(q!1, 17, 0))") (("1" (hide -2) (("1" (split) (("1" (inst - "cs+exi1" "2+cs+exi" _ _ _) (("1" (inst?) (("1" (assert) (("1" (expand "exi1") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (use from12Eto16) (("2" (hide -3) (("2" (lemma leto_transitive) (("2" (inst - 1 "cs+exi1" _ _ _ _) (("2" (inst?) (("2" (assert) (("2" (inst?) (("2" (assert) (("2" (expand "exi1") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2 -2) (("2" (use from16to17) (("2" (lemma leto_transitive) (("2" (inst - cs exi1 _ _ _ _) (("2" (inst?) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (sub_leto formula-decl nil bdUnity nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (cap const-decl "bool" ownpred nil) (iqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (iq1 const-decl "bool" tournamentSafe0 nil) (iq0 const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" mucalculus nil) (from18to17 formula-decl nil tournamentUnity0 nil) (even_minus_odd_is_odd application-judgement "odd_int" integers nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (leto_up formula-decl nil bdUnity nil) (from17to17 formula-decl nil tournamentUnity0 nil) (exi1 const-decl "posnat" tournamentUnity0 nil) (leto const-decl "bool" bdUnity nil) (leto_transitive formula-decl nil bdUnity nil) (from12Eto16 formula-decl nil tournamentUnity0 nil) (from16to17 formula-decl nil tournamentUnity0 nil) (cup_leto formula-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (- const-decl "[numfield -> numfield]" number_fields nil) (atlev const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (levleq const-decl "bool" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (cs const-decl "posnat" tournamentUnity0 nil) (exi const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil)) nil) (levleq_0_out-8 nil 3671638733 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "exi + cs + 2" "levleq(q!1, 0)" "cup(atlev(q!1, 18, -1), cup(atlev(q!1, 17, -1), cup(atlev(q!1, 16, -1), atlev(q!1, 12, -1))))" "atlev(q!1, 17, 0)" E1) (("" (assert) (("" (hide 2) (("" (split) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "levleq") (("1" (expand "atlev") (("1" (skosimp) (("1" (case "iq0(q!1, s!1) AND iq1(q!1, s!1)") (("1" (flatten) (("1" (expand "iq0") (("1" (flatten) (("1" (expand "iq1") (("1" (assert) (("1" (ground) nil))))))))))) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) nil))))))))))))))))))))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use from18to17) (("2" (assert) (("2" (lemma leto_up) (("2" (split) (("1" (inst - exi "2+cs+exi" _ _ _) (("1" (inst?) (("1" (assert) nil))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -2) (("2" (use from17to17) (("2" (assert) (("2" (split) (("1" (inst - exi1 "2 + cs + +exi" _ _ _) (("1" (inst?) (("1" (assert) (("1" (expand "exi1") (("1" (assert) nil))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (case "leto(E1)(2 + exi, atlev(q!1, 16, -1), atlev(q!1, 17, 0))") (("1" (hide -2) (("1" (split) (("1" (inst - "2+exi" "3+exi" _ _ _) (("1" (inst?) (("1" (assert) nil))))) ("2" (use from12Eto16) (("2" (hide -3) (("2" (lemma leto_transitive) (("2" (inst - 1 "2+exi" _ _ _ _) (("2" (inst?) (("2" (assert) (("2" (inst?) (("2" (assert) nil))))))))))))))))))) ("2" (hide 2 -2) (("2" (use from16to17) (("2" (lemma leto_transitive) (("2" (inst - cs exi1 _ _ _ _) (("2" (inst?) (("2" (inst?) (("2" (assert) (("2" (expand "exi1") (("2" (propax) nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) nil) nil nil) (levleq_0_out-7 nil 3671638611 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "exi + cs + 2" "levleq(q!1, 0)" "cup(atlev(q!1, 18, -1), cup(atlev(q!1, 17, -1), cup(atlev(q!1, 16, -1), atlev(q!1, 12, -1))))" "atlev(q!1, 17, 0)" E1) (("" (assert) (("" (hide 2) (("" (split) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "levleq") (("1" (expand "atlev") (("1" (skosimp) (("1" (case "iq0(q!1, s!1) AND iq1(q!1, s!1)") (("1" (flatten) (("1" (expand "iq0") (("1" (flatten) (("1" (expand "iq1") (("1" (assert) (("1" (ground) nil))))))))))) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) nil))))))))))))))))))))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use from18to17) (("2" (assert) (("2" (lemma leto_up) (("2" (split) (("1" (inst - exi "3+exi" _ _ _) (("1" (inst?) (("1" (assert) nil))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -2) (("2" (use from17to17) (("2" (assert) (("2" (split) (("1" (inst - exi1 "2 + cs + +exi" _ _ _) (("1" (inst?) (("1" (assert) (("1" (expand "exi1") (("1" (assert) nil))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (case "leto(E1)(2 + exi, atlev(q!1, 16, -1), atlev(q!1, 17, 0))") (("1" (hide -2) (("1" (split) (("1" (inst - "2+exi" "3+exi" _ _ _) (("1" (inst?) (("1" (assert) nil))))) ("2" (use from12Eto16) (("2" (hide -3) (("2" (lemma leto_transitive) (("2" (inst - 1 "2+exi" _ _ _ _) (("2" (inst?) (("2" (assert) (("2" (inst?) (("2" (assert) nil))))))))))))))))))) ("2" (hide 2 -2) (("2" (use from16to17) (("2" (lemma leto_transitive) (("2" (inst - cs exi1 _ _ _ _) (("2" (inst?) (("2" (inst?) (("2" (assert) (("2" (expand "exi1") (("2" (propax) nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) nil) nil nil) (levleq_0_out-6 nil 3671450631 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "exi + 3" "levleq(q!1, 0)" "cup(atlev(q!1, 18, -1), cup(atlev(q!1, 17, -1), cup(atlev(q!1, 16, -1), atlev(q!1, 12, -1))))" "atlev(q!1, 17, 0)" E1) (("" (assert) (("" (hide 2) (("" (split) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "levleq") (("1" (expand "atlev") (("1" (skosimp) (("1" (case "iq0(q!1, s!1) AND iq1(q!1, s!1)") (("1" (flatten) (("1" (expand "iq0") (("1" (flatten) (("1" (expand "iq1") (("1" (assert) (("1" (ground) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use from18to17) (("2" (assert) (("2" (lemma leto_up) (("2" (split) (("1" (inst - exi "3+exi" _ _ _) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -2) (("2" (use from17to17) (("2" (assert) (("2" (split) (("1" (inst - exi1 "3+exi" _ _ _) (("1" (inst?) (("1" (assert) (("1" (expand "exi1") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (case "leto(E1)(2 + exi, atlev(q!1, 16, -1), atlev(q!1, 17, 0))") (("1" (hide -2) (("1" (split) (("1" (inst - "2+exi" "3+exi" _ _ _) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil) ("2" (use from12Eto16) (("2" (hide -3) (("2" (lemma leto_transitive) (("2" (inst - 1 "2+exi" _ _ _ _) (("2" (inst?) (("2" (assert) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2 -2) (("2" (use from16to17) (("2" (lemma leto_transitive) (("2" (inst - 1 exi1 _ _ _ _) (("2" (inst?) (("2" (inst?) (("2" (assert) (("2" (expand "exi1") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (sub_leto formula-decl nil bdUnity nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (cap const-decl "bool" ownpred nil) (iqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (iq1 const-decl "bool" tournamentSafe0 nil) (iq0 const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" mucalculus nil) (from18to17 formula-decl nil tournamentUnity0 nil) (even_minus_odd_is_odd application-judgement "odd_int" integers nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (leto_up formula-decl nil bdUnity nil) (from17to17 formula-decl nil tournamentUnity0 nil) (exi1 const-decl "posnat" tournamentUnity0 nil) (leto const-decl "bool" bdUnity nil) (even_minus_even_is_even application-judgement "even_int" integers nil) (leto_transitive formula-decl nil bdUnity nil) (from12Eto16 formula-decl nil tournamentUnity0 nil) (from16to17 formula-decl nil tournamentUnity0 nil) (cup_leto formula-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (- const-decl "[numfield -> numfield]" number_fields nil) (atlev const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (levleq const-decl "bool" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (exi const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil)) nil) (levleq_0_out-5 nil 3670685854 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "exi + 3" "levleq(q!1, 0)" "cup(atlev(q!1, 12, -1), cup(atlev(q!1, 16, -1), cup(atlev(q!1, 17, -1), atlev(q!1, 18, -1))))" "atlev(q!1, 17, 0)" E1) (("" (assert) (("" (hide 2) (("" (split) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "levleq") (("1" (expand "atlev") (("1" (skosimp) (("1" (case "iq0(q!1, s!1) AND iq1(q!1, s!1) AND iq4(q!1, s!1)") (("1" (flatten) (("1" (expand "iq0") (("1" (flatten) (("1" (expand "iq1") (("1" (assert) (("1" (ground) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) (("2" (expand "kqall") (("2" (flatten) (("2" (inst? -9) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (sub_leto formula-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (cap const-decl "bool" ownpred nil) (at const-decl "bool" tournamentUnity0 nil) (between const-decl "bool" tournamentUnity0 nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (kqall const-decl "bool" tournamentSafe0 nil) (iqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (iq4 const-decl "bool" tournamentSafe0 nil) (iq1 const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" mucalculus nil) (leto_transitive formula-decl nil bdUnity nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (from12Eto16 formula-decl nil tournamentUnity0 nil) (leto_up formula-decl nil bdUnity nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (cup_leto formula-decl nil bdUnity nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (exi1 const-decl "posnat" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (out const-decl "bool" tournamentUnity0 nil) (levleq const-decl "bool" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil)) nil) (levleq_0_out-4 nil 3670682342 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - _ "levleq(q!1, 0)" _ "out(q!1)" _) (("" (inst - _ "cup(cap(levleq(q!1, 0), at(q!1, 12)), between(q!1, 16, 18))" _) (("" (inst?) (("" (assert) (("" (hide 2) (("" (split) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "levleq") (("1" (expand "between") (("1" (skosimp) (("1" (case "iq1(q!1, s!1) AND iq4(q!1, s!1)") (("1" (flatten) (("1" (expand "iq1") (("1" (expand "iq4") (("1" (assert) (("1" (expand "at") (("1" (assert) nil))))))))))) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil))))))))))))))))))))))))))))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (use from12Eto16) (("1" (use at16_to_out) (("1" (lemma leto_transitive) (("1" (inst - 1 "2 * depth(pp) + 1" _ _ _ _) (("1" (inst?) (("1" (assert) (("1" (inst?) (("1" (assert) (("1" (hide -2 2) (("1" (lemma leto_up) (("1" (inst - "1 + 2 * q!1`length" "1 + 2 * depth(pp)" _ _ _) (("1" (inst?) (("1" (assert) (("1" (hide - 2) (("1" (use thread_length_upb) (("1" (assert) nil))))))))))))))))))))))))))))))) ("2" (use between16_18_out_1) (("2" (assert) nil)))))))))))))))))))))))))) nil) nil nil) (levleq_0_out-3 nil 3670598786 ("" (skolem!) (("" (lemma sub_leto) (("" (inst - _ "levleq(q!1, 0)" _ "out(q!1)" _) (("" (inst - _ "cup(cap(levleq(q!1, 0), at(q!1, 12)), between(q!1, 16, 18))" _) (("" (inst?) (("" (assert) (("" (hide 2) (("" (split) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "levleq") (("1" (expand "between") (("1" (skosimp) (("1" (case "iq1(q!1, s!1) AND iq4(q!1, s!1)") (("1" (flatten) (("1" (expand "iq1") (("1" (expand "iq4") (("1" (assert) (("1" (expand "at") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (use from12Eto16) (("1" (use at16_to_out) (("1" (lemma leto_transitive) (("1" (inst - 1 "2 * depth(pp) + 1" _ _ _ _) (("1" (inst?) (("1" (assert) (("1" (inst?) (("1" (assert) (("1" (hide -2 2) (("1" (lemma leto_up) (("1" (inst - "1 + 2 * q!1`length" "1 + 2 * depth(pp)" _ _ _) (("1" (inst?) (("1" (assert) (("1" (hide - 2) (("1" (use thread_length_upb) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use between16_18_out_1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (sub_leto formula-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (cap const-decl "bool" ownpred nil) (at const-decl "bool" tournamentUnity0 nil) (between const-decl "bool" tournamentUnity0 nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (even_times_int_is_even application-judgement "even_int" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (kqall const-decl "bool" tournamentSafe0 nil) (iqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (iq4 const-decl "bool" tournamentSafe0 nil) (iq1 const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" mucalculus nil) (even_plus_odd_is_odd application-judgement "odd_int" integers nil) (odd_plus_even_is_odd application-judgement "odd_int" integers nil) (leto_up formula-decl nil bdUnity nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (even_minus_odd_is_odd application-judgement "odd_int" integers nil) (leto_transitive formula-decl nil bdUnity nil) (from12Eto16 formula-decl nil tournamentUnity0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (cup_leto formula-decl nil bdUnity nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (even_plus_even_is_even application-judgement "even_int" integers nil) (out const-decl "bool" tournamentUnity0 nil) (levleq const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil)) nil) (levleq_0_out-2 nil 3670595034 ("" (skolem!) (("" (lemma sub_leto) (("" (inst - _ "levleq(q!1, 0)" _ "out(q!1)" _) (("" (inst - _ "cup(cap(levleq(q!1, 0), at(q!1, 12)), between(q!1, 16, 18))" _) (("" (inst?) (("" (assert) (("" (hide 2) (("" (split) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "levleq") (("1" (expand "between") (("1" (skosimp) (("1" (case "iq1(q!1, s!1) AND iq4(q!1, s!1)") (("1" (flatten) (("1" (expand "iq1") (("1" (expand "iq4") (("1" (assert) (("1" (expand "at") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (use from12Eto16) (("1" (use at16_to_out) (("1" (lemma leto_transitive) (("1" (inst - 1 "2 * depth(pp) + 1" _ _ _ _) (("1" (inst?) (("1" (assert) (("1" (inst?) (("1" (assert) (("1" (hide -2 2) (("1" (lemma leto_up) (("1" (inst - "1 + 2 * q!1`length" "1 + 2 * depth(pp)" _ _ _) (("1" (inst?) (("1" (assert) (("1" (hide - 2) (("1" (expand "depth") (("1" (lemma maximum_prop1[digseq]) (("1" (inst - pp len q!1) (("1" (split) (("1" (name-replace mx "maximum(len, pp)") (("1" (expand "len") (("1" (assert) nil nil)) nil)) nil) ("2" (typepred q!1) (("2" (expand "thread") (("2" (expand "leaves") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use between16_18_out_1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((pred type-eq-decl nil defined_types nil) (levleq const-decl "bool" tournamentUnity0 nil) (out const-decl "bool" tournamentUnity0 nil) (even_plus_even_is_even application-judgement "even_int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (cup_leto formula-decl nil bdUnity nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (from12Eto16 formula-decl nil tournamentUnity0 nil) (leto_transitive formula-decl nil bdUnity nil) (even_minus_odd_is_odd application-judgement "odd_int" integers nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (NOT const-decl "[bool -> bool]" booleans nil) (maximum def-decl "nat" maxfinset nil) (= const-decl "[T, T -> boolean]" equalities nil) (maximum_prop1 formula-decl nil maxfinset nil) (leto_up formula-decl nil bdUnity nil) (odd_plus_even_is_odd application-judgement "odd_int" integers nil) (even_plus_odd_is_odd application-judgement "odd_int" integers nil) (<= const-decl "bool" mucalculus nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (iq1 const-decl "bool" tournamentSafe0 nil) (iq4 const-decl "bool" tournamentSafe0 nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (globinv const-decl "bool" tournamentSafe1 nil) (iqall const-decl "bool" tournamentSafe0 nil) (kqall const-decl "bool" tournamentSafe0 nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (even_times_int_is_even application-judgement "even_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (between const-decl "bool" tournamentUnity0 nil) (at const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (cup const-decl "bool" ownpred nil) (sub_leto formula-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil)) nil) (levleq_0_out-1 nil 3670339839 ("" (skolem!) (("" (lemma sub_leto) (("" (inst - _ "levleq(q!1, 0)" _ "out(q!1)" _) (("" (inst - _ "cup(cap(levleq(q!1, 0), at(q!1, 12)), between(q!1, 16, 18))" _) (("" (inst?) (("" (assert) (("" (hide 2) (("" (split) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "levleq") (("1" (expand "between") (("1" (skosimp) (("1" (case "iq1(q!1, s!1) AND iq4(q!1, s!1)") (("1" (flatten) (("1" (expand "iq1") (("1" (expand "iq4") (("1" (assert) (("1" (expand "at") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (use from12Eto16) (("1" (use at16_to_out) (("1" (lemma leto_transitive) (("1" (inst - 1 "2 * q!1`length + 1" _ _ _ _) (("1" (inst?) (("1" (assert) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use between16_18_out) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (sub_leto formula-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (cap const-decl "bool" ownpred nil) (at const-decl "bool" tournamentUnity0 nil) (between const-decl "bool" tournamentUnity0 nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (even_times_int_is_even application-judgement "even_int" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (kqall const-decl "bool" tournamentSafe0 nil) (iqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (iq4 const-decl "bool" tournamentSafe0 nil) (iq1 const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" mucalculus nil) (even_plus_odd_is_odd application-judgement "odd_int" integers nil) (odd_plus_even_is_odd application-judgement "odd_int" integers nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (even_minus_odd_is_odd application-judgement "odd_int" integers nil) (leto_transitive formula-decl nil bdUnity nil) (from12Eto16 formula-decl nil tournamentUnity0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (cup_leto formula-decl nil bdUnity nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (even_plus_even_is_even application-judgement "even_int" integers nil) (out const-decl "bool" tournamentUnity0 nil) (levleq const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil)) shostak)) (occ_unless_mubot 0 (occ_unless_mubot-1 nil 3670325469 ("" (expand "unless") (("" (expand "<=") (("" (expand "wp") (("" (expand "cap") (("" (expand "cup") (("" (expand "neg") (("" (expand "occ") (("" (skosimp*) (("" (expand "E1") (("" (expand "step") (("" (assert) (("" (assert) (("" (skolem!) 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const-decl "bool" sets nil) (member const-decl "bool" sets nil) (next15 const-decl "state" tournamentSafe0 nil) (finite_remove application-judgement "finite_set" finite_sets nil) (int_minus_int_is_int application-judgement "int" integers nil) (step15G const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (step19 const-decl "bool" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (next18 const-decl "state" tournamentSafe0 nil) (mubot const-decl "bool" tournamentUnity0 nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (number nonempty-type-decl nil numbers nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (digit type-eq-decl nil ctrees nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (occ const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (wp const-decl "bool" ownpred nil) (unless const-decl "bool" bdUnity nil)) shostak)) (mu_to_bot 0 (mu_to_bot-4 nil 3671446253 ("" (skosimp) (("" (expand "levleq_to_out") (("" (lemma sub_leto) (("" (inst - m!1 _ _ _ E1) (("" (lemma leto_union) (("" (inst -2 fullset _ "mubot(nn!1)") (("" (assert) (("" (inst - m!1 _ "mubot(nn!1)" E1) (("" (name ppset "{pp : pred[state] | EXISTS q: pp = occ(q, nn!1)}") (("" (inst -3 "cup(mubot(nn!1), Union(ppset))") (("" (split) (("1" (hide-all-but (-3 1)) (("1" (expand "<=" +) (("1" (expand "cap") (("1" (expand "fullset") (("1" (expand "cup") (("1" (skosimp) (("1" (expand "mubot") (("1" (expand "Union") (("1" (expand "E1") (("1" (case "kq1(nn!1, s!1)") (("1" (expand "kq1") (("1" (split) (("1" (flatten) (("1" (inst + "occ(s!1`occ(nn!1), nn!1)") (("1" (expand "occ") (("1" (assert) nil nil)) nil) ("2" (expand "ppset") (("2" (inst + "s!1`occ(nn!1)") nil nil)) nil)) nil)) nil) ("2" (typepred "s!1`mu(nn!1)") (("2" (assert) nil nil)) nil)) nil)) nil) ("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst? -3) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2 3) (("2" (split) (("1" (hide -) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (inst?) (("2" (assert) (("2" (hide -1 1) (("2" (skosimp) (("2" (expand "ppset") (("2" (skolem!) (("2" (replaceh -1) (("2" (inst - q!1) (("2" (lemma PSP_leto) (("2" (inst - m!1 "levleq(q!1, k!1)" _ _ "atlev(q!1, 17, k!1)" E1) (("2" (assert) (("2" (use occ_unless_mubot) (("2" (inst?) (("2" (assert) (("2" (split -4) (("1" (assert) (("1" (hide -1 -4) (("1" (case "cup(cap(atlev(q!1, 17, k!1), occ(q!1, nn!1)), mubot(nn!1)) = mubot(nn!1)") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (inst - m!1 "occ(q!1, nn!1)" "cap(levleq(q!1, k!1), occ(q!1, nn!1))" "mubot(nn!1)" E1) (("1" (assert) (("1" (hide - 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "levleq") (("1" (expand "occ") (("1" (skosimp) (("1" (assert) (("1" (case "iq4(q!1, s!1) AND kq0(q!1, s!1)") (("1" (flatten) (("1" (expand "kq0") (("1" (expand "iq4") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (prop) (("2" (expand "cap") (("2" (expand "occ") (("2" (flatten) (("2" (assert) (("2" (expand "atlev") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1 -2) (("2" (use subset_leto) (("2" (assert) (("2" (hide 3) (("2" (expand "<=") (("2" (expand "cap") (("2" (expand "occ") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((levleq_to_out const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (mubot const-decl "bool" tournamentUnity0 nil) (fullset const-decl "set" sets nil) (Union const-decl "set" sets nil) (setofsets type-eq-decl nil sets nil) (setof type-eq-decl nil defined_types nil) (cup const-decl "bool" ownpred nil) (cup_leto formula-decl nil bdUnity nil) (PSP_leto formula-decl nil bdUnity nil) (iqall const-decl "bool" tournamentSafe0 nil) (kq0 const-decl "bool" tournamentSafe0 nil) (iq4 const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (occ_unless_mubot formula-decl nil tournamentUnity0 nil) (levleq const-decl "bool" tournamentUnity0 nil) (atlev const-decl "bool" tournamentUnity0 nil) (subset_leto formula-decl nil bdUnity nil) (Union_surjective name-judgement "(surjective?[setofsets[T], set[T]])" sets_lemmas nil) (cap const-decl "bool" ownpred nil) (globinv const-decl "bool" tournamentSafe1 nil) (kqall const-decl "bool" tournamentSafe0 nil) (NOT const-decl "[bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield -> numfield]" number_fields nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (nn!1 skolem-const-decl "node" tournamentUnity0 nil) (s!1 skolem-const-decl "state[degree, node]" tournamentUnity0 nil) (ppset skolem-const-decl "[pred[state] -> boolean]" tournamentUnity0 nil) (kq1 const-decl "bool" tournamentSafe0 nil) (<= const-decl "bool" mucalculus nil) (occ const-decl "bool" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (leto_union formula-decl nil bdUnity nil) (sub_leto formula-decl nil bdUnity nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (digit type-eq-decl nil ctrees nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil)) nil) (mu_to_bot-3 nil 3671433121 ("" (skosimp) (("" (expand "levleq_to_out") (("" (lemma sub_leto) (("" (inst - m!1 _ _ _ E1) (("" (lemma leto_union) (("" (inst -2 fullset _ "mubot(nn!1)") (("" (assert) (("" (inst - m!1 _ "mubot(nn!1)" E1) (("" (name ppset "{pp : pred[state] | EXISTS q: pp = occ(q, nn!1)}") (("" (inst -3 "cup(mubot(nn!1), Union(ppset))") (("" (split) (("1" (hide-all-but (-3 1)) (("1" (expand "<=" +) (("1" (expand "cap") (("1" (expand "fullset") (("1" (expand "cup") (("1" (skosimp) (("1" (expand "mubot") (("1" (expand "Union") (("1" (expand "E1") (("1" (case "kq1(nn!1, s!1)") (("1" (expand "kq1") (("1" (split) (("1" (flatten) (("1" (inst + "occ(s!1`occ(nn!1), nn!1)") (("1" (expand "occ") (("1" (assert) nil nil)) nil) ("2" (expand "ppset") (("2" (inst + "s!1`occ(nn!1)") nil nil)) nil)) nil)) nil) ("2" (typepred "s!1`mu(nn!1)") (("2" (assert) nil nil)) nil)) nil)) nil) ("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst? -3) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2 3) (("2" (split) (("1" (hide -) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (inst?) (("2" (assert) (("2" (hide -1 1) (("2" (skosimp) (("2" (expand "ppset") (("2" (skolem!) (("2" (replaceh -1) (("2" (inst - q!1) (("2" (lemma PSP_leto) (("2" (inst - m!1 "levleq(q!1, k!1)" _ _ "atlev(q!1, 17, k!1)" E1) (("2" (assert) (("2" (use occ_unless_mubot) (("2" (inst?) (("2" (assert) (("2" (hide -1 -4) (("2" (case "cup(cap(atlev(q!1, 17, k!1), occ(q!1, nn!1)), mubot(nn!1)) = mubot(nn!1)") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (inst - m!1 "occ(q!1, nn!1)" "cap(levleq(q!1, k!1), occ(q!1, nn!1))" "mubot(nn!1)" E1) (("1" (assert) (("1" (hide -1 2) (("1" (expand "<=" +) (("1" (expand "cap") (("1" (expand "occ") (("1" (expand "levleq") (("1" (skosimp) (("1" (assert) (("1" (expand "E1") (("1" (case "iq4(q!1, s!1)") (("1" (expand "iq4") (("1" (propax) nil nil)) nil) ("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (prop) (("2" (expand "cap") (("2" (expand "occ") (("2" (flatten) (("2" (assert) (("2" (expand "atlev") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (sub_leto formula-decl nil bdUnity nil) (leto_union formula-decl nil bdUnity nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (= const-decl "[T, T -> boolean]" equalities nil) (Thread type-eq-decl nil tournamentUnity0 nil) (occ const-decl "bool" tournamentUnity0 nil) (<= const-decl "bool" mucalculus nil) (kq1 const-decl "bool" tournamentSafe0 nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (- const-decl "[numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (<= const-decl "bool" reals nil) (NOT const-decl "[bool -> bool]" booleans nil) (kqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (cap const-decl "bool" ownpred nil) (Union_surjective name-judgement "(surjective?[setofsets[T], set[T]])" sets_lemmas nil) (subset_leto formula-decl nil bdUnity nil) (atlev const-decl "bool" tournamentUnity0 nil) (levleq const-decl "bool" tournamentUnity0 nil) (occ_unless_mubot formula-decl nil tournamentUnity0 nil) (iq4 const-decl "bool" tournamentSafe0 nil) (PSP_leto formula-decl nil bdUnity nil) (cup_leto formula-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (setof type-eq-decl nil defined_types nil) (setofsets type-eq-decl nil sets nil) (Union const-decl "set" sets nil) (fullset const-decl "set" sets nil) (mubot const-decl "bool" tournamentUnity0 nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil)) nil) (mu_to_bot-2 nil 3671432955 ("" (skosimp) (("" (expand "levleq_to_out") (("" (lemma sub_leto) (("" (inst - m!1 _ _ _ E1) (("" (lemma leto_union) (("" (inst -2 fullset _ "mubot(nn!1)") (("" (assert) (("" (inst - m!1 _ "mubot(nn!1)" E1) (("" (name ppset "{pp : pred[state] | EXISTS q: pp = occ(q, nn!1)}") (("" (inst -3 "cup(mubot(nn!1), Union(ppset))") (("" (split) (("1" (hide-all-but (-3 1)) (("1" (expand "<=" +) (("1" (expand "cap") (("1" (expand "fullset") (("1" (expand "cup") (("1" (skosimp) (("1" (expand "mubot") (("1" (expand "Union") (("1" (expand "E1") (("1" (case "kq1(nn!1, s!1)") (("1" (expand "kq1") (("1" (split) (("1" (flatten) (("1" (inst + "occ(s!1`occ(nn!1), nn!1)") (("1" (expand "occ") (("1" (assert) nil))) ("2" (expand "ppset") (("2" (inst + "s!1`occ(nn!1)") nil))))))) ("2" (typepred "s!1`mu(nn!1)") (("2" (assert) nil))))))) ("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst? -3) nil))))))))))))))))))))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2 3) (("2" (split) (("1" (hide -) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil))))))))))))) ("2" (inst?) (("2" (assert) (("2" (hide -1 1) (("2" (skosimp) (("2" (expand "ppset") (("2" (skolem!) (("2" (replaceh -1) (("2" (inst - q!1) (("2" (lemma PSP_leto) (("2" (inst - m!1 "levleq(q!1, k!1)" _ _ "atlev(q!1, 17, k!1)" E1) (("2" (assert) (("2" (use occ_unless_mubot) (("2" (inst?) (("2" (assert) (("2" (hide -1 -4) (("2" (case "cup(cap(out(q!1), occ(q!1, nn!1)), mubot(nn!1)) = mubot(nn!1)") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (inst - m!1 "occ(q!1, nn!1)" "cap(levleq(q!1, k!1), occ(q!1, nn!1))" "mubot(nn!1)" E1) (("1" (assert) (("1" (hide -1 2) (("1" (expand "<=" +) (("1" (expand "cap") (("1" (expand "occ") (("1" (expand "levleq") (("1" (skosimp) (("1" (assert) (("1" (expand "E1") (("1" (case "iq4(q!1, s!1)") (("1" (expand "iq4") (("1" (propax) nil))) ("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil))))))))))))))))))))))))))))))))))) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (prop) (("2" (expand "cap") (("2" (expand "out") (("2" (expand "occ") (("2" (flatten) (("2" (assert) nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) nil) nil nil) (mu_to_bot-1 nil 3670314852 ("" (skosimp) (("" (expand "levleq_to_out") (("" (lemma sub_leto) (("" (inst - m!1 _ _ _ E1) (("" (lemma leto_union) (("" (inst -2 fullset _ "mubot(nn!1)") (("" (assert) (("" (inst - m!1 _ "mubot(nn!1)" E1) (("" (name ppset "{pp : pred[state] | EXISTS q: pp = occ(q, nn!1)}") (("" (inst -3 "cup(mubot(nn!1), Union(ppset))") (("" (split) (("1" (hide-all-but (-3 1)) (("1" (expand "<=" +) (("1" (expand "cap") (("1" (expand "fullset") (("1" (expand "cup") (("1" (skosimp) (("1" (expand "mubot") (("1" (expand "Union") (("1" (expand "E1") (("1" (case "kq1(nn!1, s!1)") (("1" (expand "kq1") (("1" (split) (("1" (flatten) (("1" (inst + "occ(s!1`occ(nn!1), nn!1)") (("1" (expand "occ") (("1" (assert) nil nil)) nil) ("2" (expand "ppset") (("2" (inst + "s!1`occ(nn!1)") nil nil)) nil)) nil)) nil) ("2" (typepred "s!1`mu(nn!1)") (("2" (assert) nil nil)) nil)) nil)) nil) ("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst? -3) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2 3) (("2" (split) (("1" (hide -) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (inst?) (("2" (assert) (("2" (hide -1 1) (("2" (skosimp) (("2" (expand "ppset") (("2" (skolem!) (("2" (replaceh -1) (("2" (inst - q!1) (("2" (lemma PSP_leto) (("2" (inst - m!1 "levleq(q!1, k!1)" _ _ "out(q!1)" E1) (("2" (assert) (("2" (use occ_unless_mubot) (("2" (inst?) (("2" (assert) (("2" (hide -1 -4) (("2" (case "cup(cap(out(q!1), occ(q!1, nn!1)), mubot(nn!1)) = mubot(nn!1)") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (inst - m!1 "occ(q!1, nn!1)" "cap(levleq(q!1, k!1), occ(q!1, nn!1))" "mubot(nn!1)" E1) (("1" (assert) (("1" (hide -1 2) (("1" (expand "<=" +) (("1" (expand "cap") (("1" (expand "occ") (("1" (expand "levleq") (("1" (skosimp) (("1" (assert) (("1" (expand "E1") (("1" (case "iq4(q!1, s!1)") (("1" (expand "iq4") (("1" (propax) nil nil)) nil) ("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (prop) (("2" (expand "cap") (("2" (expand "out") (("2" (expand "occ") (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((levleq_to_out const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (mubot const-decl "bool" tournamentUnity0 nil) (fullset const-decl "set" sets nil) (Union const-decl "set" sets nil) (setofsets type-eq-decl nil sets nil) (setof type-eq-decl nil defined_types nil) (cup const-decl "bool" ownpred nil) (cup_leto formula-decl nil bdUnity nil) (PSP_leto formula-decl nil bdUnity nil) (int_minus_int_is_int application-judgement "int" integers nil) (iq4 const-decl "bool" tournamentSafe0 nil) (occ_unless_mubot formula-decl nil tournamentUnity0 nil) (levleq const-decl "bool" tournamentUnity0 nil) (out const-decl "bool" tournamentUnity0 nil) (subset_leto formula-decl nil bdUnity nil) (Union_surjective name-judgement "(surjective?[setofsets[T], set[T]])" sets_lemmas nil) (cap const-decl "bool" ownpred nil) (globinv const-decl "bool" tournamentSafe1 nil) (kqall const-decl "bool" tournamentSafe0 nil) (NOT const-decl "[bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield -> numfield]" number_fields nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (kq1 const-decl "bool" tournamentSafe0 nil) (<= const-decl "bool" mucalculus nil) (occ const-decl "bool" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (leto_union formula-decl nil bdUnity nil) (sub_leto formula-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil)) shostak)) (inbranches_TCC1 0 (inbranches_TCC1-1 nil 3671283495 ("" (skolem!) (("" (lemma finite_subset[Thread]) (("" (inst - thread _) (("" (inst?) (("" (assert) (("" (hide 2) (("" (expand "subset?") (("" (expand "member") (("" (expand "restrict") (("" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (finite_subset formula-decl nil finite_sets nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (digit type-eq-decl nil ctrees nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (depth const-decl "nat" ctrees nil) (= const-decl "[T, T -> boolean]" equalities nil) (path const-decl "node" ctrees nil) (member const-decl "bool" sets nil) (subset? const-decl "bool" sets nil) (subset_is_partial_order name-judgement "(partial_order?[set[T]])" sets_lemmas nil) (restrict const-decl "R" restrict nil) (finite_restrict application-judgement "finite_set[S]" restrict_set_props nil)) nil)) (card_inbranches 0 (card_inbranches-2 nil 3678615233 ("" (skosimp) (("" (lemma Card_injection[Thread]) (("" (inst - "inbranches(nn!1, x!1)" degree) (("" (name kl "depth(nn!1)") (("" (assert) (("" (hide 2) (("" (inst + "lambda (q: (inbranches(nn!1, x!1))): IF kl < depth(q) THEN sib(q, kl) ELSE 0 ENDIF") (("" (expand "injective?") (("" (skosimp) (("" (name-replace qq x1!1) (("" (name-replace rr x2!1) (("" (typepred qq) (("" (typepred rr) (("" (expand "inbranches") (("" (flatten) (("" (assert) (("" (replace -9) (("" (case "mx(qq, rr, kl+1, x!1)") (("1" (expand "mx") (("1" (lemma joining_paths) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (use mx_j_implied) (("2" (assert) (("2" (expand "globinv") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (Card_injection formula-decl nil finite_sets nil) (= const-decl "[T, T -> boolean]" equalities nil) (depth const-decl "nat" ctrees nil) (injective? const-decl "bool" functions nil) (NOT const-decl "[bool -> bool]" booleans nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (mx const-decl "bool" tournamentSafe0 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (joining_paths formula-decl nil ctrees nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (int_minus_int_is_int application-judgement "int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (globinv const-decl "bool" tournamentSafe1 nil) (mx_j_implied formula-decl nil tournamentSafe0 nil) (sib const-decl "digit" ctrees nil) (IF const-decl "[boolean, T, T -> T]" if_def nil) (below type-eq-decl nil nat_types nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (inbranches const-decl "finite_set[Thread]" tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (digit type-eq-decl nil ctrees nil)) nil) (card_inbranches-1 nil 3671283496 ("" (skosimp) (("" (lemma Card_injection[Thread]) (("" (inst - "inbranches(nn!1, x!1)" degree) (("" (name kl "nn!1`length") (("" (assert) (("" (hide 2) (("" (inst + "lambda (q: (inbranches(nn!1, x!1))): IF kl < q`length THEN q`seq(kl) ELSE 0 ENDIF") (("" (expand "injective?") (("" (skosimp) (("" (name-replace qq x1!1) (("" (name-replace rr x2!1) (("" (typepred qq) (("" (typepred rr) (("" (expand "inbranches") (("" (flatten) (("" (assert) (("" (replace -9) (("" (use inductive_eq) (("" (assert) (("" (case "mx(qq, rr, kl+1, x!1)") (("1" (expand "mx") (("1" (propax) nil nil)) nil) ("2" (use mx_j_implied) (("2" (assert) (("2" (expand "globinv") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (Card_injection formula-decl nil finite_sets nil) (= const-decl "[T, T -> boolean]" equalities nil) (injective? const-decl "bool" functions nil) (NOT const-decl "[bool -> bool]" booleans nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (globinv const-decl "bool" tournamentSafe1 nil) (mx_j_implied formula-decl nil tournamentSafe0 nil) (IF const-decl "[boolean, T, T -> T]" if_def nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (inbranches const-decl "finite_set[Thread]" tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil)) shostak)) (cprio_TCC1 0 (cprio_TCC1-1 nil 3670228151 ("" (skosimp) (("" (lemma finite_subset[Thread]) (("" (inst - thread _) (("" (assert) (("" (inst?) (("" (assert) (("" (hide 2) (("" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (finite_subset formula-decl nil finite_sets nil) (subset_is_partial_order name-judgement "(partial_order?[set[T]])" sets_lemmas nil) (member const-decl "bool" sets nil) (leaf const-decl "finite_set[node]" ctrees nil) (subset? const-decl "bool" sets nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (<= const-decl "bool" reals nil) (curbranch const-decl "digit" tournamentSafe0 nil) (NOT const-decl "[bool -> bool]" booleans nil) (curnode const-decl "node" tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (digit type-eq-decl nil ctrees nil) (= const-decl "[T, T -> boolean]" equalities nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (restrict const-decl "R" restrict nil) (finite_restrict application-judgement "finite_set[S]" restrict_set_props nil)) nil)) (cprio_sub_inbranches 0 (cprio_sub_inbranches-1 nil 3671284268 ("" (expand "inbranches") (("" (expand "cprio") (("" (skosimp) (("" (expand "curnode") (("" (lemma depth_path) (("" (inst-cp - _ q!1) (("" (case "iq0(q!1, x!1) AND iq1(q!1, x!1) AND iq0(r!1, x!1) AND iq1(r!1, x!1)") (("1" (flatten) (("1" (inst? -6) (("1" (inst - _ r!1) (("1" (inst?) (("1" (expand "iq0") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil) ("2" (expand "iq1") (("2" (assert) nil nil)) nil)) nil)) nil) ("2" (expand "iq1") (("2" (assert) nil nil)) nil)) nil)) nil) ("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (hide-all-but (-7 1)) (("2" (inst-cp - q!1) (("2" (inst - r!1) (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cprio const-decl "finite_set[Thread]" tournamentUnity0 nil) (curnode const-decl "node" tournamentSafe0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (iqall const-decl "bool" tournamentSafe0 nil) (int_minus_int_is_int application-judgement "int" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (r!1 skolem-const-decl "Thread" tournamentUnity0 nil) (q!1 skolem-const-decl "Thread" tournamentUnity0 nil) (x!1 skolem-const-decl "state[degree, node]" tournamentUnity0 nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (digit type-eq-decl nil ctrees nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (iq0 const-decl "bool" tournamentSafe0 nil) (iq1 const-decl "bool" tournamentSafe0 nil) (depth_path formula-decl nil ctrees nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (inbranches const-decl "finite_set[Thread]" tournamentUnity0 nil)) shostak)) (level_cprio 0 (level_cprio-1 nil 3671279021 ("" (skosimp) (("" (expand "cprio") (("" (flatten) (("" (assert) (("" (expand "globinv") (("" (flatten) (("" (assert) (("" (expand "curnode") (("" (hide 1) (("" (case "iq0(q!1, x!1) AND iq0(r!1, x!1) AND iq1(q!1, x!1) AND iq1(r!1, x!1)") (("1" (flatten) (("1" (expand "iq0") (("1" (expand "iq1") (("1" (flatten) (("1" (use equal_paths) (("1" (assert) nil nil) ("2" (assert) nil nil) ("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "iqall") (("2" (flatten) (("2" (inst-cp - q!1) (("2" (inst - r!1) (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cprio const-decl "finite_set[Thread]" tournamentUnity0 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (curnode const-decl "node" tournamentSafe0 nil) (iq1 const-decl "bool" tournamentSafe0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (iq0 const-decl "bool" tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (digit type-eq-decl nil ctrees nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (int_minus_int_is_int application-judgement "int" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (x!1 skolem-const-decl "state[degree, node]" tournamentUnity0 nil) (r!1 skolem-const-decl "Thread" tournamentUnity0 nil) (q!1 skolem-const-decl "Thread" tournamentUnity0 nil) (equal_paths formula-decl nil ctrees nil) (iqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil)) shostak)) (cprio_shrinks_at15 0 (cprio_shrinks_at15-6 nil 3678801276 ("" (expand "cprio") (("" (skosimp) (("" (assert) (("" (expand "curnode") (("" (case "y!1`level(q!1) = x!1`level(q!1)") (("1" (expand "curbranch") (("1" (replaceh -1) (("1" (case "r!1=p!1") (("1" (replaceh -1) (("1" (case "step13(p!1, x!1, y!1) OR step14(p!1, x!1, y!1)") (("1" (hide -6) (("1" (split) (("1" (expand "step13") (("1" (flatten) (("1" (replaceh -1) (("1" (expand "next13") (("1" (assert) (("1" (lift-if) (("1" (assert) (("1" (expand "curnode") (("1" (expand "curbranch") (("1" (expand "lq1") (("1" (expand "curnode") (("1" (expand "curbranch") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "step14") (("2" (flatten) (("2" (replaceh -1) (("2" (expand "next14") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (flatten) (("2" (expand "step") (("2" (assert) (("2" (hide-all-but (-3 -4 -5)) (("2" (split) (("1" (grind) nil nil) ("2" (grind) nil nil) ("3" (grind) nil nil) ("4" (grind) nil nil) ("5" (grind) nil nil) ("6" (grind) nil nil) ("7" (grind) nil nil) ("8" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (case "y!1`pc(r!1) = x!1`pc(r!1) AND y!1`level(r!1) = x!1`level(r!1)") (("1" (flatten) (("1" (replaceh -1) (("1" (replaceh -1) (("1" (assert) (("1" (case "step13(p!1, x!1, y!1)") (("1" (hide -6) (("1" (expand "step13") (("1" (flatten) (("1" (replaceh -1) (("1" (expand "next13") (("1" (case "(curnode(p!1, x!1), curbranch(p!1, x!1)) = (path(r!1, x!1`level(r!1)), sib(r!1, x!1`level(r!1)))") (("1" (assert) (("1" (flatten) (("1" (expand "curnode") (("1" (expand "curbranch") (("1" (use mx_used) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (lift-if) (("2" (assert) (("2" (hide -) (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (case "x!1`pc(p!1) = 15 AND y!1 = next15(p!1, x!1)") (("1" (flatten) (("1" (hide -7 1) (("1" (replaceh -2) (("1" (expand "next15") (("1" (assert) (("1" (split +) (("1" (flatten) (("1" (expand "remove") (("1" (expand "member") (("1" (flatten) (("1" (expand "curnode") (("1" (expand "curbranch") (("1" (replaceh -5) (("1" (use mx_used) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "step") (("2" (case "step15F(p!1, x!1, y!1) OR step15G(p!1, x!1, y!1)") (("1" (hide-all-but (-1 1)) (("1" (expand "step15F") (("1" (expand "step15G") (("1" (ground) nil nil)) nil)) nil)) nil) ("2" (flatten) (("2" (assert) (("2" (hide-all-but (-5 -9 6)) (("2" (split -) (("1" (grind) nil nil) ("2" (grind) nil nil) ("3" (grind) nil nil) ("4" (grind) nil nil) ("5" (grind) nil nil) ("6" (grind) nil nil) ("7" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide-all-but (-5 1 2)) (("2" (split) (("1" (grind) nil nil) ("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide-all-but (-5 1 4)) (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((curnode const-decl "node" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (step13 const-decl "bool" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (lq1 const-decl "bool" tournamentSafe1 nil) (next14 const-decl "state" tournamentSafe0 nil) (step const-decl "bool" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (next18 const-decl "state" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (step17 const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (next15 const-decl "state" tournamentSafe0 nil) (member const-decl "bool" sets nil) (empty? const-decl "bool" sets nil) (step15F const-decl "bool" tournamentSafe0 nil) (int_minus_int_is_int application-judgement "int" integers nil) (finite_remove application-judgement "finite_set" finite_sets nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (goto const-decl "state" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (next11 const-decl "state" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (step11 const-decl "bool" tournamentSafe0 nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (path const-decl "node" ctrees nil) (sib const-decl "digit" ctrees nil) (mx_used formula-decl nil tournamentSafe1 nil) (remove const-decl "set" sets nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) 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(real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (goto const-decl "state" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (next11 const-decl "state" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (step11 const-decl "bool" tournamentSafe0 nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (next14 const-decl "state" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (remove const-decl "set" sets nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (cprio const-decl "finite_set[Thread]" tournamentUnity0 nil)) shostak)) (card_cprio_shrinks 0 (card_cprio_shrinks-1 nil 3670395986 ("" (skosimp) (("" (case "subset?(cprio(q!1, y!1), cprio(q!1, x!1))") (("1" (use card_subset[Thread]) (("1" (assert) nil nil)) nil) ("2" (hide 2) (("2" (expand "subset?") (("2" (expand "member") (("2" (skosimp) (("2" (lemma cprio_shrinks_at15) (("2" (inst - p!1 q!1 x!2 x!1 y!1) (("2" (assert) (("2" (expand "globinv") (("2" (expand "lqall") (("2" (flatten) (("2" (inst? -7) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cprio const-decl "finite_set[Thread]" tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (digit type-eq-decl nil ctrees nil) (subset? const-decl "bool" sets nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (subset_is_partial_order name-judgement "(partial_order?[set[T]])" sets_lemmas nil) (card_subset formula-decl nil finite_sets nil) (globinv const-decl "bool" tournamentSafe1 nil) (lqall const-decl "bool" tournamentSafe1 nil) (cprio_shrinks_at15 formula-decl nil tournamentUnity0 nil) (member const-decl "bool" sets nil)) shostak)) (card_cprio 0 (card_cprio-3 nil 3671285202 ("" (skosimp) (("" (use card_inbranches (nn "curnode(q!1, x!1)")) (("" (assert) (("" (lemma card_subset[Thread]) (("" (inst - "cprio(q!1, x!1)" "inbranches(curnode(q!1, x!1), x!1)") (("" (assert) (("" (hide -1 2) (("" (expand "subset?") 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const-decl "bool" sets nil) (cprio const-decl "finite_set[Thread]" tournamentUnity0 nil) (remove const-decl "set" sets nil) (subset_is_partial_order name-judgement "(partial_order?[set[T]])" sets_lemmas nil) (card_remove formula-decl nil finite_sets nil) (card_subset formula-decl nil finite_sets nil) (mubot const-decl "bool" tournamentUnity0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (no_step15G formula-decl nil tournamentSafe1 nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (neg const-decl "bool" ownpred nil) (wp const-decl "bool" ownpred nil) (unless const-decl "bool" bdUnity nil)) shostak)) (leadsto_at15levpri 0 (leadsto_at15levpri-3 nil 3678784962 ("" (skosimp) (("" (expand "ass_waiting") (("" (inst?) (("" (lemma PSP_leto) (("" (inst?) (("" (assert) (("" (hide -2) (("" (use at15levpri_unless) (("" (inst?) 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(("" (lemma PSP_leto) (("" (inst?) (("" (assert) (("" (hide -2) (("" (use at15levpri_unless) (("" (inst?) (("" (assert) (("" (hide -1) (("" (name-replace pp0 "cap(at15levpri(q!1, k!1, 1 + m!1), mubot(take(k!1, q!1)))") (("" (name-replace pp1 "cup(at15levpri(q!1, k!1, m!1), atlev(q!1, 12, k!1 - 1))") (("" (case "cap(cap(atlev(q!1, 15, k!1), mubot(take(k!1, q!1))), pp0) = pp0") (("1" (replaceh -1) (("1" (case "cup(cap(neg(mubot(take(k!1, q!1))), pp0), pp1)=pp1") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (prop) (("2" (expand "pp1") (("2" (expand "cup") (("2" (expand "cap") (("2" (expand "pp0") (("2" (expand "cap") (("2" (expand "at15levpri") (("2" (expand "mubot") (("2" (expand "neg") (("2" (flatten) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "pp0") (("2" (expand "cap") (("2" (prop) (("2" (expand "at15levpri") (("2" (expand "atlev") (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((ass_waiting const-decl "bool" tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (PSP_leto formula-decl nil bdUnity nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (at15levpri_unless formula-decl nil tournamentUnity0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (cup const-decl "bool" ownpred nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (neg const-decl "bool" ownpred nil) (mubot const-decl "bool" tournamentUnity0 nil) (atlev const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (W const-decl "posnat" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil)) nil) (leadsto_at15levpri-1 nil 3670402226 ("" (skosimp) (("" (expand "ass_waiting") (("" (inst?) (("" (lemma PSP_leto) (("" (inst?) (("" (assert) (("" (hide -2) (("" (use at15levpri_unless) (("" (inst?) (("" (assert) (("" (hide -1) (("" (name-replace pp0 "cap(at15levpri(q!1, k!1, 1 + m!1), mubot(take(k!1, q!1)))") (("" (name-replace pp1 "cup(at15levpri(q!1, k!1, m!1), at12levmin(q!1, k!1))") (("" (case "cap(cap(at15lev(q!1, k!1), mubot(take(k!1, q!1))), pp0) = pp0") (("1" (replaceh -1) (("1" (case "cup(cap(neg(mubot(take(k!1, q!1))), pp0), pp1)=pp1") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (prop) (("2" (expand "pp1") (("2" (expand "cup") (("2" (expand "cap") (("2" (expand "pp0") (("2" (expand "cap") (("2" (expand "at15levpri") (("2" (expand "mubot") (("2" (expand "neg") (("2" (flatten) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "pp0") (("2" (expand "cap") (("2" (prop) (("2" (expand "at15levpri") (("2" (expand "at15lev") (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((ass_waiting const-decl "bool" tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (PSP_leto formula-decl nil bdUnity nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (at15levpri_unless formula-decl nil tournamentUnity0 nil) (int_minus_int_is_int application-judgement "int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (cup const-decl "bool" ownpred nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (neg const-decl "bool" ownpred nil) (mubot const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (W const-decl "posnat" tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil)) shostak)) (unless_mubot 0 (unless_mubot-1 nil 3670411687 ("" (expand "unless") (("" (expand "<=") (("" (expand "wp") (("" (expand "cap") (("" (expand "neg") (("" (expand "cup") (("" (expand "E1") (("" (skosimp*) (("" (assert) (("" (expand "step") (("" (skolem!) (("" (hide 3) (("" (expand "at15levpri") (("" (flatten) (("" (use card_cprio_shrinks) (("" (assert) (("" (case "q!1=p!1") (("1" (replaceh -1) (("1" (expand "mubot") (("1" (hide 2 -3) (("1" (case "step15F(p!1, s!1, y!1) OR step15G(p!1, s!1, y!1)") (("1" (hide -5) (("1" (split) (("1" (expand "step15F") (("1" (flatten) (("1" (expand "curnode") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (expand "step15G") (("2" (flatten) (("2" (use no_step15G) (("2" (assert) (("2" (expand "globinv") (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (flatten) (("2" (expand "step") (("2" (assert) (("2" (hide-all-but (-1 -4)) (("2" (expand "step11") (("2" (expand "step12") (("2" (expand "step13") (("2" (expand "step14") (("2" (expand "step16") (("2" (expand "step17") (("2" (expand "step18") (("2" (expand "step19") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) (("2" (hide-all-but (-2 -3 -6 1 3)) (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((<= const-decl "bool" mucalculus nil) (cap const-decl "bool" ownpred nil) (cup const-decl "bool" ownpred nil) (step const-decl "bool" tournamentUnity0 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (next19 const-decl "state" tournamentSafe0 nil) (next18 const-decl "state" tournamentSafe0 nil) (empty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (next15 const-decl "state" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (goto const-decl "state" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (next11 const-decl "state" tournamentSafe0 nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (finite_remove application-judgement "finite_set" finite_sets nil) (int_minus_int_is_int application-judgement "int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (step11 const-decl "bool" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (step const-decl "bool" tournamentSafe0 nil) (no_step15G formula-decl nil tournamentSafe1 nil) (globinv const-decl "bool" tournamentSafe1 nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (curnode const-decl "node" tournamentSafe0 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (step15G const-decl "bool" tournamentSafe0 nil) (step15F const-decl "bool" tournamentSafe0 nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (mubot const-decl "bool" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (number nonempty-type-decl nil numbers nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (digit type-eq-decl nil ctrees nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (card_cprio_shrinks formula-decl nil tournamentUnity0 nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (neg const-decl "bool" ownpred nil) (wp const-decl "bool" ownpred nil) (unless const-decl "bool" bdUnity nil)) shostak)) (at15_mubot 0 (at15_mubot-4 nil 3678785097 ("" (skosimp) (("" (use mu_to_bot) (("" (assert) (("" (split) (("1" (lemma PSP_leto) (("1" (inst?) (("1" (use unless_mubot) (("1" (inst?) (("1" (assert) (("1" (hide -1 -3 -4) (("1" (name-replace pp1 "at15levpri(q!1, k!1, 1 + i!1)") (("1" (name-replace pp2 "mubot(path(q!1, k!1))") (("1" (case "cap(fullset, pp1) = pp1") (("1" (replaceh -1) (("1" (case "cup(cap(pp2, pp1), cap(pp1, pp2)) = cap(pp1, pp2)") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (expand "cup") (("2" (prop) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (expand "fullset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -) (("2" (use depth_path) (("2" (lift-if) (("2" (assert) (("2" (split) (("1" (propax) nil nil) ("2" (flatten) (("2" (hide -1 2) (("2" (use subset_leto) (("2" (assert) (("2" (hide 3) (("2" (expand "<=" 1) (("2" (expand "cap") (("2" (expand "at15levpri") (("2" (skosimp) (("2" (case "iq0(q!1, s!1)") (("1" (expand "iq0") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((mu_to_bot formula-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (path const-decl "node" ctrees nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (fullset const-decl "set" sets nil) (mubot const-decl "bool" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil) (cap const-decl "bool" ownpred nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (= const-decl "[T, T -> boolean]" equalities nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (unless_mubot formula-decl nil tournamentUnity0 nil) (PSP_leto formula-decl nil bdUnity nil) (digit type-eq-decl nil ctrees nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (depth_path formula-decl nil ctrees nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (subset_leto formula-decl nil bdUnity nil) (iqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (iq0 const-decl "bool" tournamentSafe0 nil) (<= const-decl "bool" mucalculus nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil)) nil) (at15_mubot-3 nil 3678785060 ("" (skosimp) (("" (use mu_to_bot) (("" (assert) (("" (split) (("1" (lemma PSP_leto) (("1" (inst?) (("1" (use unless_mubot) (("1" (inst?) (("1" (assert) (("1" (hide -1 -3 -4) (("1" (name-replace pp1 "at15levpri(q!1, k!1, 1 + i!1)") (("1" (name-replace pp2 "mubot(path(q!1, k!1))") (("1" (case "cap(fullset, pp1) = pp1") (("1" (replaceh -1) (("1" (case "cup(cap(pp2, pp1), cap(pp1, pp2)) = cap(pp1, pp2)") (("1" (assert) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (expand "cup") (("2" (prop) nil))))))))))))))) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (expand "fullset") (("2" (propax) nil))))))))))))))))))))))))))))) ("2" (hide -) (("2" (case "k!1 < q!1`length") (("1" (hide 2) (("1" (expand "take") (("1" (expand "max") (("1" (expand "min") (("1" (assert) nil))))))))) ("2" (hide 2) (("2" (name-replace goal "cap(at15levpri(q!1, k!1, 1 + i!1), mubot(path(q!1, k!1)))") (("2" (use subset_leto) (("2" (assert) (("2" (hide 3) (("2" (expand "<=") (("2" (expand "cap") (("2" (expand "at15levpri") (("2" (skosimp) (("2" (case "iq0(q!1, s!1)") (("1" (expand "iq0") (("1" (flatten) (("1" (assert) nil))))) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil)))))))))))))))))))))))))))))))))))))))))) nil) nil nil) (at15_mubot-2 nil 3671446719 ("" (skosimp) (("" (use mu_to_bot) (("" (assert) (("" (split) (("1" (lemma PSP_leto) (("1" (inst?) (("1" (use unless_mubot) (("1" (inst?) (("1" (assert) (("1" (hide -1 -3 -4) (("1" (name-replace pp1 "at15levpri(q!1, k!1, 1 + i!1)") (("1" (name-replace pp2 "mubot(take(k!1, q!1))") (("1" (case "cap(fullset, pp1) = pp1") (("1" (replaceh -1) (("1" (case "cup(cap(pp2, pp1), cap(pp1, pp2)) = cap(pp1, pp2)") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (expand "cup") (("2" (prop) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (expand "fullset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -) (("2" (case "k!1 < q!1`length") (("1" (hide 2) (("1" (expand "take") (("1" (expand "max") (("1" (expand "min") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (name-replace goal "cap(at15levpri(q!1, k!1, 1 + i!1), mubot(take(k!1, q!1)))") (("2" (use subset_leto) (("2" (assert) (("2" (hide 3) (("2" (expand "<=") (("2" (expand "cap") (("2" (expand "at15levpri") (("2" (skosimp) (("2" (case "iq0(q!1, s!1)") (("1" (expand "iq0") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((mu_to_bot formula-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (pred type-eq-decl nil defined_types nil) (fullset const-decl "set" sets nil) (mubot const-decl "bool" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil) (cap const-decl "bool" ownpred nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (= const-decl "[T, T -> boolean]" equalities nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (unless_mubot formula-decl nil tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (PSP_leto formula-decl nil bdUnity nil) (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil) (<= const-decl "bool" mucalculus nil) (iq0 const-decl "bool" tournamentSafe0 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (globinv const-decl "bool" tournamentSafe1 nil) (iqall const-decl "bool" tournamentSafe0 nil) (subset_leto formula-decl nil bdUnity nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil)) nil) (at15_mubot-1 nil 3670411345 ("" (skosimp) (("" (use mu_to_bot) (("" (assert) (("" (split) (("1" (lemma PSP_leto) (("1" (inst?) (("1" (use unless_mubot) (("1" (inst?) (("1" (assert) (("1" (hide -1 -3 -4) (("1" (name-replace pp1 "at15levpri(q!1, k!1, 1 + i!1)") (("1" (name-replace pp2 "mubot(take(k!1, q!1))") (("1" (case "cap(fullset, pp1) = pp1") (("1" (replaceh -1) (("1" (case "cup(cap(pp2, pp1), cap(pp1, pp2)) = cap(pp1, pp2)") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (expand "cup") (("2" (prop) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (expand "fullset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (expand "take") (("2" (expand "max") (("2" (expand "min") (("2" (lift-if) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((mu_to_bot formula-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (pred type-eq-decl nil defined_types nil) (fullset const-decl "set" sets nil) (mubot const-decl "bool" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil) (cap const-decl "bool" ownpred nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (= const-decl "[T, T -> boolean]" equalities nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (unless_mubot formula-decl nil tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (PSP_leto formula-decl nil bdUnity nil) (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil)) shostak)) (at15levpri_down 0 (at15levpri_down-4 nil 3678788457 ("" (skosimp) (("" (use at15_mubot) (("" (assert) (("" (use leadsto_at15levpri) (("" (lemma leto_transitive) (("" (name-replace pp1 "at15levpri(q!1, k!1, 1 + i!1)") (("" (name-replace goal "cup(at15levpri(q!1, k!1, i!1), atlev(q!1, 12, k!1-1))") (("" (name-replace pp2 "cap(pp1, mubot(path(q!1, k!1)))") (("" (inst - m!1 W _ _ _ E1) (("" (inst?) (("" (assert) (("" (inst?) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15_mubot formula-decl nil tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (leadsto_at15levpri formula-decl nil tournamentUnity0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (path const-decl "node" ctrees nil) (mubot const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (W const-decl "posnat" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (cup const-decl "bool" ownpred nil) (atlev const-decl "bool" tournamentUnity0 nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (digit type-eq-decl nil ctrees nil) (leto_transitive formula-decl nil bdUnity nil)) nil) (at15levpri_down-3 nil 3671100243 ("" (skosimp) (("" (use at15_mubot) (("" (assert) (("" (use leadsto_at15levpri) (("" (lemma leto_transitive) (("" (name-replace pp1 "at15levpri(q!1, k!1, 1 + i!1)") (("" (name-replace goal "cup(at15levpri(q!1, k!1, i!1), atlev(q!1, 12, k!1-1))") (("" (name-replace pp2 "cap(pp1, mubot(take(k!1, q!1)))") (("" (inst - m!1 W _ _ _ E1) (("" (inst?) (("" (assert) (("" (inst?) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15_mubot formula-decl nil tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (leadsto_at15levpri formula-decl nil tournamentUnity0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (mubot const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (W const-decl "posnat" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (cup const-decl "bool" ownpred nil) (atlev const-decl "bool" tournamentUnity0 nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (leto_transitive formula-decl nil bdUnity nil)) nil) (at15levpri_down-2 nil 3670564248 ("" (skosimp) (("" (use at15_mubot) (("" (assert) (("" (use leadsto_at15levpri) (("" (lemma leto_transitive) (("" (name-replace pp1 "at15levpri(q!1, k!1, 1 + i!1)") (("" (name-replace goal "cup(at15levpri(q!1, k!1, i!1), at12levmin(q!1, k!1))") (("" (name-replace pp2 "cap(pp1, mubot(take(k!1, q!1)))") (("" (inst - m!1 W _ _ _ E1) (("" (inst?) (("" (assert) (("" (inst?) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15_mubot formula-decl nil tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (leadsto_at15levpri formula-decl nil tournamentUnity0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (mubot const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (atlev const-decl "bool" tournamentUnity0 nil) (W const-decl "posnat" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (cup const-decl "bool" ownpred nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (leto_transitive formula-decl nil bdUnity nil)) nil) (at15levpri_down-1 nil 3670412493 ("" (skosimp) (("" (use at15_mubot) (("" (assert) (("" (use leadsto_at15levpri) (("" (lemma leto_transitive) (("" (name-replace pp1 "at15levpri(q!1, k!1, 1 + i!1)") (("" (name-replace goal "cup(at15levpri(q!1, k!1, i!1), at12levmin(q!1, k!1))") (("" (name-replace pp2 "cap(pp1, mubot(take(k!1, q!1)))") (("" (inst - m!1 1 _ _ _ E1) (("" (inst?) (("" (assert) (("" (inst?) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15_mubot formula-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (leadsto_at15levpri formula-decl nil tournamentUnity0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (mubot const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (cup const-decl "bool" ownpred nil) (leto_transitive formula-decl nil bdUnity nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil)) shostak)) (at15levpri_induct 0 (at15levpri_induct-5 nil 3671264654 ("" (induct i) (("1" (assert) (("1" (skosimp) (("1" (use subset_leto) (("1" (assert) (("1" (hide - 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "at15levpri") (("1" (skosimp) (("1" (use empty_card[Thread]) (("1" (assert) (("1" (expand "empty?") (("1" (expand "member") (("1" (inst - q!1) (("1" (expand "cprio") (("1" (hide -4 +) (("1" (expand "E1") (("1" (case "lq0(q!1, s!1)") (("1" (expand "lq0") (("1" (propax) nil nil)) nil) ("2" (expand "globinv") (("2" (expand "lqall") (("2" (flatten) (("2" (inst? -7) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (inst?) (("2" (inst - m!1) (("2" (assert) (("2" (lemma at15levpri_down) (("2" (inst - j!1 k!1 m!1 q!1) (("2" (assert) (("2" (name-replace jm "W * j!1 + j!1 * m!1") (("2" (name-replace m1 "W + m!1") (("2" (name-replace pp0 "at15levpri(q!1, k!1, 1 + j!1)") (("2" (name-replace pp1 "at15levpri(q!1, k!1, j!1)") (("2" (name-replace goal "atlev(q!1, 12, k!1 - 1)") (("2" (lemma leto_transitive_1) (("2" (inst - m1 jm _ _ _ E1) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15levpri_down formula-decl nil tournamentUnity0 nil) (posint nonempty-type-eq-decl nil integers nil) (leto_transitive_1 formula-decl nil bdUnity nil) (= const-decl "[T, T -> boolean]" equalities nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (subset_leto formula-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (member const-decl "bool" sets nil) (globinv const-decl "bool" tournamentSafe1 nil) (lqall const-decl "bool" tournamentSafe1 nil) (lq0 const-decl "bool" tournamentSafe1 nil) (empty? const-decl "bool" sets nil) (cprio const-decl "finite_set[Thread]" tournamentUnity0 nil) (empty_card formula-decl nil finite_sets nil) (<= const-decl "bool" mucalculus nil) (nat_induction formula-decl nil naturalnumbers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (atlev const-decl "bool" tournamentUnity0 nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (W const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (leto const-decl "bool" bdUnity nil) (specification type-eq-decl nil bdUnity nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (digit type-eq-decl nil ctrees nil) (ass_waiting const-decl "bool" tournamentUnity0 nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (int_minus_int_is_int application-judgement "int" integers nil)) nil) (at15levpri_induct-4 nil 3671100307 ("" (induct i) (("1" (assert) (("1" (skosimp) (("1" (use subset_leto) (("1" (assert) (("1" (hide - 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "at15levpri") (("1" (skosimp) (("1" (use empty_card[Thread]) (("1" (assert) (("1" (expand "empty?") (("1" (expand "member") (("1" (inst - q!1) (("1" (expand "cprio") (("1" (hide -4 +) (("1" (expand "E1") (("1" (use prio_irreflexive) (("1" (expand "globinv") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (inst?) (("2" (inst - m!1) (("2" (assert) (("2" (lemma at15levpri_down) (("2" (inst - j!1 k!1 m!1 q!1) (("2" (assert) (("2" (name-replace jm "W * j!1 + j!1 * m!1") (("2" (name-replace m1 "W + m!1") (("2" (name-replace pp0 "at15levpri(q!1, k!1, 1 + j!1)") (("2" (name-replace pp1 "at15levpri(q!1, k!1, j!1)") (("2" (name-replace goal "atlev(q!1, 12, k!1 - 1)") (("2" (lemma leto_transitive_1) (("2" (inst - m1 jm _ _ _ E1) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15levpri_down formula-decl nil tournamentUnity0 nil) (posint nonempty-type-eq-decl nil integers nil) (leto_transitive_1 formula-decl nil bdUnity nil) (= const-decl "[T, T -> boolean]" equalities nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (subset_leto formula-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (member const-decl "bool" sets nil) (globinv const-decl "bool" tournamentSafe1 nil) (empty? const-decl "bool" sets nil) (cprio const-decl "finite_set[Thread]" tournamentUnity0 nil) (empty_card formula-decl nil finite_sets nil) (<= const-decl "bool" mucalculus nil) (nat_induction formula-decl nil naturalnumbers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (atlev const-decl "bool" tournamentUnity0 nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (W const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (leto const-decl "bool" bdUnity nil) (specification type-eq-decl nil bdUnity nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (ass_waiting const-decl "bool" tournamentUnity0 nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (int_minus_int_is_int application-judgement "int" integers nil)) nil) (at15levpri_induct-3 nil 3670564795 ("" (induct i) (("1" (assert) (("1" (skosimp) (("1" (use subset_leto) (("1" (assert) (("1" (hide - 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "at15levpri") (("1" (skosimp) (("1" (use empty_card[Thread]) (("1" (assert) (("1" (expand "empty?") (("1" (expand "member") (("1" (inst - q!1) (("1" (expand "cprio") (("1" (hide -4 +) (("1" (expand "E1") (("1" (use prio_irreflexive) (("1" (expand "globinv") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (inst?) (("2" (inst - m!1) (("2" (assert) (("2" (lemma at15levpri_down) (("2" (inst - j!1 k!1 m!1 q!1) (("2" (assert) (("2" (name-replace jm "W * j!1 + j!1 * m!1") (("2" (name-replace m1 "W + m!1") (("2" (name-replace pp0 "at15levpri(q!1, k!1, 1 + j!1)") (("2" (name-replace pp1 "at15levpri(q!1, k!1, j!1)") (("2" (name-replace goal "at12levmin(q!1, k!1)") (("2" (lemma leto_transitive_1) (("2" (inst - m1 jm _ _ _ E1) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15levpri_down formula-decl nil tournamentUnity0 nil) (posint nonempty-type-eq-decl nil integers nil) (leto_transitive_1 formula-decl nil bdUnity nil) (= const-decl "[T, T -> boolean]" equalities nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (subset_leto formula-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (member const-decl "bool" sets nil) (globinv const-decl "bool" tournamentSafe1 nil) (empty? const-decl "bool" sets nil) (cprio const-decl "finite_set[Thread]" tournamentUnity0 nil) (empty_card formula-decl nil finite_sets nil) (<= const-decl "bool" mucalculus nil) (nat_induction formula-decl nil naturalnumbers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (atlev const-decl "bool" tournamentUnity0 nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (W const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (leto const-decl "bool" bdUnity nil) (specification type-eq-decl nil bdUnity nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (ass_waiting const-decl "bool" tournamentUnity0 nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (int_minus_int_is_int application-judgement "int" integers nil)) nil) (at15levpri_induct-2 nil 3670564560 ("" (induct i) (("1" (assert) (("1" (skosimp) (("1" (use subset_leto) (("1" (assert) (("1" (hide - 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "at15levpri") (("1" (skosimp) (("1" (use empty_card[Thread]) (("1" (assert) (("1" (expand "empty?") (("1" (expand "member") (("1" (inst - q!1) (("1" (expand "cprio") (("1" (hide -4 +) (("1" (expand "E1") (("1" (use prio_irreflexive) (("1" (expand "globinv") (("1" (assert) nil))))))))))))))))))))))))))))))))))))))) ("2" (skosimp*) (("2" (inst?) (("2" (inst - m!1) (("2" (assert) (("2" (lemma at15levpri_down) (("2" (inst - j!1 k!1 m!1 q!1) (("2" (assert) (("2" (name-replace jm "j!1 * m!1 + j!1") (("2" (name-replace m1 "m!1 + W") (("2" (name-replace pp0 "at15levpri(q!1, k!1, 1 + j!1)") (("2" (name-replace pp1 "at15levpri(q!1, k!1, j!1)") (("2" (name-replace goal "at12levmin(q!1, k!1)") (("2" (lemma leto_transitive_1) (("2" (inst - m1 jm _ _ _ E1) (("2" (inst?) (("2" (assert) nil)))))))))))))))))))))))))))))))) nil) nil nil) (at15levpri_induct-1 nil 3670412904 ("" (induct i) (("1" (assert) (("1" (skosimp) (("1" (use subset_leto) (("1" (assert) (("1" (hide - 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "at15levpri") (("1" (skosimp) (("1" (use empty_card[Thread]) (("1" (assert) (("1" (expand "empty?") (("1" (expand "member") (("1" (inst - q!1) (("1" (expand "cprio") (("1" (hide -4 +) (("1" (expand "E1") (("1" (use prio_irreflexive) (("1" (expand "globinv") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (inst?) (("2" (inst - m!1) (("2" (assert) (("2" (lemma at15levpri_down) (("2" (inst - j!1 k!1 m!1 q!1) (("2" (assert) (("2" (name-replace jm "j!1 * m!1 + j!1") (("2" (name-replace m1 "1+m!1") (("2" (name-replace pp0 "at15levpri(q!1, k!1, 1 + j!1)") (("2" (name-replace pp1 "at15levpri(q!1, k!1, j!1)") (("2" (name-replace goal "at12levmin(q!1, k!1)") (("2" (lemma leto_transitive_1) (("2" (inst - m1 jm _ _ _ E1) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15levpri_down formula-decl nil tournamentUnity0 nil) (posint nonempty-type-eq-decl nil integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (leto_transitive_1 formula-decl nil bdUnity nil) (= const-decl "[T, T -> boolean]" equalities nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (subset_leto formula-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (member const-decl "bool" sets nil) (globinv const-decl "bool" tournamentSafe1 nil) (empty? const-decl "bool" sets nil) (cprio const-decl "finite_set[Thread]" tournamentUnity0 nil) (empty_card formula-decl nil finite_sets nil) (Thread type-eq-decl nil tournamentUnity0 nil) (<= const-decl "bool" mucalculus nil) (nat_induction formula-decl nil naturalnumbers nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (leto const-decl "bool" bdUnity nil) (specification type-eq-decl nil bdUnity nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil)) shostak)) (degW_TCC1 0 (degW_TCC1-1 nil 3671292455 ("" (skolem!) (("" (use pos_times_le) (("" (assert) nil nil)) nil)) nil) ((pos_times_le formula-decl nil real_props nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (W const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (at15levpri_degree 0 (at15levpri_degree-5 nil 3678788626 ("" (skosimp) (("" (lemma sub_leto) (("" (use at15levpri_induct (i "degree - 1" m m!1)) (("1" (assert) (("1" (use leadsto_at15levpri (m "degree-1")) (("1" (assert) (("1" (name-replace pp0 "at15levpri(q!1, k!1, degree)") (("1" (name-replace goal "atlev(q!1, 12, k!1 - 1)") (("1" (name-replace pp1 "at15levpri(q!1, k!1, degree - 1)") (("1" (case "-1 * W - m!1 + (W * degree + degree * m!1) = degW(m!1)") (("1" (replaceh -1) (("1" (name-replace pp2 "cap(pp0, mubot(path(q!1, k!1)))") (("1" (assert) (("1" (inst - "degW(m!1) + W" pp0 "cup(pp1, pp2)" goal E1) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "pp2") (("1" (expand "pp0") (("1" (expand "pp1") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "at15levpri") (("1" (skosimp) (("1" (assert) (("1" (expand "mubot") (("1" (expand "E1") (("1" (use card_cprio_mu) (("1" (assert) (("1" (expand "curnode") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (hide -1) (("1" (lemma leto_up) (("1" (inst - "degW(m!1)" "degW(m!1)+W" _ _ _) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (lemma leto_transitive_1) (("2" (inst - W "degW(m!1)" _ _ _ _) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "degW") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (sub_leto formula-decl nil bdUnity nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (atlev const-decl "bool" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (- const-decl "[numfield -> numfield]" number_fields nil) (W const-decl "posnat" tournamentUnity0 nil) (degW const-decl "nat" tournamentUnity0 nil) (path const-decl "node" ctrees nil) (mubot const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (cup_leto formula-decl nil bdUnity nil) (leto_transitive_1 formula-decl nil bdUnity nil) (leto_up formula-decl nil bdUnity nil) (pp2 skolem-const-decl "[state[degree, node] -> bool]" tournamentUnity0 nil) (pp1 skolem-const-decl "[state[degree, node] -> bool]" tournamentUnity0 nil) (card_cprio_mu formula-decl nil tournamentUnity0 nil) (curnode const-decl "node" tournamentSafe0 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (pp0 skolem-const-decl "[state[degree, node] -> bool]" tournamentUnity0 nil) (<= const-decl "bool" mucalculus nil) (= const-decl "[T, T -> boolean]" equalities nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (leadsto_at15levpri formula-decl nil tournamentUnity0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (int_minus_int_is_int application-judgement "int" integers nil) (at15levpri_induct formula-decl nil tournamentUnity0 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil) (at15levpri_degree-4 nil 3671341828 ("" (skosimp) (("" (lemma sub_leto) (("" (use at15levpri_induct (i "degree - 1" m m!1)) (("1" (assert) (("1" (use leadsto_at15levpri (m "degree-1")) (("1" (assert) (("1" (name-replace pp0 "at15levpri(q!1, k!1, degree)") (("1" (name-replace goal "atlev(q!1, 12, k!1 - 1)") (("1" (name-replace pp1 "at15levpri(q!1, k!1, degree - 1)") (("1" (case "-1 * W - m!1 + (W * degree + degree * m!1) = degW(m!1)") (("1" (replaceh -1) (("1" (name-replace pp2 "cap(pp0, mubot(take(k!1, q!1)))") (("1" (assert) (("1" (inst - "degW(m!1) + W" pp0 "cup(pp1, pp2)" goal E1) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "pp2") (("1" (expand "pp0") (("1" (expand "pp1") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "at15levpri") (("1" (skosimp) (("1" (assert) (("1" (expand "mubot") (("1" (expand "E1") (("1" (use card_cprio_mu) (("1" (assert) (("1" (expand "curnode") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (hide -1) (("1" (lemma leto_up) (("1" (inst - "degW(m!1)" "degW(m!1)+W" _ _ _) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (lemma leto_transitive_1) (("2" (inst - W "degW(m!1)" _ _ _ _) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "degW") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (sub_leto formula-decl nil bdUnity nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (atlev const-decl "bool" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (- const-decl "[numfield -> numfield]" number_fields nil) (W const-decl "posnat" tournamentUnity0 nil) (degW const-decl "nat" tournamentUnity0 nil) (mubot const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (cup_leto formula-decl nil bdUnity nil) (leto_transitive_1 formula-decl nil bdUnity nil) (leto_up formula-decl nil bdUnity nil) (card_cprio_mu formula-decl nil tournamentUnity0 nil) (curnode const-decl "node" tournamentSafe0 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (<= const-decl "bool" mucalculus nil) (= const-decl "[T, T -> boolean]" equalities nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (leadsto_at15levpri formula-decl nil tournamentUnity0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (int_minus_int_is_int application-judgement "int" integers nil) (at15levpri_induct formula-decl nil tournamentUnity0 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil) (at15levpri_degree-3 nil 3671341558 ("" (skosimp) (("" (lemma sub_leto) (("" (use at15levpri_induct (i "degree - 1" m m!1)) (("1" (assert) (("1" (use leadsto_at15levpri (m "degree-1")) (("1" (assert) (("1" (name-replace pp0 "at15levpri(q!1, k!1, degree)") (("1" (name-replace goal "atlev(q!1, 12, k!1 - 1)") (("1" (name-replace pp1 "at15levpri(q!1, k!1, degree - 1)") (("1" (case "-1 * W - m!1 + (W * degree + degree * m!1) = degW(m!1)") (("1" (replaceh -1) (("1" (name-replace pp2 "cap(pp0, mubot(take(k!1, q!1)))") (("1" (case "nn1 >= 0") (("1" (inst - nn1 pp0 "cup(pp1, pp2)" goal E1) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "pp2") (("1" (expand "pp1") (("1" (expand "pp0") (("1" (expand "cup") (("1" (expand "cap") (("1" (expand "at15levpri") (("1" (skosimp) (("1" (assert) (("1" (expand "mubot") (("1" (use card_cprio_mu) (("1" (assert) (("1" (expand "E1") (("1" (assert) (("1" (expand "curnode") (("1" (assert) nil))))))))))))))))))))))))))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (hide -1) (("1" (lemma leto_up) (("1" (postpone) (("1" (inst?) (("1" (assert) (("1" (expand "nn1") (("1" (assert) nil))))))) ("2" (hide - 2) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" "W + m!1") (("2" (assert) nil))))))))))))) ("2" (expand "pp2") (("2" (name-replace pp3 "cap(pp0, mubot(take(k!1, q!1)))") (("2" (lemma leto_transitive_1) (("2" (inst - W _ pp3 pp1 goal E1) (("2" (inst - "-1 * W - m!1 + (W * degree + degree * m!1)") (("1" (assert) (("1" (expand "nn1") (("1" (assert) nil))))) ("2" (hide - 2) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" "W + m!1") (("2" (assert) nil))))))))))))))))))))))))))))))))) ("2" (hide - 2) (("2" (expand "nn1") (("2" (lemma pos_times_le) (("2" (inst - "degree-1" m!1) (("2" (assert) nil))))))))))))))))))))))))))))) ("2" (assert) nil)))))) nil) nil nil) (at15levpri_degree-2 nil 3671290527 ("" (skosimp) (("" (lemma sub_leto) (("" (use at15levpri_induct (i "degree - 1" m m!1)) (("1" (assert) (("1" (use leadsto_at15levpri (m "degree-1")) (("1" (assert) (("1" (name-replace pp0 "at15levpri(q!1, k!1, degree)") (("1" (name-replace goal "atlev(q!1, 12, k!1 - 1)") (("1" (name-replace pp1 "at15levpri(q!1, k!1, degree - 1)") (("1" (name-replace nn1 "degree * W - m!1 + degree * m!1") (("1" (name-replace pp2 "cap(pp0, mubot(take(k!1, q!1)))") (("1" (case "nn1 >= 0") (("1" (inst - nn1 pp0 "cup(pp1, pp2)" goal E1) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "pp2") (("1" (expand "pp1") (("1" (expand "pp0") (("1" (expand "cup") (("1" (expand "cap") (("1" (expand "at15levpri") (("1" (skosimp) (("1" (assert) (("1" (expand "mubot") (("1" (use card_cprio_mu) (("1" (assert) (("1" (expand "E1") (("1" (assert) (("1" (expand "curnode") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (hide -1) (("1" (lemma leto_up) (("1" (inst - "-1 * W - m!1 + (W * degree + degree * m!1)" nn1 _ _ E1) (("1" (inst?) (("1" (assert) (("1" (expand "nn1") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" "W + m!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "pp2") (("2" (name-replace pp3 "cap(pp0, mubot(take(k!1, q!1)))") (("2" (lemma leto_transitive_1) (("2" (inst - W _ pp3 pp1 goal E1) (("2" (inst - "-1 * W - m!1 + (W * degree + degree * m!1)") (("1" (assert) (("1" (expand "nn1") (("1" (assert) nil nil)) nil)) nil) ("2" (hide - 2) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" "W + m!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (expand "nn1") (("2" (lemma pos_times_le) (("2" (inst - "degree-1" m!1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (sub_leto formula-decl nil bdUnity nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (atlev const-decl "bool" tournamentUnity0 nil) (W const-decl "posnat" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (<= const-decl "bool" mucalculus nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (card_cprio_mu formula-decl nil tournamentUnity0 nil) (curnode const-decl "node" tournamentSafe0 nil) (leto_up formula-decl nil bdUnity nil) (pos_times_le formula-decl nil real_props nil) (- const-decl "[numfield -> numfield]" number_fields nil) (leto_transitive_1 formula-decl nil bdUnity nil) (cup_leto formula-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (cap const-decl "bool" ownpred nil) (mubot const-decl "bool" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (leadsto_at15levpri formula-decl nil tournamentUnity0 nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (int_minus_int_is_int application-judgement "int" integers nil) (at15levpri_induct formula-decl nil tournamentUnity0 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil) (at15levpri_degree-1 nil 3671286988 ("" (skosimp) (("" (lemma sub_leto) (("" (use at15levpri_induct (i "degree - 1" m m!1)) (("1" (assert) (("1" (use leadsto_at15levpri (m "degree-1")) (("1" (assert) (("1" (name-replace pp0 "at15levpri(q!1, k!1, degree)") (("1" (name-replace goal "atlev(q!1, 12, k!1 - 1)") (("1" (name-replace pp1 "at15levpri(q!1, k!1, degree - 1)") (("1" (name-replace nn1 "degree * W - m!1 + degree * m!1") (("1" (name-replace pp2 "cap(pp0, mubot(take(k!1, q!1)))") (("1" (inst - nn1 pp0 "cup(pp1, pp2)" goal E1) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "pp2") (("1" (expand "pp1") (("1" (expand "pp0") (("1" (expand "cup") (("1" (expand "cap") (("1" (expand "at15levpri") (("1" (skosimp) (("1" (assert) (("1" (expand "mubot") (("1" (use card_cprio_mu) (("1" (assert) (("1" (expand "E1") (("1" (assert) (("1" (expand "curnode") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -1) (("1" (lemma leto_up) (("1" (inst - "-1 * W - m!1 + (W * degree + degree * m!1)" nn1 _ _ E1) (("1" (inst?) (("1" (assert) (("1" (expand "nn1") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (expand "nn1") (("2" (hide - 2) (("2" (lemma pos_times_le) (("2" (inst - "degree -1" m!1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil) ("3" (hide - 2) (("3" (lemma pos_times_le) (("3" (inst - "degree -1" "W+m!1") (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "pp2") (("2" (name-replace pp3 "cap(pp0, mubot(take(k!1, q!1)))") (("2" (lemma leto_transitive_1) (("2" (inst - W _ pp3 pp1 goal E1) (("2" (inst - "-1 * W - m!1 + (W * degree + degree * m!1)") (("1" (assert) (("1" (expand "nn1") (("1" (assert) nil nil)) nil)) nil) ("2" (hide - 2) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" "W + m!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (expand "nn1") (("2" (lemma pos_times_le) (("2" (inst - "degree-1" m!1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (postpone) nil nil)) nil)) nil)) nil) nil shostak)) (atlev15_to12 0 (atlev15_to12-4 nil 3671291000 ("" (skosimp) (("" (use at15levpri_degree) (("" (assert) (("" (lemma sub_leto) (("" (inst - _ "atlev(q!1, 15, k!1)" "at15levpri(q!1, k!1, degree)" _ _) (("" (inst?) (("" (assert) (("" (hide - 2) (("" (expand "<=") (("" (expand "cap") (("" (expand "at15levpri") (("" (expand "atlev") (("" (skosimp) (("" (assert) (("" (use card_cprio) (("" (assert) (("" (expand "E1") (("" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15levpri_degree formula-decl nil tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (digit type-eq-decl nil ctrees nil) (sub_leto formula-decl nil bdUnity nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (degW const-decl "nat" tournamentUnity0 nil) (W const-decl "posnat" tournamentUnity0 nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (card_cprio formula-decl nil tournamentUnity0 nil) (<= const-decl "bool" mucalculus nil) (pred type-eq-decl nil defined_types nil) (atlev const-decl "bool" tournamentUnity0 nil) (at15levpri const-decl "bool" tournamentUnity0 nil)) nil) (atlev15_to12-3 nil 3670734079 ("" (skosimp) (("" (use at15levpri_induct) (("" (assert) (("" (lemma sub_leto) (("" (inst - _ "atlev(q!1, 15, k!1)" "at15levpri(q!1, k!1, degree)" _ _) (("" (inst?) (("" (assert) (("" (hide - 2) (("" (expand "<=") (("" (expand "cap") (("" (expand "at15levpri") (("" (expand "atlev") (("" (skosimp) (("" (assert) (("" (use card_cprio) (("" (expand "E1") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15levpri_induct formula-decl nil tournamentUnity0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (sub_leto formula-decl nil bdUnity nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (W const-decl "posnat" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (cap const-decl "bool" ownpred nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (card_cprio formula-decl nil tournamentUnity0 nil) (<= const-decl "bool" mucalculus nil) (pred type-eq-decl nil defined_types nil) (atlev const-decl "bool" tournamentUnity0 nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil)) nil) (atlev15_to12-2 nil 3670414608 ("" (skosimp) (("" (use at15levpri_induct) (("" (assert) (("" (lemma sub_leto) (("" (inst - _ "at15lev(q!1, k!1)" "at15levpri(q!1, k!1, degree)" _ _) (("" (inst?) (("" (assert) (("" (hide - 2) (("" (expand "<=") (("" (expand "cap") (("" (expand "at15levpri") (("" (expand "at15lev") (("" (skosimp) (("" (assert) (("" (use card_cprio) (("" (expand "E1") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at15levpri_induct formula-decl nil tournamentUnity0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (sub_leto formula-decl nil bdUnity nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (atlev const-decl "bool" tournamentUnity0 nil) (W const-decl "posnat" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (cap const-decl "bool" ownpred nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (card_cprio formula-decl nil tournamentUnity0 nil) (<= const-decl "bool" mucalculus nil) (pred type-eq-decl nil defined_types nil) (at15levpri const-decl "bool" tournamentUnity0 nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil)) nil) (atlev15_to12-1 nil 3670414392 ("" (skosimp) (("" (use at15levpri_induct) (("" (assert) (("" (lemma sub_leto) (("" (inst - _ "at15lev(q!1, k!1)" "at15levpri(q!1, k!1, degree)" _ _) (("" (inst?) (("" (assert) (("" (hide - 2) (("" (expand "<=") (("" (expand "cap") (("" (expand "at15levpri") (("" (expand "at15lev") (("" (skosimp) (("" (assert) (("" (use card_prio) (("" (expand "E1") (("" (assert) (("" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) nil shostak)) (ass_doorway_extended 0 (ass_doorway_extended-5 nil 3670734501 ("" (skosimp) (("" (case "leto(E1)(D, leveq_betw(q!1, 13, 14, k!1), atlev(q!1, 15, k!1))") (("1" (hide -2) (("1" (case "leveq_betw(q!1, 12, 15, k!1) = cup(leveq_betw(q!1, 13, 14, k!1), cup(atlev(q!1, 15, k!1), atlev(q!1, 12, k!1)))") (("1" (replaceh -1) (("1" (use cup_leto) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (use leto_up (i D j "1+D")) (("1" (assert) nil nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (hide -1) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (lemma leto_transitive) (("2" (inst - 1 D _ _ _ E1) (("2" (inst?) (("2" (assert) (("2" (inst?) (("2" (assert) (("2" (hide -1 2) (("2" (s-ensures) (("2" (split) (("1" (skosimp*) (("1" (expand "E1") (("1" (expand "step") (("1" (assert) (("1" (skolem!) (("1" (case "q!1=p!1") (("1" (replaceh -1) (("1" (expand "atlev") (("1" (flatten) (("1" (expand "step") (("1" (expand "step11") (("1" (expand "step14") (("1" (assert) (("1" (expand "step15F") (("1" (expand "step15G") (("1" (expand "step16") (("1" (expand "step17") (("1" (expand "step13") (("1" (expand "step18") (("1" (expand "step19") (("1" (expand "step12") (("1" (replaceh -4) (("1" (expand "leveq_betw") (("1" (expand "goto") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2 4 -2) (("2" (expand "atlev") (("2" (flatten) (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (typepred enum_thread) (("2" (expand "bijective?") (("2" (flatten) (("2" (expand "surjective?") (("2" (inst?) (("2" (skolem!) (("2" (inst + x!1) (("2" (split) (("1" (skosimp) (("1" (use enabled_E1) (("1" (assert) (("1" (hide 3) (("1" (expand "enabled1") (("1" (expand "atlev") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp) (("2" (expand "E1") (("2" (expand "atlev") (("2" (flatten) (("2" (replaceh -8) (("2" (expand "forward1") (("2" (expand "step17") (("2" (assert) (("2" (expand "step19") (("2" (expand "step12") (("2" (replaceh -3) (("2" (expand "goto") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2 -1) (("2" (apply-extensionality :hide? t) (("2" (expand "cup") (("2" (expand "leveq_betw") (("2" (expand "atlev") (("2" (iff) (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (expand "ass_doorway") (("2" (inst?) (("2" (lemma PSP_leto) (("2" (inst - D "between(q!1, 13, 14)" "leveq_betw(q!1, 13, 14, k!1)" "atlev(q!1, 15, k!1)" "neg(between(q!1, 13, 14))" E1) (("2" (assert) (("2" (split) (("1" (case "cap(between(q!1, 13, 14), leveq_betw(q!1, 13, 14, k!1)) = leveq_betw(q!1, 13, 14, k!1)") (("1" (replaceh -1) (("1" (case "cup(cap(neg(between(q!1, 13, 14)), leveq_betw(q!1, 13, 14, k!1)), atlev(q!1, 15, k!1)) = atlev(q!1, 15, k!1)") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (expand "cap") (("2" (prop) (("2" (expand "neg") (("2" (expand "leveq_betw") (("2" (flatten) (("2" (expand "between") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (prop) (("2" (expand "leveq_betw") (("2" (expand "between") (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (lemma sub_leto) (("2" (inst - D "between(q!1, 13, 14)" fullset "neg(between(q!1, 13, 14))" E1) (("2" (assert) (("2" (hide - 2) (("2" (expand "<=") (("2" (expand "fullset") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("3" (hide - 2) (("3" (expand "unless") (("3" (expand "<=") (("3" (expand "wp") (("3" (expand "cup") (("3" (expand "leveq_betw") (("3" (expand "cap") (("3" (expand "neg") (("3" (expand "atlev") (("3" (expand "E1") (("3" (skosimp*) (("3" (expand "step") (("3" (split -) (("1" (assert) nil nil) ("2" (skolem!) (("2" (assert) (("2" (case "q!1=p!1") (("1" (replaceh -1) (("1" (expand "step") (("1" (expand "step11") (("1" (assert) (("1" (expand "step12") (("1" (expand "step15F") (("1" (expand "step15G") (("1" (expand "step16") (("1" (expand "step17") (("1" (expand "step18") (("1" (expand "step19") (("1" (split -) (("1" (expand "step13") (("1" (flatten) (("1" (replaceh -1) (("1" (expand "next13") (("1" (propax) nil nil)) nil)) nil)) nil)) nil) ("2" (expand "step14") (("2" (flatten) (("2" (replaceh -1) (("2" (expand "next14") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide-all-but (-1 -2 -3 -4 1 3)) (("2" (split) (("1" (grind) nil nil) ("2" (grind) nil nil) ("3" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((atlev const-decl "bool" tournamentUnity0 nil) (leveq_betw const-decl "bool" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (D const-decl "posnat" tournamentUnity0 nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (leto const-decl "bool" bdUnity nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (= const-decl "[T, T -> boolean]" equalities nil) (cup const-decl "bool" ownpred nil) (cup_leto formula-decl nil bdUnity nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (leto_transitive formula-decl nil bdUnity nil) (step const-decl "bool" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (step15F const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (goto const-decl "state" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (step11 const-decl "bool" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (next18 const-decl "state" tournamentSafe0 nil) (empty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (next15 const-decl "state" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (next11 const-decl "state" tournamentSafe0 nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (finite_remove application-judgement "finite_set" finite_sets nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_plus_int_is_int application-judgement "int" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (step const-decl "bool" tournamentUnity0 nil) (surjective? const-decl "bool" functions nil) (enabled_E1 formula-decl nil tournamentUnity0 nil) (enabled1 const-decl "bool" tournamentUnity0 nil) (forward1 const-decl "bool" tournamentUnity0 nil) (enum_thread const-decl "(bijective?[below[N], (thread)])" tournamentSafe0 nil) (bijective? const-decl "bool" functions nil) (below type-eq-decl nil nat_types nil) (N const-decl "posnat" tournamentSafe0 nil) (NOT const-decl "[bool -> bool]" booleans nil) (neg const-decl "bool" ownpred nil) (wp const-decl "bool" ownpred nil) (transient const-decl "bool" bdUnity nil) (co const-decl "bool" bdUnity nil) (ensures const-decl "bool" bdUnity nil) (ensures_leto formula-decl nil bdUnity nil) (<= const-decl "bool" mucalculus nil) (cap const-decl "bool" ownpred nil) (subset_leto formula-decl nil bdUnity nil) (leto_up formula-decl nil bdUnity nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (ass_doorway const-decl "bool" tournamentUnity0 nil) (PSP_leto formula-decl nil bdUnity nil) (unless const-decl "bool" bdUnity nil) (fullset const-decl "set" sets nil) (sub_leto formula-decl nil bdUnity nil) (between const-decl "bool" tournamentUnity0 nil)) nil) (ass_doorway_extended-4 nil 3670734223 ("" (skosimp) (("" (lemma PSP_leto) (("" (case "leto(E1)(1 + D, cup(at12body(q!1), between(q!1, 13, 15)), at(q!1, 15))") (("1" (inst?) (("1" (name-replace pp0 "leveq_betw(q!1, 12, 15, k!1)") (("1" (name-replace pp1 "atlev(q!1, 15, k!1)") (("1" (inst - pp0 pp1) (("1" (assert) (("1" (split) (("1" (hide -2 -3) (("1" (case "cap(cup(at12body(q!1), between(q!1, 13, 15)), pp0)=pp0") (("1" (replaceh -1) (("1" (case " cup(cap(at(q!1, 15), pp0), pp1) = pp1") (("1" (replaceh -1) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (prop) (("2" (expand "pp1") (("2" (expand "pp0") (("2" (expand "cap") (("2" (expand "leveq_betw") (("2" (flatten) (("2" (expand "atlev") (("2" (expand "at") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (prop) (("1" (expand "pp0") (("1" (expand "leveq_betw") (("1" (expand "cap") (("1" (expand "between") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "pp0") (("2" (expand "cap") (("2" (assert) (("2" (expand "leveq_betw") (("2" (expand "between") (("2" (flatten) (("2" (assert) (("2" (expand "cup") (("2" (expand "at12body") (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (expand "pp0") (("2" (expand "pp1") (("2" (expand "unless") (("2" (expand "<=") (("2" (expand "wp") (("2" (expand "cup") (("2" (expand "cap") (("2" (expand "neg") (("2" (expand "leveq_betw") (("2" (skosimp*) (("2" (expand "atlev") (("2" (expand "E1") (("2" (expand "step") (("2" (split -) (("1" (assert) nil nil) ("2" (skolem!) (("2" (assert) (("2" (case "q!1=p!1") (("1" (replaceh -1) (("1" (hide 3 -5) (("1" (grind) nil nil)) nil)) nil) ("2" (case "y!1`pc(q!1) = s!1`pc(q!1) AND y!1`level(q!1) = s!1`level(q!1)") (("1" (flatten) (("1" (replaceh -1) (("1" (replaceh -1) (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (hide-all-but (-1 1 2)) (("2" (split) (("1" (grind) nil nil) ("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1 2) (("2" (expand "ass_doorway") (("2" (inst?) (("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (lemma leto_transitive) (("1" (inst - 1 D _ _ _ E1) (("1" (inst?) (("1" (assert) (("1" (inst?) (("1" (assert) (("1" (hide - 2) (("1" (s-ensures) (("1" (expand "at12body") (("1" (expand "between") (("1" (split) (("1" (skosimp*) (("1" (expand "E1") (("1" (expand "step") (("1" (assert) (("1" (split -) (("1" (assert) nil nil) ("2" (skolem!) (("2" (case "q!1=p!1") (("1" (replaceh -1) (("1" (hide -4 1) (("1" (grind) nil nil)) nil)) nil) ("2" (hide 2 4 -4) (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (typepred enum_thread) (("2" (expand "bijective?") (("2" (flatten) (("2" (hide -1) (("2" (expand "surjective?") (("2" (inst - q!1) (("2" (skolem!) (("2" (name-replace kq x!1) (("2" (inst + kq) (("2" (split) (("1" (skosimp) (("1" (use enabled_E1) (("1" (assert) (("1" (replaceh -4) (("1" (hide 2) (("1" (expand "enabled1") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp) (("2" (expand "E1") (("2" (assert) (("2" (replaceh -5) (("2" (hide -3) (("2" (expand "forward1") (("2" (expand "step16") (("2" (expand "step17") (("2" (expand "step18") (("2" (expand "step19") (("2" (expand "step12") (("2" (replaceh -3) (("2" (expand "goto") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (case "between(q!1, 13, 15) = cup(at(q!1, 15), between(q!1, 13, 14))") (("1" (replaceh -1) (("1" (use cup_leto) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (lemma leto_up) (("2" (inst - D "1+D" _ _ _) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "between") (("2" (expand "cup") (("2" (expand "at") (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((at const-decl "bool" tournamentUnity0 nil) (between const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (D const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (leto const-decl "bool" bdUnity nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (leveq_betw const-decl "bool" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (cap const-decl "bool" ownpred nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (unless const-decl "bool" bdUnity nil) (wp const-decl "bool" ownpred nil) (step const-decl "bool" tournamentUnity0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (finite_remove application-judgement "finite_set" finite_sets nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (rat_max application-judgement "{s: rat | s >= q AND s >= r}" real_defs nil) (int_max application-judgement "{k: int | i <= k AND j <= k}" real_defs nil) (nat_min application-judgement "{k: nat | k <= i AND k <= j}" real_defs nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (next11 const-decl "state" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (step11 const-decl "bool" tournamentSafe0 nil) (goto const-decl "state" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil) (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil) (next13 const-decl "state" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (next15 const-decl "state" tournamentSafe0 nil) (member const-decl "bool" sets nil) (empty? const-decl "bool" sets nil) (step15F const-decl "bool" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (next18 const-decl "state" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (step const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (neg const-decl "bool" ownpred nil) (<= const-decl "bool" mucalculus nil) (atlev const-decl "bool" tournamentUnity0 nil) (ass_doorway const-decl "bool" tournamentUnity0 nil) (cup_leto formula-decl nil bdUnity nil) (leto_up formula-decl nil bdUnity nil) (subset_leto formula-decl nil bdUnity nil) (leto_transitive formula-decl nil bdUnity nil) (enabled_E1 formula-decl nil tournamentUnity0 nil) (enabled1 const-decl "bool" tournamentUnity0 nil) (forward1 const-decl "bool" tournamentUnity0 nil) (surjective? const-decl "bool" functions nil) (enum_thread const-decl "(bijective?[below[N], (thread)])" tournamentSafe0 nil) (bijective? const-decl "bool" functions nil) (N const-decl "posnat" tournamentSafe0 nil) (NOT const-decl "[bool -> bool]" booleans nil) (cobar const-decl "bool" bdUnity nil) (co const-decl "bool" bdUnity nil) (ensures const-decl "bool" bdUnity nil) (ensures_leto formula-decl nil bdUnity nil) (PSP_leto formula-decl nil bdUnity nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil nat_types nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil)) nil) (ass_doorway_extended-3 nil 3670585200 ("" (skosimp) (("" (lemma PSP_leto) (("" (case "leto(E1)(1 + D, cup(at12body(q!1), between(q!1, 13, 15)), at(q!1, 15))") (("1" (inst?) (("1" (name-replace pp0 "leveq_betw(q!1, 12, 15, k!1)") (("1" (name-replace pp1 "at15lev(q!1, k!1)") (("1" (inst - pp0 pp1) (("1" (assert) (("1" (split) (("1" (hide -2 -3) (("1" (case "cap(cup(at12body(q!1), between(q!1, 13, 15)), pp0)=pp0") (("1" (replaceh -1) (("1" (case " cup(cap(at(q!1, 15), pp0), pp1) = pp1") (("1" (replaceh -1) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (prop) (("2" (expand "pp1") (("2" (expand "pp0") (("2" (expand "cap") (("2" (expand "leveq_betw") (("2" (flatten) (("2" (expand "at15lev") (("2" (expand "at") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (prop) (("1" (expand "pp0") (("1" (expand "leveq_betw") (("1" (expand "cap") (("1" (expand "between") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "pp0") (("2" (expand "cap") (("2" (assert) (("2" (expand "leveq_betw") (("2" (expand "between") (("2" (flatten) (("2" (assert) (("2" (expand "cup") (("2" (expand "at12body") (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (expand "pp0") (("2" (expand "pp1") (("2" (expand "unless") (("2" (expand "<=") (("2" (expand "wp") (("2" (expand "cup") (("2" (expand "cap") (("2" (expand "neg") (("2" (expand "leveq_betw") (("2" (skosimp*) (("2" (expand "at15lev") (("2" (expand "E1") (("2" (expand "step") (("2" (split -) (("1" (assert) nil nil) ("2" (skolem!) (("2" (assert) (("2" (case "q!1=p!1") (("1" (replaceh -1) (("1" (hide 3 -5) (("1" (grind) nil nil)) nil)) nil) ("2" (case "y!1`pc(q!1) = s!1`pc(q!1) AND y!1`level(q!1) = s!1`level(q!1)") (("1" (flatten) (("1" (replaceh -1) (("1" (replaceh -1) (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (hide-all-but (-1 1 2)) (("2" (split) (("1" (grind) nil nil) ("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1 2) (("2" (expand "ass_doorway") (("2" (inst?) (("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (lemma leto_transitive) (("1" (inst - 1 D _ _ _ E1) (("1" (inst?) (("1" (assert) (("1" (inst?) (("1" (assert) (("1" (hide - 2) (("1" (s-ensures) (("1" (expand "at12body") (("1" (expand "between") (("1" (split) (("1" (skosimp*) (("1" (expand "E1") (("1" (expand "step") (("1" (assert) (("1" (split -) (("1" (assert) nil nil) ("2" (skolem!) (("2" (case "q!1=p!1") (("1" (replaceh -1) (("1" (hide -4 1) (("1" (grind) nil nil)) nil)) nil) ("2" (hide 2 4 -4) (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (typepred enum_thread) (("2" (expand "bijective?") (("2" (flatten) (("2" (hide -1) (("2" (expand "surjective?") (("2" (inst - q!1) (("2" (skolem!) (("2" (name-replace kq x!1) (("2" (inst + kq) (("2" (split) (("1" (skosimp) (("1" (use enabled_E1) (("1" (assert) (("1" (replaceh -4) (("1" (hide 2) (("1" (expand "enabled1") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp) (("2" (expand "E1") (("2" (assert) (("2" (replaceh -5) (("2" (hide -3) (("2" (expand "forward1") (("2" (expand "step16") (("2" (expand "step17") (("2" (expand "step18") (("2" (expand "step19") (("2" (expand "step12") (("2" (replaceh -3) (("2" (expand "goto") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (case "between(q!1, 13, 15) = cup(at(q!1, 15), between(q!1, 13, 14))") (("1" (replaceh -1) (("1" (use cup_leto) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (lemma leto_up) (("2" (inst - D "1+D" _ _ _) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "between") (("2" (expand "cup") (("2" (expand "at") (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (PSP_leto formula-decl nil bdUnity nil) (ensures_leto formula-decl nil bdUnity nil) (ensures const-decl "bool" bdUnity nil) (co const-decl "bool" bdUnity nil) (cobar const-decl "bool" bdUnity nil) (NOT const-decl "[bool -> bool]" booleans nil) (N const-decl "posnat" tournamentSafe0 nil) (bijective? const-decl "bool" functions nil) (enum_thread const-decl "(bijective?[below[N], (thread)])" tournamentSafe0 nil) (surjective? const-decl "bool" functions nil) (forward1 const-decl "bool" tournamentUnity0 nil) (enabled1 const-decl "bool" tournamentUnity0 nil) (enabled_E1 formula-decl nil tournamentUnity0 nil) (leto_transitive formula-decl nil bdUnity nil) (subset_leto formula-decl nil bdUnity nil) (leto_up formula-decl nil bdUnity nil) (cup_leto formula-decl nil bdUnity nil) (ass_doorway const-decl "bool" tournamentUnity0 nil) (<= const-decl "bool" mucalculus nil) (neg const-decl "bool" ownpred nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (step const-decl "bool" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (next18 const-decl "state" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (step15F const-decl "bool" tournamentSafe0 nil) (empty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (next15 const-decl "state" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil) (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil) (step12 const-decl "bool" tournamentSafe0 nil) (goto const-decl "state" tournamentSafe0 nil) (step11 const-decl "bool" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (next11 const-decl "state" tournamentSafe0 nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nat_min application-judgement "{k: nat | k <= i AND k <= j}" real_defs nil) (int_max application-judgement "{k: int | i <= k AND j <= k}" real_defs nil) (rat_max application-judgement "{s: rat | s >= q AND s >= r}" real_defs nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (finite_remove application-judgement "finite_set" finite_sets nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_plus_int_is_int application-judgement "int" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (step const-decl "bool" tournamentUnity0 nil) (wp const-decl "bool" ownpred nil) (unless const-decl "bool" bdUnity nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (cap const-decl "bool" ownpred nil) (= const-decl "[T, T -> boolean]" equalities nil) (leveq_betw const-decl "bool" tournamentUnity0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (pred type-eq-decl nil defined_types nil) (specification type-eq-decl nil bdUnity nil) (leto const-decl "bool" bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (D const-decl "posnat" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (between const-decl "bool" tournamentUnity0 nil) (at const-decl "bool" tournamentUnity0 nil)) nil) (ass_doorway_extended-2 nil 3670565809 ("" (skosimp) (("" (lemma PSP_leto) (("" (case "leto(E1)(1 + D, between(q!1, 12, 15), at(q!1, 15))") (("1" (inst?) (("1" (name-replace pp0 "leveq_betw(q!1, 12, 15, k!1)") (("1" (name-replace pp1 "at15lev(q!1, k!1)") (("1" (inst - pp0 pp1) (("1" (assert) (("1" (split) (("1" (hide -2 -3) (("1" (case "cap(between(q!1, 12, 15), pp0)=pp0") (("1" (replaceh -1) (("1" (case " cup(cap(at(q!1, 15), pp0), pp1) = pp1") (("1" (replaceh -1) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (prop) (("2" (expand "pp1") (("2" (expand "pp0") (("2" (expand "cap") (("2" (expand "leveq_betw") (("2" (flatten) (("2" (expand "at15lev") (("2" (expand "at") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (prop) (("1" (expand "pp0") (("1" (expand "leveq_betw") (("1" (expand "cap") (("1" (expand "between") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "pp0") (("2" (expand "cap") (("2" (assert) (("2" (expand "leveq_betw") (("2" (expand "between") (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (expand "pp0") (("2" (expand "pp1") (("2" (expand "unless") (("2" (expand "<=") (("2" (expand "wp") (("2" (expand "cup") (("2" (expand "cap") (("2" (expand "neg") (("2" (expand "leveq_betw") (("2" (skosimp*) (("2" (expand "at15lev") (("2" (expand "E1") (("2" (expand "step") (("2" (split -) (("1" (assert) nil nil) ("2" (skolem!) 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(("2" (case "between(q!1, 12, 15) = cup(at(q!1, 15), between(q!1, 12, 14))") (("1" (replaceh -1) (("1" (use cup_leto) (("1" (assert) (("1" (split) (("1" (hide - 2) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (case "between(q!1, 12, 14) = cup(at(q!1, 12), between(q!1, 13, 14))") (("1" (replaceh -1) (("1" (use cup_leto) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (postpone) nil nil) ("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (expand "between") (("2" (expand "at") (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (expand "between") (("2" (expand "at") (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) nil nil) (ass_doorway_extended-1 nil 3670415248 ("" (skosimp) (("" (lemma PSP_leto) (("" (case "leto(E1)(D, between(q!1, 12, 15), at(q!1, 15))") (("1" (inst?) (("1" (name-replace pp0 "leveq_betw(q!1, 12, 15, k!1)") (("1" (name-replace pp1 "at15lev(q!1, k!1)") (("1" (inst - pp0 pp1) (("1" (assert) (("1" (split) (("1" (hide -2 -3) (("1" (case "cap(between(q!1, 12, 15), pp0)=pp0") (("1" (replaceh -1) (("1" (case " cup(cap(at(q!1, 15), pp0), pp1) = pp1") (("1" (replaceh -1) (("1" (postpone) nil nil)) nil) ("2" (postpone) nil nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (prop) (("1" (expand "pp0") (("1" (expand "leveq_betw") (("1" (expand "cap") (("1" (expand "between") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "pp0") (("2" (expand "cap") (("2" (assert) (("2" (expand "leveq_betw") (("2" (expand "between") (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (expand "pp0") (("2" (expand "pp1") (("2" (expand "unless") (("2" (expand "<=") (("2" (expand "wp") (("2" (expand "cup") (("2" (expand "cap") (("2" (expand "neg") (("2" (expand "leveq_betw") (("2" (skosimp*) (("2" (expand "at15lev") (("2" (expand "E1") (("2" (expand "step") (("2" (split -) (("1" (assert) nil nil) ("2" (skolem!) 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(("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (depth const-decl "nat" ctrees nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (< const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (posint nonempty-type-eq-decl nil integers nil) (D const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (int_plus_int_is_int application-judgement "int" integers nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (leveq_betw const-decl "bool" tournamentUnity0 nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (pos_times_le formula-decl nil real_props nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (sub_leto formula-decl nil bdUnity nil) (<= const-decl "bool" mucalculus nil) (cap const-decl "bool" ownpred nil) (pp2 skolem-const-decl "[state[degree, node] -> bool]" tournamentUnity0 nil) (levleq const-decl "bool" tournamentUnity0 nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (mid skolem-const-decl "posint" tournamentUnity0 nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (atlev const-decl "bool" tournamentUnity0 nil) (degW const-decl "nat" tournamentUnity0 nil) (W const-decl "posnat" tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (digit type-eq-decl nil ctrees nil) (leto_transitive formula-decl nil bdUnity nil) (atlev15_to12 formula-decl nil tournamentUnity0 nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (ass_doorway_extended formula-decl nil tournamentUnity0 nil) (subset_leto formula-decl nil bdUnity nil) (iqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (iq0 const-decl "bool" tournamentSafe0 nil)) nil) (level_step-7 nil 3671447383 ("" (skosimp) (("" (case "k!1 < q!1`length") (("1" (use ass_doorway_extended) (("1" (assert) (("1" (use atlev15_to12 (m m!1)) (("1" (assert) (("1" (lemma leto_transitive) (("1" (name-replace D1 "1 +D") (("1" (name-replace mid "degW(m!1) + W") (("1" (name-replace pp0 "leveq_betw(q!1, 12, 15, k!1)") (("1" (name-replace pp1 "atlev(q!1, 15, k!1)") (("1" (name-replace pp2 "atlev(q!1, 12, k!1 - 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(("2" (assert) (("2" (hide - 2) (("2" (expand "<=") (("2" (expand "pp2") (("2" (expand "cap") (("2" (expand "at12levmin") (("2" (expand "levleq") (("2" (skosimp) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((ass_doorway_extended formula-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (int_minus_int_is_int application-judgement "int" integers nil) (atlev15_to12 formula-decl nil tournamentUnity0 nil) (leto_transitive formula-decl nil bdUnity nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (W const-decl "posnat" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil) (sub_leto formula-decl nil bdUnity nil) (levleq const-decl "bool" tournamentUnity0 nil) (<= const-decl "bool" mucalculus nil) (cap const-decl "bool" ownpred nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (out const-decl "bool" tournamentUnity0 nil) (leveq_betw const-decl "bool" tournamentUnity0 nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (D const-decl "posnat" tournamentUnity0 nil) (posint nonempty-type-eq-decl nil integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil)) shostak)) (level_step_1 0 (level_step_1-2 nil 3671439136 ("" (skosimp) (("" (case "leveq_betw(q!1, 12, 18, k!1) = cup( leveq_betw(q!1, 12, 15, k!1), leveq_betw(q!1, 16, 18, k!1))") (("1" (replaceh -1) (("1" (use cup_leto) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (use level_step (m m!1)) (("1" (assert) (("1" (use from17to17) (("1" (assert) (("1" (lemma leto_transitive) (("1" (inst - "1 + D + W * degree + degree * m!1" exi1 _ _ _ _) (("1" (inst?) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1 -2 -3) (("2" (lemma leto_up) (("2" (inst - exi1 "1 + D + W * degree + degree * m!1 + exi1" _ _ _) (("2" (inst?) (("2" (assert) (("2" (hide 2) (("2" (case "leveq_betw(q!1, 16, 18, k!1) = cup(atlev(q!1, 16, k!1), cup(atlev(q!1, 17, k!1), atlev(q!1, 18, k!1)) )") (("1" (replaceh -1) (("1" (use cup_leto) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "atlev") (("1" (skosimp) (("1" (case "iq2(q!1, s!1)") (("1" (expand "iq2") (("1" (assert) nil nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (use from17to17) (("1" (assert) nil nil)) nil) ("2" (use from18to17) (("2" (assert) (("2" (lemma leto_up) (("2" (inst - exi exi1 _ _ _) (("2" (inst?) (("2" (assert) (("2" (expand "exi1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "leveq_betw") (("2" (expand "cup") (("2" (expand "atlev") (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (expand "leveq_betw") (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cup const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (leveq_betw const-decl "bool" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (cup_leto formula-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (atlev const-decl "bool" tournamentUnity0 nil) (exi1 const-decl "posnat" tournamentUnity0 nil) (W const-decl "posnat" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (D const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (from18to17 formula-decl nil tournamentUnity0 nil) (exi const-decl "posnat" tournamentUnity0 nil) (subset_leto formula-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (iqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (iq2 const-decl "bool" tournamentSafe0 nil) (<= const-decl "bool" mucalculus nil) (leto_up formula-decl nil bdUnity nil) (level_step formula-decl nil tournamentUnity0 nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (from17to17 formula-decl nil tournamentUnity0 nil) (leto_transitive formula-decl nil bdUnity nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil)) nil) (level_step_1-1 nil 3671438246 ("" (skosimp) (("" (case "leveq_betw(q!1, 12, 18, k!1) = cup( leveq_betw(q!1, 12, 15, k!1), leveq_betw(q!1, 16, 18, k!1))") (("1" (replaceh -1) (("1" (use cup_leto) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (use level_step (m m!1)) (("1" (assert) (("1" (use from17to17) (("1" (assert) (("1" (lemma leto_transitive) (("1" (inst - "1 + D + W * degree + degree * m!1" exi1 _ _ _ _) (("1" (inst?) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1 -2 -3) (("2" (lemma leto_up) (("2" (inst - exi1 "1 + D + W * degree + degree * m!1 + exi1" _ _ _) (("2" (inst?) (("2" (assert) (("2" (hide 2) (("2" (case "leveq_betw(q!1, 16, 18, k!1) = cup(atlev(q!1, 16, k!1), cup(atlev(q!1, 16, k!1), atlev(q!1, 16, k!1)) )") (("1" (replaceh -1) (("1" (use cup_leto) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "atlev") (("1" (skosimp) (("1" (case "iq2(q!1, s!1)") (("1" (expand "iq2") (("1" (assert) nil nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (postpone) nil nil) ("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (postpone) nil nil)) nil)) nil) nil shostak)) (level_step_2 0 (level_step_2-3 nil 3671461901 ("" (skosimp) (("" (use level_step) (("" (assert) (("" (lemma sub_leto) (("" (inst - "1 + D + W * degree + degree * m!1" "leveq_betw(q!1, 12, 18, k!1)" "cup(leveq_betw(q!1, 12, 15, k!1), atlev(q!1, 17, k!1))" "atlev(q!1, 17, k!1)" E1) (("" (assert) (("" (hide 2) (("" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "leveq_betw") (("1" (expand "atlev") (("1" (skosimp) (("1" (assert) (("1" (case "iq3(q!1, s!1) AND iq2(q!1, s!1)") (("1" (flatten) (("1" (expand "iq3") (("1" (expand "iq2") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (flatten) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide - 2) (("2" (use subset_leto) (("2" (assert) (("2" (hide 2) (("2" (expand "<=") (("2" (expand "cap") (("2" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((level_step formula-decl nil tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (even_minus_odd_is_odd application-judgement "odd_int" integers nil) (sub_leto formula-decl nil bdUnity nil) (digit type-eq-decl nil ctrees nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (<= const-decl "bool" mucalculus nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (iqall const-decl "bool" tournamentSafe0 nil) (globinv const-decl "bool" tournamentSafe1 nil) (iq2 const-decl "bool" tournamentSafe0 nil) (iq3 const-decl "bool" tournamentSafe0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (cap const-decl "bool" ownpred nil) (subset_leto formula-decl nil bdUnity nil) (cup_leto formula-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (atlev const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (leveq_betw const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (W const-decl "posnat" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (D const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil)) nil) (level_step_2-2 nil 3671461799 ("" (skosimp) (("" (use level_step) (("" (assert) (("" (lemma sub_leto) (("" (inst - "1 + D + W * degree + degree * m!1" "leveq_betw(q!1, 12, 18, k!1)" "cup(leveq_betw(q!1, 12, 15, k!1), cup(atlev(q!1, 17, k!1)))" "atlev(q!1, 17, k!1)" E1) (("" (assert) (("" (hide 2) (("" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "leveq_betw") (("1" (expand "atlev") (("1" (skosimp) (("1" (assert) (("1" (case "iq3(q!1, s!1)") (("1" (expand "iq3") (("1" (propax) nil))) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) 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(("1" (assert) nil))))))))))) ("2" (use from16_18_out) (("2" (assert) (("2" (lemma leto_up) (("2" (inst - "1 + exi1 * depth(pp)" nn1 _ _ _) (("2" (inst?) (("2" (assert) nil))))))))))))) ("2" (hide 2) (("2" (expand "nn1") (("2" (lemma both_sides_times_pos_le1) (("2" (assert) (("2" (expand "addend") (("2" (hide -) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" m!1) (("2" (assert) nil))))))))))))))))))))))))))))))))))))))))))))))))) ("2" (hide - 2) (("2" (expand "addend") (("2" (assert) nil)))))))))))))))) nil) nil nil) (levleq_to_out_step-7 nil 3671447753 ("" (skosimp) (("" (expand levleq_to_out +) (("" (skolem!) (("" (use level_step_1) (("" (ground) (("" (case "1 + D + W * degree + degree * m!1 + exi1 = degree * m!1 + addend") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (name-replace nn1 "degree * m!1 + addend") (("1" (inst - nn1 "levleq(q!1, 1 + k!1)" _ "atlev(q!1, 1 + k!1)" E1) (("1" (inst - "cup(leveq_betw(q!1, 12, 15, k!1), cup(levleq(q!1, k!1), between(q!1, 16, 18)))") (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cup") (("1" (expand "cap") (("1" (expand "levleq") (("1" (expand "leveq_betw") (("1" (expand "between") (("1" (skosimp) (("1" (assert) (("1" (assert) nil))))))))))))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -1) (("2" (case "m!1 <= nn1") (("1" (split) (("1" (expand "levleq_to_out") (("1" (inst?) (("1" (lemma leto_up) (("1" (inst - m!1 nn1 _ _ E1) (("1" (inst?) (("1" (assert) nil))))))))))) ("2" (use from16_18_out) (("2" (assert) (("2" (lemma leto_up) (("2" (inst - "1 + exi1 * depth(pp)" nn1 _ _ _) (("2" (inst?) (("2" (assert) nil))))))))))))) ("2" (hide 2) (("2" (expand "nn1") (("2" (lemma both_sides_times_pos_le1) (("2" (assert) (("2" (expand "addend") (("2" (hide -) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" m!1) (("2" (assert) nil))))))))))))))))))))))))))))))))))))))))))))))))) ("2" (hide - 2) (("2" (expand "addend") (("2" (assert) nil)))))))))))))))) nil) nil nil) (levleq_to_out_step-6 nil 3671440061 ("" (skosimp) (("" (expand levleq_to_out +) (("" (skolem!) (("" (use level_step_1) (("" (assert) (("" (case "1 + D + W * degree + degree * m!1 + exi1 = degree * m!1 + addend") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (name-replace nn1 "degree * m!1 + addend") (("1" (inst - nn1 "levleq(q!1, 1 + k!1)" _ "atlev(q!1, 1 + k!1)" E1) (("1" (inst - "cup(leveq_betw(q!1, 12, 15, k!1), cup(levleq(q!1, k!1), between(q!1, 16, 18)))") (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cup") (("1" (expand "cap") (("1" (expand "levleq") (("1" (expand "leveq_betw") (("1" (expand "between") (("1" (skosimp) (("1" (assert) (("1" (assert) nil))))))))))))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -1) (("2" (case "m!1 <= nn1") (("1" (split) (("1" (expand "levleq_to_out") (("1" (inst?) (("1" (lemma leto_up) (("1" (inst - m!1 nn1 _ _ E1) (("1" (inst?) (("1" (assert) nil))))))))))) ("2" (use from16_18_out) (("2" (assert) (("2" (lemma leto_up) (("2" (inst - "1 + exi1 * depth(pp)" nn1 _ _ _) (("2" (inst?) (("2" (assert) nil))))))))))))) ("2" (hide 2) (("2" (expand "nn1") (("2" (lemma both_sides_times_pos_le1) (("2" (assert) (("2" (expand "addend") (("2" (hide -) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" m!1) (("2" (assert) nil))))))))))))))))))))))))))))))))))))))))))))))))) ("2" (hide - 2) (("2" (expand "addend") (("2" (assert) nil)))))))))))))))) nil) nil nil) (levleq_to_out_step-5 nil 3671439910 ("" (skosimp) (("" (expand levleq_to_out +) (("" (skolem!) (("" (use level_step_1) (("" (assert) (("" (case "1 + D + W * degree + degree * m!1 + exi1 = degree * m!1 + addend") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (name-replace nn1 "degree * m!1 + addend") (("1" (inst - nn1 "levleq(q!1, 1 + k!1)" _ "out(q!1)" E1) (("1" (inst - "cup(leveq_betw(q!1, 12, 15, k!1), cup(levleq(q!1, k!1), between(q!1, 16, 18)))") (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cup") (("1" (expand "cap") (("1" (expand "levleq") (("1" (expand "leveq_betw") (("1" (expand "between") (("1" (skosimp) (("1" (assert) (("1" (assert) nil))))))))))))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -1) (("2" (case "m!1 <= nn1") (("1" (split) (("1" (expand "levleq_to_out") (("1" (inst?) (("1" (lemma leto_up) (("1" (inst - m!1 nn1 _ _ E1) (("1" (inst?) (("1" (assert) nil))))))))))) ("2" (use from16_18_out) (("2" (assert) (("2" (lemma leto_up) (("2" (inst - "1 + exi1 * depth(pp)" nn1 _ _ _) (("2" (inst?) (("2" (assert) nil))))))))))))) ("2" (hide 2) (("2" (expand "nn1") (("2" (lemma both_sides_times_pos_le1) (("2" (assert) (("2" (expand "addend") (("2" (hide -) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" m!1) (("2" (assert) nil))))))))))))))))))))))))))))))))))))))))))))))))) ("2" (hide - 2) (("2" (expand "addend") (("2" (assert) nil)))))))))))))))) nil) nil nil) (levleq_to_out_step-4 nil 3671439781 ("" (skosimp) (("" (expand levleq_to_out +) (("" (skolem!) (("" (use level_step_1) (("" (assert) (("" (case "1 + D + W * degree + degree * m!1 = degree * m!1 + addend") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (name-replace nn1 "degree * m!1 + addend") (("1" (inst - nn1 "levleq(q!1, 1 + k!1)" _ "out(q!1)" E1) (("1" (inst - "cup(leveq_betw(q!1, 12, 15, k!1), cup(levleq(q!1, k!1), between(q!1, 16, 18)))") (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cup") (("1" (expand "cap") (("1" (expand "levleq") (("1" (expand "leveq_betw") (("1" (expand "between") (("1" (skosimp) (("1" (assert) (("1" (assert) nil))))))))))))))))))) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -1) (("2" (case "m!1 <= nn1") (("1" (split) (("1" (expand "levleq_to_out") (("1" (inst?) (("1" (lemma leto_up) (("1" (inst - m!1 nn1 _ _ E1) (("1" (inst?) (("1" (assert) nil))))))))))) ("2" (use from16_18_out) (("2" (assert) (("2" (lemma leto_up) (("2" (inst - "1 + exi1 * depth(pp)" nn1 _ _ _) (("2" (inst?) (("2" (assert) nil))))))))))))) ("2" (hide 2) (("2" (expand "nn1") (("2" (lemma both_sides_times_pos_le1) (("2" (assert) (("2" (expand "addend") (("2" (hide -) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" m!1) (("2" (assert) nil))))))))))))))))))))))))))))))))))))))))))))))))) ("2" (hide - 2) (("2" (expand "addend") (("2" (assert) nil)))))))))))))))) nil) nil nil) (levleq_to_out_step-3 nil 3671348729 ("" (skosimp) (("" (expand levleq_to_out +) (("" (skolem!) (("" (use level_step) (("" (assert) (("" (case "1 + D + W * degree + degree * m!1 = degree * m!1 + addend") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (name-replace nn1 "degree * m!1 + addend") (("1" (inst - nn1 "levleq(q!1, 1 + k!1)" _ "out(q!1)" E1) (("1" (inst - "cup(leveq_betw(q!1, 12, 15, k!1), cup(levleq(q!1, k!1), between(q!1, 16, 18)))") (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cup") (("1" (expand "cap") (("1" (expand "levleq") (("1" (expand "leveq_betw") (("1" (expand "between") (("1" (skosimp) (("1" (assert) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -1) (("2" (case "m!1 <= nn1") (("1" (split) (("1" (expand "levleq_to_out") (("1" (inst?) (("1" (lemma leto_up) (("1" (inst - m!1 nn1 _ _ E1) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (use from16_18_out) (("2" (assert) (("2" (lemma leto_up) (("2" (inst - "1 + exi1 * depth(pp)" nn1 _ _ _) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (expand "nn1") (("2" (lemma both_sides_times_pos_le1) (("2" (assert) (("2" (expand "addend") (("2" (hide -) (("2" (lemma pos_times_le) (("2" (inst - "degree-1" m!1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (expand "addend") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (level_step formula-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (D const-decl "posnat" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (W const-decl "posnat" tournamentUnity0 nil) (addend const-decl "posnat" tournamentUnity0 nil) (sub_leto formula-decl nil bdUnity nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (out const-decl "bool" tournamentUnity0 nil) (levleq const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (<= const-decl "bool" mucalculus nil) (cap const-decl "bool" ownpred nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (<= const-decl "bool" reals nil) (exi1 const-decl "posnat" tournamentUnity0 nil) (leto_up formula-decl nil bdUnity nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (pos_times_le formula-decl nil real_props nil) (both_sides_times_pos_le1 formula-decl nil real_props nil) (cup_leto formula-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (leveq_betw const-decl "bool" tournamentUnity0 nil) (between const-decl "bool" tournamentUnity0 nil) (posint nonempty-type-eq-decl nil integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil) (levleq_to_out_step-2 nil 3670595318 ("" (skosimp) (("" (expand levleq_to_out +) (("" (skolem!) (("" (use level_step) (("" (assert) (("" (case "1 + D + W * degree + degree * m!1 + m!1= degree1 * m!1 + addend") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (name-replace nn1 "degree1 * m!1 + addend") (("1" (inst - nn1 "levleq(q!1, 1 + k!1)" _ "out(q!1)" E1) (("1" (inst - "cup(leveq_betw(q!1, 12, 15, k!1), cup(levleq(q!1, k!1), between(q!1, 16, 18)))") (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cup") (("1" (expand "cap") (("1" (expand "levleq") (("1" (expand "leveq_betw") (("1" (expand "between") (("1" (skosimp) (("1" (assert) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -1) (("2" (case "m!1 <= nn1") (("1" (split) (("1" (expand "levleq_to_out") (("1" (inst?) (("1" (lemma leto_up) (("1" (inst - m!1 nn1 _ _ E1) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (use from16_18_out) (("2" (assert) (("2" (lemma leto_up) (("2" (inst - "1 + exi1 * depth(pp)" nn1 _ _ _) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (expand "nn1") (("2" (lemma both_sides_times_pos_le1) (("2" (inst - m!1 1 degree1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (expand "degree1") (("2" (expand "addend") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (level_step formula-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (D const-decl "posnat" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (W const-decl "posnat" tournamentUnity0 nil) (addend const-decl "posnat" tournamentUnity0 nil) (sub_leto formula-decl nil bdUnity nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (out const-decl "bool" tournamentUnity0 nil) (levleq const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (<= const-decl "bool" mucalculus nil) (cap const-decl "bool" ownpred nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (<= const-decl "bool" reals nil) (exi1 const-decl "posnat" tournamentUnity0 nil) (leto_up formula-decl nil bdUnity nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (posreal nonempty-type-eq-decl nil real_types nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (both_sides_times_pos_le1 formula-decl nil real_props nil) (cup_leto formula-decl nil bdUnity nil) (cup const-decl "bool" ownpred nil) (leveq_betw const-decl "bool" tournamentUnity0 nil) (between const-decl "bool" tournamentUnity0 nil) (posint nonempty-type-eq-decl nil integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil) (levleq_to_out_step-1 nil 3670588615 ("" (skosimp) (("" (expand levleq_to_out +) (("" (skolem!) (("" (use level_step) (("" (assert) (("" (case "1 + D + W * degree + degree * m!1 + m!1= degree1 * m!1 + addend") (("1" (replaceh -1) (("1" (lemma sub_leto) (("1" (name-replace nn1 "degree1 * m!1 + addend") (("1" (inst - nn1 "levleq(q!1, 1 + k!1)" _ "out(q!1)" E1) (("1" (inst - "cup(leveq_betw(q!1, 12, 15, k!1), cup(levleq(q!1, k!1), between(q!1, 16, 18)))") (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cup") (("1" (expand "cap") (("1" (expand "levleq") (("1" (expand "leveq_betw") (("1" (expand "between") (("1" (skosimp) (("1" (assert) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (hide -1) (("2" (case "m!1 <= nn1") (("1" (split) (("1" (expand "levleq_to_out") (("1" (inst?) (("1" (lemma leto_up) (("1" (inst - m!1 nn1 _ _ E1) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (use between16_18_out) (("2" (postpone) nil nil)) nil)) nil) ("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (expand "degree1") (("2" (expand "addend") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) nil shostak)) (fun_TCC1 0 (fun_TCC1-1 nil 3670595930 ("" (termination-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (>= const-decl "bool" reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (fun_TCC2 0 (fun_TCC2-1 nil 3670597687 ("" (termination-tcc) nil nil) nil nil)) (fun_eq_TCC1 0 (fun_eq_TCC1-1 nil 3671348239 ("" (use degree_gt_1) (("" (assert) nil nil)) nil) ((int_minus_int_is_int application-judgement "int" integers nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (degree_gt_1 formula-decl nil tournamentUnity0 nil)) nil)) (fun_eq 0 (fun_eq-1 nil 3670743239 ("" (induct k) (("1" (expand "power") (("1" (expand "fun") (("1" (propax) nil nil)) nil)) nil) ("2" (skosimp) (("2" (expand fun +) (("2" (expand power +) (("2" (replaceh -1) (("2" (assert) (("2" (assert) (("2" (name-replace gg "2 * (power(j!1, degree) * degree)") (("2" (name deg1 "degree - 1") (("2" (case "degree = deg1 + 1") (("1" (replaceh -1) (("1" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("3" (assert) (("3" (use degree_gt_1) (("3" (assert) nil nil)) nil)) nil)) nil) ((real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (degree_gt_1 formula-decl nil tournamentUnity0 nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (nzrat_times_nzrat_is_nzrat application-judgement "nzrat" rationals nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (even_int nonempty-type-eq-decl nil integers nil) (even? const-decl "bool" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (rat_plus_rat_is_rat application-judgement "rat" rationals nil) (even_times_int_is_even application-judgement "even_int" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals nil) (nat_induction formula-decl nil naturalnumbers nil) (addend const-decl "posnat" tournamentUnity0 nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (exi const-decl "posnat" tournamentUnity0 nil) (cs const-decl "posnat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (power def-decl "int" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (fun def-decl "nat" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (/= const-decl "boolean" notequal nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (int_minus_int_is_int application-judgement "int" integers nil)) shostak)) (levleq_to_out_all 0 (levleq_to_out_all-3 nil 3670735352 ("" (induct k) (("1" (flatten) (("1" (expand "levleq_to_out") (("1" (expand "fun") (("1" (skolem!) (("1" (use levleq_0_out) (("1" (assert) (("1" (flatten) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp) (("2" (assert) (("2" (expand fun +) (("2" (use levleq_to_out_step) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (levleq_to_out_step formula-decl nil tournamentUnity0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (levleq_0_out formula-decl nil tournamentUnity0 nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nat_induction formula-decl nil naturalnumbers nil) (fun def-decl "nat" tournamentUnity0 nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (ass_exit const-decl "bool" tournamentUnity0 nil) (ass_doorway const-decl "bool" tournamentUnity0 nil) (ass_waiting const-decl "bool" tournamentUnity0 nil) (ass_cs const-decl "bool" tournamentUnity0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) nil) (levleq_to_out_all-2 nil 3670596182 ("" (induct k) (("1" (flatten) (("1" (expand "levleq_to_out") (("1" (expand "fun") (("1" (skolem!) (("1" (use levleq_0_out) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp) (("2" (assert) (("2" (expand fun +) (("2" (use levleq_to_out_step) (("2" (assert) (("2" (assert) (("2" (hide - 2) (("2" (case "forall k: 2 + 2 * depth(pp) <= fun (k)") (("1" (inst?) nil nil) ("2" (hide 2) (("2" (induct k) (("1" (expand "fun") (("1" (assert) nil nil)) nil) ("2" (skosimp) (("2" (expand fun +) (("2" (lemma both_sides_times_pos_le1) (("2" (inst - "fun(j!2)" 1 degree1) (("1" (assert) nil nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (both_sides_times_pos_le1 formula-decl nil real_props nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (<= const-decl "bool" reals nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (int_minus_int_is_int application-judgement "int" integers nil) (levleq_to_out_step formula-decl nil tournamentUnity0 nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (even_times_int_is_even application-judgement "even_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (levleq_0_out formula-decl nil tournamentUnity0 nil) (below type-eq-decl nil nat_types nil) (< const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (even_plus_even_is_even application-judgement "even_int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (nat_induction formula-decl nil naturalnumbers nil) (fun def-decl "nat" tournamentUnity0 nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (ass_doorway const-decl "bool" tournamentUnity0 nil) (ass_waiting const-decl "bool" tournamentUnity0 nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) nil) (levleq_to_out_all-1 nil 3670595931 ("" (induct k) (("1" (expand "levleq_to_out") (("1" (expand "fun") (("1" (skolem!) (("1" (use levleq_0_out) (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (skosimp) (("2" (postpone) nil nil)) nil)) nil) nil shostak)) (from12_18to_out 0 (from12_18to_out-1 nil 3670599536 ("" (skosimp) (("" (lemma sub_leto) (("" (use levleq_to_out_all) (("" (assert) (("" (use level_step_2 (m "fun(k!1)")) (("" (assert) (("" (name-replace nn1 "1 + D + fun(k!1) * degree + W * degree") (("" (expand "levleq_to_out") (("" (inst?) (("" (assert) (("" (name-replace goal "atlev(q!1, 17, k!1)") (("" (inst - nn1 "between(q!1, 12, 18)" "cup(leveq_betw(q!1, 12, 18, k!1), levleq(q!1, k!1))" goal E1) (("" (assert) (("" (hide 2) (("" (split) (("1" (hide-all-but -6 -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "cup") (("1" (expand "between") (("1" (expand "leveq_betw") (("1" (expand "levleq") (("1" (skosimp) (("1" (assert) (("1" (case "iq0(q!1, s!1)") (("1" (expand "iq0") (("1" (propax) nil nil)) nil) ("2" (assert) (("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide -1 2) (("2" (lemma leto_up) (("2" (inst - "fun(k!1)" nn1 _ _ _) (("2" (inst?) (("2" (assert) (("2" (hide -1 2) (("2" (expand "nn1") (("2" (lemma pos_times_le) (("2" (inst - "degree - 1" "fun(k!1)") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (sub_leto formula-decl nil bdUnity nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (levleq_to_out const-decl "bool" tournamentUnity0 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (levleq const-decl "bool" tournamentUnity0 nil) (leveq_betw const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (between const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (cup_leto formula-decl nil bdUnity nil) (nn1 skolem-const-decl "posint" tournamentUnity0 nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (pos_times_le formula-decl nil real_props nil) (leto_up formula-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (globinv const-decl "bool" tournamentSafe1 nil) (iqall const-decl "bool" tournamentSafe0 nil) (iq0 const-decl "bool" tournamentSafe0 nil) (<= const-decl "bool" mucalculus nil) (atlev const-decl "bool" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (D const-decl "posnat" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (W const-decl "posnat" tournamentUnity0 nil) (posint nonempty-type-eq-decl nil integers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (level_step_2 formula-decl nil tournamentUnity0 nil) (fun def-decl "nat" tournamentUnity0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (levleq_to_out_all formula-decl nil tournamentUnity0 nil)) shostak)) (individual_progress 0 (individual_progress-6 nil 3671515538 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "fun1(k!1) + 2" fullset _ "at(q!1, 11)" E1) (("" (inst - "cup(at(q!1, 11), cup(between(q!1, 12, 18), at(q!1, 19)))") (("" (assert) (("" (hide 2) (("" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "fullset") (("1" (expand "cup") (("1" (expand "at") (("1" (expand "between") (("1" (skosimp) (("1" (case "kq0(q!1, s!1)") (("1" (expand "kq0") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (hide -) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (use from12_18to_out) (("1" (use out_to11) (("1" (assert) (("1" (case "atlev(q!1, 17, k!1) = out(q!1)") (("1" (replaceh -1) (("1" (lemma leto_transitive) (("1" (inst - "1 + D + fun(k!1) * degree + W * degree" 2 _ _ _ _) (("1" (inst?) (("1" (inst?) (("1" (assert) (("1" (expand "fun1") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1 -2 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "atlev") (("2" (expand "out") (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use from19to11) (("2" (lemma leto_up) (("2" (inst - 1 "2 + fun1(k!1)" _ _ _) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity0 nil) (sub_leto formula-decl nil bdUnity nil) (between const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (cup_leto formula-decl nil bdUnity nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (from19to11 formula-decl nil tournamentUnity0 nil) (odd_minus_even_is_odd application-judgement "odd_int" integers nil) (leto_up formula-decl nil bdUnity nil) (from12_18to_out formula-decl nil tournamentUnity0 nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (W const-decl "posnat" tournamentUnity0 nil) (fun def-decl "nat" tournamentUnity0 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (D const-decl "posnat" tournamentUnity0 nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (leto_transitive formula-decl nil bdUnity nil) (out const-decl "bool" tournamentUnity0 nil) (atlev const-decl "bool" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (out_to11 formula-decl nil tournamentUnity0 nil) (subset_leto formula-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (kq0 const-decl "bool" tournamentSafe0 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (globinv const-decl "bool" tournamentSafe1 nil) (kqall const-decl "bool" tournamentSafe0 nil) (<= const-decl "bool" mucalculus nil) (int_minus_int_is_int application-judgement "int" integers nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (at const-decl "bool" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (fullset const-decl "set" sets nil) (pred type-eq-decl nil defined_types nil) (fun1 const-decl "nat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil)) nil) (individual_progress-5 nil 3671515333 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "fun1(k!1) + 2" fullset _ "at(q!1, 11)" E1) (("" (inst - "cup(at(q!1, 11), cup(between(q!1, 12, 18), at(q!1, 19)))") (("" (assert) (("" (hide 2) (("" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "fullset") (("1" (expand "cup") (("1" (expand "at") (("1" (expand "between") (("1" (skosimp) (("1" (case "kq0(q!1, s!1)") (("1" (expand "kq0") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (hide -) (("1" (use subset_leto) (("1" (assert) (("1" (hide 2) (("1" (expand "<=") (("1" (expand "cap") (("1" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use cup_leto) (("2" (assert) (("2" (hide 2) (("2" (split) (("1" (use from12_18to_out) (("1" (use out_to11) (("1" (assert) (("1" (case "atlev(q!1, 17, k!1) = out(q!1)") (("1" (replaceh -1) (("1" (lemma leto_transitive) (("1" (inst - "1 + D + fun(k!1) * degree + W * degree" 2 _ _ _ _) (("1" (inst?) (("1" (inst?) (("1" (assert) (("1" (expand "fun1") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1 -2 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "atlev") (("2" (expand "out") (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (use from19to11) (("2" (lemma leto_up) (("2" (inst - 1 "2 + fun(depth(pp))" _ _ _) (("2" (inst?) (("2" (assert) (("2" (assert) (("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) nil nil) (individual_progress-4 nil 3671515250 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "fun1(k!1) + 2" fullset _ "at(q!1, 11)" E1) (("" (inst - "cup(at(q!1, 11), cup(between(q!1, 12, 18), at(q!1, 19)))") (("" (assert) (("" (hide 2) (("" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "fullset") (("1" (expand "cup") (("1" (expand "at") (("1" (expand "between") (("1" (skosimp) (("1" (case "kq0(q!1, s!1)") (("1" (expand "kq0") (("1" (flatten) (("1" (assert) nil))))) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) 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(("2" (assert) nil)))))))))))))))))))))))))))))))))))))) nil) nil nil) (individual_progress-3 nil 3671515093 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "fun1(k!1) + 2" fullset _ "at(q!1, 11)" E1) (("" (inst - "cup(at(q!1, 11), cup(between(q!1, 12, 18), at(q!1, 19)))") (("" (assert) (("" (hide 2) (("" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "fullset") (("1" (expand "cup") (("1" (expand "at") (("1" (expand "between") (("1" (skosimp) (("1" (case "kq0(q!1, s!1)") (("1" (expand "kq0") (("1" (flatten) (("1" (assert) nil))))) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) 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(("2" (assert) nil)))))))))))))))))))))))))))))))))))))) nil) nil nil) (individual_progress-2 nil 3671514732 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "fun1(k!1) + 2" fullset _ "at(q!1, 11)" E1) (("" (inst - "cup(at(q!1, 11), cup(between(q!1, 12, 18), at(q!1, 19)))") (("" (assert) (("" (hide 2) (("" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "fullset") (("1" (expand "cup") (("1" (expand "at") (("1" (expand "between") (("1" (skosimp) (("1" (case "kq0(q!1, s!1)") (("1" (expand "kq0") (("1" (flatten) (("1" (assert) nil))))) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) 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(("2" (assert) nil)))))))))))))))))))))))))))))))))))))) nil) nil nil) (individual_progress-1 nil 3670643881 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - "fun(depth(pp)) + 2" fullset _ "at(q!1, 11)" E1) (("" (inst - "cup(at(q!1, 11), cup(between(q!1, 12, 18), at(q!1, 19)))") (("" (assert) (("" (hide 2) (("" (split) (("1" (hide -) (("1" (expand "<=") (("1" (expand "cap") (("1" (expand "fullset") (("1" (expand "cup") (("1" (expand "at") (("1" (expand "between") (("1" (skosimp) (("1" (case "kq0(q!1, s!1)") (("1" (expand "kq0") (("1" (flatten) (("1" (assert) nil nil)) nil)) nil) ("2" (expand "E1") (("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst?) 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(("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (sub_leto formula-decl nil bdUnity nil) (between const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (cup_leto formula-decl nil bdUnity nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (from19to11 formula-decl nil tournamentUnity0 nil) (odd_minus_even_is_odd application-judgement "odd_int" integers nil) (leto_up formula-decl nil bdUnity nil) (from12_18to_out formula-decl nil tournamentUnity0 nil) (out const-decl "bool" tournamentUnity0 nil) (even_minus_even_is_even application-judgement "even_int" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (leto_transitive formula-decl nil bdUnity nil) (out_to11 formula-decl nil tournamentUnity0 nil) (subset_leto formula-decl nil bdUnity nil) (cap const-decl "bool" ownpred nil) (kq0 const-decl "bool" tournamentSafe0 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (globinv const-decl "bool" tournamentSafe1 nil) (kqall const-decl "bool" tournamentSafe0 nil) (<= const-decl "bool" mucalculus nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (at const-decl "bool" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (fullset const-decl "set" sets nil) (pred type-eq-decl nil defined_types nil) (fun def-decl "nat" tournamentUnity0 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil)) shostak)) (fun1_equals0 0 (fun1_equals0-1 nil 3671694156 ("" (skosimp) (("" (expand power) (("" (expand "fun1") (("" (use fun_eq) (("" (case "cs + exi + 2 + addend / (degree - 1)= factor") (("1" (replaceh -1) (("1" (assert) (("1" (replaceh -1) (("1" (assert) (("1" (expand "term0") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "factor") (("2" (propax) nil nil)) nil) ("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (power def-decl "int" tournamentUnity0 nil) (fun_eq formula-decl nil tournamentUnity0 nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals nil) (rat_plus_rat_is_rat application-judgement "rat" rationals nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (real_plus_real_is_real application-judgement "real" reals nil) (real_times_real_is_real application-judgement "real" reals nil) (term0 const-decl "real" tournamentUnity0 nil) (nzrat_times_nzrat_is_nzrat application-judgement "nzrat" rationals nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (real_minus_real_is_real application-judgement "real" reals nil) (factor const-decl "real" tournamentUnity0 nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (addend const-decl "posnat" tournamentUnity0 nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/= const-decl "boolean" notequal nil) (exi const-decl "posnat" tournamentUnity0 nil) (cs const-decl "posnat" tournamentUnity0 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (fun1 const-decl "nat" tournamentUnity0 nil)) shostak)) (factor_equals 0 (factor_equals-1 nil 3671696936 ("" (expand "factor") (("" (expand "addend") (("" (expand "constant0") (("" (expand "exi1") (("" (name deg1 "degree - 1") (("" (case "degree = deg1 + 1") (("1" (replaceh -1) (("1" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((posint_plus_nnint_is_posint application-judgement "posint" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (addend const-decl "posnat" tournamentUnity0 nil) (exi1 const-decl "posnat" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (rat_div_nzrat_is_rat application-judgement "rat" rationals nil) (nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals nil) (rat_plus_rat_is_rat application-judgement "rat" rationals nil) (even_times_int_is_even application-judgement "even_int" integers nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (constant0 const-decl "real" tournamentUnity0 nil) (factor const-decl "real" tournamentUnity0 nil) (int_minus_int_is_int application-judgement "int" integers nil)) shostak)) (term0_equals 0 (term0_equals-1 nil 3671697250 ("" (expand "term0") (("" (expand "addend") (("" (expand "constant0") (("" (expand "exi1") (("" (name deg1 "degree -1 ") (("" (case "degree = deg1 + 1") (("1" (replaceh -1) (("1" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((posint_plus_nnint_is_posint application-judgement "posint" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (addend const-decl "posnat" tournamentUnity0 nil) (exi1 const-decl "posnat" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (rat_div_nzrat_is_rat application-judgement "rat" rationals nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil) (rat_plus_rat_is_rat application-judgement "rat" rationals nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (even_times_int_is_even application-judgement "even_int" integers nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity0 nil) (constant0 const-decl "real" tournamentUnity0 nil) (term0 const-decl "real" tournamentUnity0 nil) (nzrat_times_nzrat_is_nzrat application-judgement "nzrat" rationals nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals nil) (int_minus_int_is_int application-judgement "int" integers nil)) shostak)) (fun1_equals 0 (fun1_equals-1 nil 3671697861 ("" (skolem!) (("" (use fun1_equals0) (("" (use factor_equals) (("" (use term0_equals) (("" (replace* -1 -2) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((fun1_equals0 formula-decl nil tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (real_times_real_is_real application-judgement "real" reals nil) (real_plus_real_is_real application-judgement "real" reals nil) (real_minus_real_is_real application-judgement "real" reals nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (term0_equals formula-decl nil tournamentUnity0 nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (factor_equals formula-decl nil tournamentUnity0 nil)) shostak))) $$$tournamentUnity1.pvs % Wim H. Hesselink, May-August 2016 % Proofs for: Tournaments for mutual exclusion: % verification and concurrent complexity. % Part 5. Throughput (general progress) tournamentUnity1 [ degree: posnat, node: TYPE+ ]: THEORY BEGIN IMPORTING tournamentUnity0[degree, node] p, q, r: VAR Thread x, y: VAR state i, n, k, kk, m: VAR nat b: VAR bool se: VAR finite_set[(thread)] z: VAR int nn: VAR node col(q, x): int = depth(q) - 1 - x`level(q) lev1(q, x): int = x`level(q) + 1 DW1: posnat = D + W + 1 lvf(q, x): int = % IF x`pc(q) < 16 THEN col(q, x) * DW1 + IF x`pc(q) = 15 THEN D + 1 ELSIF 13 <= x`pc(q) THEN 1 ELSE 0 ENDIF ELSIF x`pc(q) = 16 THEN depth(q) * DW1 + 1 ELSIF x`pc(q) < 19 THEN depth(q) * DW1 + exi1 * lev1(q, x) + x`pc(q) - 16 + cs ELSE depth(q) * (DW1 + exi1) + cs + 2 ENDIF lvf_at_12: LEMMA step12(q, x, y) AND iq0(q, x) IMPLIES lvf(q, y) = lvf(q, x) + 1 lvf_at_16: LEMMA step16(q, x, y) AND iq2(q, x) IMPLIES lvf(q, y) = lvf(q, x) + cs lvf_at_17: LEMMA step17(q, x, y) AND iq0(q, x) IMPLIES lvf(q, y) = lvf(q, x) + 1 AA: posnat = depthnode * (DW1 + exi1) + cs + 3 lvf_bounded: LEMMA % globinv(x) IMPLIES 0 <= lvf(q, x) AND lvf(q, x) < AA avf(q, x): int = lvf(q, x) + AA * x`cnt(q) avf_bounded: LEMMA globinv(x) IMPLIES AA * x`cnt(q) <= avf(q, x) AND avf(q, x) < AA * x`cnt(q) + AA avf_increases_fwd: LEMMA forward1(q)(x, y) AND globinv(x) IMPLIES avf(q, x) < avf(q, y) avf_at_14: LEMMA step14(q, x, y) IMPLIES avf(q, y) = avf(q, x) + D avf_at_15: LEMMA step15F(q, x, y) OR step15G(q, x, y) IMPLIES avf(q, y) = avf(q, x) + W avf_at_16: LEMMA step16(q, x, y) AND globinv(x) IMPLIES avf(q, y) = avf(q, x) + cs avf_at_18: LEMMA step18(q, x, y) IMPLIES avf(q, y) = avf(q, x) + exi avf_at_11_or_13: LEMMA step11(q, x, y) OR step13(q, x, y) IMPLIES avf(q, y) = avf(q, x) avf_constant_dif: LEMMA step(p, x, y) AND q /= p IMPLIES avf(q, y) = avf(q, x) avf_ascends: LEMMA % step(p, x, y) AND globinv(x) IMPLIES avf(q, x) <= avf(q, y) savf(x): int = LET f = LAMBDA n: IF n < N THEN avf(enum_thread(n), x) ELSE 0 ENDIF IN sum(N, f) savf_LWB: LEMMA globinv(x) IMPLIES AA * sinc(x) <= savf(x) savf_UPB: LEMMA % globinv(x) AND competing_leq(kk)(x) IMPLIES savf(x) <= AA * sinc(x) + kk * (AA - 1) savf_ascends: LEMMA % step(p, x, y) AND globinv(x) IMPLIES savf(x) <= savf(y) savf_increases_fwd: LEMMA % forward1(p)(x, y) AND globinv(x) IMPLIES savf(x) < savf(y) savf_at_14: LEMMA step14(p, x, y) IMPLIES savf(y) = savf(x) + D savf_at_15: LEMMA step15F(p, x, y) OR step15G(p, x, y) IMPLIES savf(y) = savf(x) + W savf_at_16: LEMMA step16(p, x, y) AND globinv(x) IMPLIES savf(y) = savf(x) + cs savf_at_18: LEMMA step18(p, x, y) IMPLIES savf(y) = savf(x) + exi at_fwd(q)(x): bool = x`pc(q) = 12 OR x`pc(q) = 17 OR x`pc(q) = 19 at_fwd_ensures: LEMMA % leto(E1)(1, cap(leq(z, savf), at_fwd(q)), leq(z + 1, savf)) some_at_fwd(x): bool = EXISTS q: at_fwd(q)(x) some_fwd_progress: LEMMA leto(E1)(1, cap(leq(z, savf), some_at_fwd), leq(z + 1, savf)) savf_13_14_unless: LEMMA % unless(E1)(cap(leq(z, savf), between(q, 13, 14)), leq(z + D, savf)) doorway_progress: LEMMA % use PSP0-rule % fails ass_doorway IMPLIES leto(E1)(D, cap(leq(z, savf), between(q, 13, 14)), leq(z + D, savf)) some_doorway(x): bool = EXISTS q: 13 <= x`pc(q) AND x`pc(q) <= 14 doorway_progress_1: LEMMA ass_doorway IMPLIES leto(E1)(D, cap(leq(z, savf), some_doorway), leq(z + D, savf)) cs_unless: LEMMA unless(E1)(cap(leq(z, savf), at(q, 16)), leq(z + cs, savf)) cs_progress: LEMMA % use PSP0-rule ass_cs IMPLIES leto(E1)(cs, cap(leq(z, savf), at(q, 16)), leq(z + cs, savf)) some_cs(x): bool = EXISTS q: x`pc(q) = 16 cs_progress_1: LEMMA ass_cs IMPLIES leto(E1)(cs, cap(leq(z, savf), some_cs), leq(z + cs, savf)) exi_unless: LEMMA unless(E1)(cap(leq(z, savf), at(q, 18)), leq(z + exi, savf)) exi_progress: LEMMA % use PSP0-rule ass_exit IMPLIES leto(E1)(exi, cap(leq(z, savf), at(q, 18)), leq(z + exi, savf)) some_exit(x): bool = EXISTS q: x`pc(q) = 18 exi_progress_1: LEMMA ass_exit IMPLIES leto(E1)(exi, cap(leq(z, savf), some_exit), leq(z + exi, savf)) waiting_unless: LEMMA unless(E1)(cap(leq(z, savf), cap(atlev(q, 15, k), mubot(path(q, k)))), leq(z + W, savf)) waiting_progress_lev_mu: LEMMA % ass_waiting IMPLIES leto(E1)(W, cap(leq(z, savf), cap(atlev(q, 15, k), mubot(path(q, k)))), leq(z + W, savf)) only_some_waiting(x): bool = (FORALL q: x`pc(q) = 11 OR x`pc(q) = 15) AND (EXISTS q: x`pc(q) = 15) waiting_progress: LEMMA % sub-leto, disjunction rule, % % minimum of levels at 15, kq1, iq4, iq1 ass_waiting IMPLIES leto(E1)(W, cap(leq(z, savf), only_some_waiting), leq(z + W, savf)) allidle(x): bool = FORALL q: x`pc(q) = 11 cover(i): set[state] = IF i = 0 THEN allidle ELSIF i = 1 THEN some_doorway ELSIF i = 2 THEN only_some_waiting ELSIF i = 3 THEN some_exit ELSIF i = 4 THEN some_cs ELSE some_at_fwd ENDIF weight(r: posnat): posnat = IF r = 1 THEN D ELSIF r = 2 THEN W ELSIF r = 3 THEN exi ELSIF r = 4 THEN cs ELSE 1 ENDIF covering: LEMMA globinv(x) IMPLIES EXISTS i: cover(i)(x) disgrowth_cover: LEMMA % ass_doorway AND ass_waiting AND ass_cs AND ass_exit IMPLIES disgrowth(E1, savf, weight, cover) maxDWE: posnat = max(D, max(W, max(cs, exi))) eventual_growth_savf: LEMMA ass_doorway AND ass_waiting AND ass_cs AND ass_exit IMPLIES leto(E1)(n + maxDWE - 1, leq(z, savf), cup(leq(z + n, savf), allidle) ) eventual_growth_sinc: LEMMA ass_doorway AND ass_waiting AND ass_cs AND ass_exit IMPLIES leto(E1)(AA * i + kk * (AA - 1) + maxDWE - 1, leq(z, sinc), cup(leq(z + i, sinc), cup(allidle, neg(competing_leq(kk)))) ) END tournamentUnity1 $$$tournamentUnity1.prf (tournamentUnity1 (lvf_at_12 0 (lvf_at_12-1 nil 3670745796 ("" (expand "step12") (("" (skosimp) (("" (replaceh -1) (("" (lift-if) (("" (split) (("1" (flatten) (("1" (expand "lvf") (("1" (expand "goto") (("1" (assert) (("1" (expand "col") (("1" (expand "iq0") (("1" (case "x!1`level(q!1)=-1") (("1" (replaceh -1) (("1" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (flatten) (("2" (expand "lvf") (("2" (expand "goto") (("2" (assert) (("2" (expand "col") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) 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(("" (lemma leto_union) (("" (inst?) (("" (inst?) (("" (inst - _ "leq(z!1 + 1, savf)") (("" (name ppset "{pp: pred[state] | EXISTS q: pp = cap(leq(z!1, savf), at_fwd(q))}") (("" (inst - ppset) (("" (hide -1) (("" (case "Union(ppset) = cap(leq(z!1, savf), some_at_fwd)") (("1" (assert) (("1" (hide - 2) (("1" (skosimp) (("1" (expand "ppset") (("1" (skolem!) (("1" (replaceh -1) (("1" (use at_fwd_ensures) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (prop) (("1" (expand "Union") (("1" (skolem!) (("1" (typepred a!1) (("1" (expand "ppset") (("1" (skolem!) (("1" (replaceh -1) (("1" (expand "cap") (("1" (flatten) (("1" (assert) (("1" (expand "some_at_fwd") (("1" (inst?) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "Union") (("2" (expand "cap") (("2" (flatten) (("2" (expand "some_at_fwd") (("2" (skolem!) (("2" (inst + "cap(leq(z!1, savf), at_fwd(q!1))") (("1" (expand "cap") (("1" (assert) nil nil)) nil) ("2" (expand "ppset") (("2" (inst?) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil) (leto_union formula-decl nil bdUnity nil) (= const-decl "[T, T -> boolean]" equalities nil) (Thread type-eq-decl nil tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (at_fwd const-decl "bool" tournamentUnity1 nil) (q!1 skolem-const-decl "Thread[degree, node]" tournamentUnity1 nil) (z!1 skolem-const-decl "int" tournamentUnity1 nil) (NOT const-decl "[bool -> bool]" booleans nil) (Union_surjective name-judgement "(surjective?[setofsets[T], set[T]])" sets_lemmas nil) (at_fwd_ensures formula-decl nil tournamentUnity1 nil) (int_minus_int_is_int application-judgement "int" integers nil) (ppset skolem-const-decl "[pred[state] -> boolean]" tournamentUnity1 nil) (some_at_fwd const-decl "bool" tournamentUnity1 nil) (Union const-decl "set" sets nil) (setofsets type-eq-decl nil sets nil) (setof type-eq-decl nil defined_types nil) (savf const-decl "int" tournamentUnity1 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (leq const-decl "bool" bdUnity nil) (int_plus_int_is_int application-judgement "int" integers nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil)) shostak)) (savf_13_14_unless 0 (savf_13_14_unless-1 nil 3670852538 ("" (expand "unless") (("" (expand "<=") (("" (expand "wp") (("" (expand "cap") (("" (expand "cup") (("" (expand "neg") (("" (expand "between") (("" (skosimp*) (("" (expand "E1") (("" (expand "step") (("" (split -) (("1" (assert) nil nil) ("2" (skolem!) (("2" (expand "leq") (("2" (use savf_ascends) (("2" (assert) (("2" (case "q!1=p!1") (("1" (replaceh -1) (("1" (expand "step") (("1" (expand "step11") (("1" (assert) (("1" (expand "step12") (("1" (expand "step15F") (("1" (expand "step19") (("1" (expand "step17") (("1" (expand "step18") (("1" (expand "step15G") (("1" (expand "step16") (("1" (split) (("1" (expand "step13") (("1" (flatten) (("1" (hide 3) (("1" (replaceh -1) (("1" (expand "next13") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 1 2 -4 -5 -2) (("2" (use savf_at_14) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide-all-but (-2 -4 -5 1 3)) (("2" (case "y!1`pc(q!1) = s!1`pc(q!1)") (("1" (assert) nil nil) ("2" (hide -2 -3 3) (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((<= const-decl "bool" mucalculus nil) (cap const-decl "bool" ownpred nil) (neg const-decl "bool" ownpred nil) (step const-decl "bool" tournamentUnity0 nil) (savf_ascends formula-decl nil tournamentUnity1 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (digit type-eq-decl nil ctrees nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil) (= const-decl "[T, T -> boolean]" equalities nil) (step const-decl "bool" tournamentSafe0 nil) (step15F const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (savf_at_14 formula-decl nil tournamentUnity1 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (step11 const-decl "bool" tournamentSafe0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (finite_remove application-judgement "finite_set" finite_sets nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (next11 const-decl "state" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (goto const-decl "state" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (next15 const-decl "state" tournamentSafe0 nil) (member const-decl "bool" sets nil) (empty? const-decl "bool" sets nil) (next18 const-decl "state" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (leq const-decl "bool" bdUnity nil) (int_plus_int_is_int application-judgement "int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (between const-decl "bool" tournamentUnity0 nil) (cup const-decl "bool" ownpred nil) (wp const-decl "bool" ownpred nil) (unless const-decl "bool" bdUnity nil)) shostak)) (doorway_progress 0 (doorway_progress-1 nil 3670852890 ("" (skosimp) (("" (expand "ass_doorway") (("" (inst?) (("" (lemma PSP0_leto) (("" (inst - D "cap(leq(z!1, savf), between(q!1, 13, 14))" "between(q!1, 13, 14)" "leq(z!1 + D, savf)" E1) (("" (assert) (("" (hide - 2) (("" (split) (("1" (use savf_13_14_unless) (("1" (assert) nil nil)) nil) ("2" (expand "<=") (("2" (expand "cap") (("2" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((ass_doorway const-decl "bool" tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (digit type-eq-decl nil ctrees nil) (PSP0_leto formula-decl nil bdUnity nil) (savf_13_14_unless formula-decl nil tournamentUnity1 nil) (<= const-decl "bool" mucalculus nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (between const-decl "bool" tournamentUnity0 nil) (savf const-decl "int" tournamentUnity1 nil) (leq const-decl "bool" bdUnity nil) (cap const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (D const-decl "posnat" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil)) shostak)) (doorway_progress_1 0 (doorway_progress_1-1 nil 3670903537 ("" (skosimp) (("" (lemma leto_union) (("" (inst - D _ "leq(z!1 + D, savf)" E1) (("" (name ppset "{pp: pred[state] | EXISTS q: pp = cap(leq(z!1, savf), between(q, 13, 14)) }") (("" (inst - ppset) (("" (split) (("1" (hide -2) (("1" (case "Union(ppset) = cap(leq(z!1, savf), some_doorway)") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (prop) (("1" (expand "Union") (("1" (skolem!) (("1" (typepred a!1) (("1" (expand "ppset") (("1" (skolem!) (("1" (replaceh -1) (("1" (expand "cap") (("1" (flatten) (("1" (assert) (("1" (expand "some_doorway") (("1" (inst?) (("1" (expand "between") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "cap") (("2" (flatten) (("2" (expand "some_doorway") (("2" (skosimp) (("2" (expand "Union") (("2" (inst + "cap(leq(z!1, savf), between(q!1, 13, 14))") (("1" (expand "cap") (("1" (expand "between") (("1" (assert) nil nil)) nil)) nil) ("2" (expand "ppset") (("2" (inst?) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (skosimp) (("2" (hide -2) (("2" (expand "ppset") (("2" (skolem!) (("2" (replaceh -1) (("2" (use doorway_progress) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil) (leto_union formula-decl nil bdUnity nil) (= const-decl "[T, T -> boolean]" equalities nil) (Thread type-eq-decl nil tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (between const-decl "bool" tournamentUnity0 nil) (setof type-eq-decl nil defined_types nil) (setofsets type-eq-decl nil sets nil) (Union const-decl "set" sets nil) (some_doorway const-decl "bool" tournamentUnity1 nil) (Union_surjective name-judgement "(surjective?[setofsets[T], set[T]])" sets_lemmas nil) (ppset skolem-const-decl "[pred[state] -> boolean]" tournamentUnity1 nil) (NOT const-decl "[bool -> bool]" booleans nil) (z!1 skolem-const-decl "int" tournamentUnity1 nil) (q!1 skolem-const-decl "Thread[degree, node]" tournamentUnity1 nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (doorway_progress formula-decl nil tournamentUnity1 nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (savf const-decl "int" tournamentUnity1 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (leq const-decl "bool" bdUnity nil) (pred type-eq-decl nil defined_types nil) (D const-decl "posnat" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil)) shostak)) (cs_unless 0 (cs_unless-1 nil 3671701894 ("" (expand "unless") (("" (expand "<=") (("" (expand "wp") (("" (expand "cap") (("" (expand "cup") (("" (expand "neg") (("" (skosimp*) (("" (expand "E1") (("" (expand "step") (("" (split -) (("1" (assert) nil nil) ("2" (skolem!) 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(("2" (replaceh -1) (("2" (use cs_progress) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil) (leto_union formula-decl nil bdUnity nil) (cs const-decl "posnat" tournamentUnity0 nil) (= const-decl "[T, T -> boolean]" equalities nil) (Thread type-eq-decl nil tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (at const-decl "bool" tournamentUnity0 nil) (cs_progress formula-decl nil tournamentUnity1 nil) (setof type-eq-decl nil defined_types nil) (setofsets type-eq-decl nil sets nil) (Union const-decl "set" sets nil) (some_cs const-decl "bool" tournamentUnity1 nil) (Union_surjective name-judgement "(surjective?[setofsets[T], set[T]])" sets_lemmas nil) (ppset skolem-const-decl "[pred[state] -> boolean]" tournamentUnity1 nil) (NOT const-decl "[bool -> bool]" booleans nil) (z!1 skolem-const-decl "int" tournamentUnity1 nil) (q!1 skolem-const-decl "Thread[degree, node]" tournamentUnity1 nil) (savf const-decl "int" tournamentUnity1 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (leq const-decl "bool" bdUnity nil) (int_plus_int_is_int application-judgement "int" integers nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (pred type-eq-decl nil defined_types nil)) shostak)) (exi_unless 0 (exi_unless-1 nil 3670857284 ("" (expand "unless") (("" (expand "<=") (("" (expand "wp") (("" (expand "cap") (("" (expand "cup") (("" (skosimp*) (("" (expand "E1") (("" (expand "step") (("" (split -) (("1" (assert) nil nil) ("2" (skolem!) 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(("" (use exi_unless) (("" (lemma PSP0_leto) (("" (name-replace pp0 "cap(leq(z!1, savf), at(q!1, 18))") (("" (name-replace pp1 "leq(z!1 + exi, savf)") (("" (name-replace pp2 "at(q!1, 18)") (("" (inst - exi pp0 pp2 pp1 E1) (("" (assert) (("" (hide - 2) (("" (expand "<=") (("" (expand "pp0") (("" (expand "pp2") (("" (expand "cap") (("" (skosimp) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((ass_exit const-decl "bool" tournamentUnity0 nil) (exi_unless formula-decl nil tournamentUnity1 nil) (= const-decl "[T, T -> boolean]" equalities nil) (pred type-eq-decl nil defined_types nil) (cap const-decl "bool" ownpred nil) (leq const-decl "bool" bdUnity nil) (savf const-decl "int" tournamentUnity1 nil) (at const-decl "bool" tournamentUnity0 nil) (<= const-decl "bool" mucalculus nil) (pp2 skolem-const-decl "[state[degree, node] -> bool]" tournamentUnity1 nil) (pp0 skolem-const-decl "[state[degree, node] -> bool]" tournamentUnity1 nil) (specification type-eq-decl nil bdUnity nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (exi const-decl "posnat" tournamentUnity0 nil) (PSP0_leto formula-decl nil bdUnity nil) (digit type-eq-decl nil ctrees nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil)) shostak)) (exi_progress_1 0 (exi_progress_1-1 nil 3670904019 ("" (skosimp) (("" (lemma leto_union) (("" (inst - exi _ "leq(z!1 + exi, savf)" E1) (("" (name ppset "{pp: pred[state] | EXISTS q: pp = cap(leq(z!1, savf), at(q, 18))}") (("" (inst - ppset) (("" (hide -1) (("" (split) (("1" (case "Union(ppset) = cap(leq(z!1, savf), some_exit)") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (prop) (("1" (expand "Union") (("1" (skolem!) (("1" (typepred a!1) (("1" (expand "ppset") (("1" (skolem!) (("1" (replaceh -1) (("1" (expand "cap") (("1" (flatten) (("1" (assert) (("1" (expand "some_exit") (("1" (inst?) (("1" (expand "at") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "Union") (("2" (expand "cap") (("2" (flatten) (("2" (expand "some_exit") (("2" (skolem!) (("2" (inst + "cap(leq(z!1, savf), at(q!1, 18))") (("1" (expand "cap") (("1" (expand "at") (("1" (assert) nil nil)) nil)) nil) ("2" (expand "ppset") (("2" (inst?) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (skosimp) (("2" (expand "ppset") (("2" (skolem!) (("2" (replaceh -1) (("2" (use exi_progress) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil) (leto_union formula-decl nil bdUnity nil) (= const-decl "[T, T -> boolean]" equalities nil) (Thread type-eq-decl nil tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (at const-decl "bool" tournamentUnity0 nil) (exi_progress formula-decl nil tournamentUnity1 nil) (setof type-eq-decl nil defined_types nil) (setofsets type-eq-decl nil sets nil) (Union const-decl "set" sets nil) (some_exit const-decl "bool" tournamentUnity1 nil) (Union_surjective name-judgement "(surjective?[setofsets[T], set[T]])" sets_lemmas nil) (ppset skolem-const-decl "[pred[state] -> boolean]" tournamentUnity1 nil) (NOT const-decl "[bool -> bool]" booleans nil) (z!1 skolem-const-decl "int" tournamentUnity1 nil) (q!1 skolem-const-decl "Thread[degree, node]" tournamentUnity1 nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (savf const-decl "int" tournamentUnity1 nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (leq const-decl "bool" bdUnity nil) (pred type-eq-decl nil defined_types nil) (exi const-decl "posnat" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil)) shostak)) (waiting_unless 0 (waiting_unless-1 nil 3670859026 ("" (expand "unless") (("" (expand "<=") (("" (expand "wp") (("" (expand "cup") (("" (expand "cap") (("" (expand "neg") (("" (skosimp*) (("" (expand "E1") (("" (expand "step") (("" (split -) (("1" (assert) nil nil) ("2" (skolem!) (("2" (expand "leq") (("2" (use savf_ascends) (("2" (assert) (("2" (hide -1 1) (("2" (case "s!1`pc(p!1) = 15") (("1" (expand "step") (("1" (expand "step11") (("1" (assert) (("1" (expand "step12") (("1" (expand "step13") (("1" (expand "step14") (("1" (expand "step16") (("1" (expand "step17") (("1" (expand "step18") (("1" (expand "step19") (("1" (use savf_at_15) (("1" (split -3) (("1" (assert) nil nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -2 -5 3) (("2" (expand "atlev") (("2" (flatten) (("2" (expand "mubot") (("2" (split) (("1" (grind) nil nil) ("2" (grind) nil nil) ("3" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((<= const-decl "bool" mucalculus nil) (cup const-decl "bool" ownpred nil) (neg const-decl "bool" ownpred nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil) (leq const-decl "bool" bdUnity nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (= const-decl "[T, T -> boolean]" equalities nil) (step11 const-decl "bool" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (savf_at_15 formula-decl nil tournamentUnity1 nil) (step18 const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (step const-decl "bool" tournamentSafe0 nil) (atlev const-decl "bool" tournamentUnity0 nil) (mubot const-decl "bool" tournamentUnity0 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (finite_remove application-judgement "finite_set" finite_sets nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nonempty_add_finite application-judgement "non_empty_finite_set" finite_sets nil) (next11 const-decl "state" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (goto const-decl "state" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (next15 const-decl "state" tournamentSafe0 nil) (member const-decl "bool" sets nil) (empty? const-decl "bool" sets nil) (step15F const-decl "bool" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (next18 const-decl "state" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (set type-eq-decl nil sets nil) (is_finite const-decl "bool" finite_sets nil) (finite_set type-eq-decl nil finite_sets nil) (number nonempty-type-decl nil numbers nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (digit type-eq-decl nil ctrees nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (edigit type-eq-decl nil tournamentSafe0 nil) (state type-eq-decl nil tournamentSafe0 nil) (savf_ascends formula-decl nil tournamentUnity1 nil) (step const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (wp const-decl "bool" ownpred nil) (unless const-decl "bool" bdUnity nil)) shostak)) (waiting_progress_lev_mu 0 (waiting_progress_lev_mu-2 nil 3678791244 ("" (skosimp) (("" (expand "ass_waiting") (("" (inst?) (("" (lemma PSP_leto) (("" (inst?) (("" (assert) (("" (hide -2) (("" (use waiting_unless) (("" (inst?) (("" (assert) (("" (hide -1) (("" (case "cap(atlev(q!1, 15, k!1), cap(leq(z!1, savf), cap(atlev(q!1, 15, k!1), mubot(path(q!1, k!1))))) = cap(leq(z!1, savf), cap(atlev(q!1, 15, k!1), mubot(path(q!1, k!1))))") (("1" (replaceh -1) (("1" (case "cup(cap(neg(mubot(path(q!1, k!1))), cap(leq(z!1, savf), cap(atlev(q!1, 15, k!1), mubot(path(q!1, k!1))))), leq(W + z!1, savf)) = leq(W + z!1, savf)") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cup") (("2" (prop) (("2" (expand "cap") (("2" (expand "neg") (("2" (prop) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (prop) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((ass_waiting const-decl "bool" tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (digit type-eq-decl nil ctrees nil) (PSP_leto formula-decl nil bdUnity nil) (int_plus_int_is_int application-judgement "int" integers nil) (waiting_unless formula-decl nil tournamentUnity1 nil) (= const-decl "[T, T -> boolean]" equalities nil) (cup const-decl "bool" ownpred nil) (cap const-decl "bool" ownpred nil) (leq const-decl "bool" bdUnity nil) (savf const-decl "int" tournamentUnity1 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (path const-decl "node" ctrees nil) (mubot const-decl "bool" tournamentUnity0 nil) (neg const-decl "bool" ownpred nil) (atlev const-decl "bool" tournamentUnity0 nil) (pred type-eq-decl nil defined_types nil) (W const-decl "posnat" tournamentUnity0 nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil)) nil) (waiting_progress_lev_mu-1 nil 3670858868 ("" (skosimp) (("" (expand "ass_waiting") (("" (inst?) (("" (lemma PSP_leto) (("" (inst?) (("" (assert) (("" (hide -2) (("" (use waiting_unless) (("" (inst?) (("" (assert) (("" (hide -1) (("" (case "cap(cap(atlev(q!1, 15, k!1), mubot(take(k!1, q!1))), cap(leq(z!1, savf), cap(atlev(q!1, 15, k!1), mubot(take(k!1, q!1))))) = cap(leq(z!1, savf), cap(atlev(q!1, 15, k!1), mubot(take(k!1, q!1))))") (("1" (replaceh -1) (("1" (case "cup(cap(neg(mubot(take(k!1, q!1))), cap(leq(z!1, savf), cap(atlev(q!1, 15, k!1), mubot(take(k!1, q!1))))), leq(W + z!1, savf)) = leq(W + z!1, savf)") (("1" (assert) nil nil) ("2" (hide - 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (expand "cup") (("2" (expand "neg") (("2" (prop) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1 2) (("2" (apply-extensionality :hide? t) (("2" (iff) (("2" (expand "cap") (("2" (prop) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((ass_waiting const-decl "bool" tournamentUnity0 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (PSP_leto formula-decl nil bdUnity nil) (int_plus_int_is_int application-judgement "int" integers nil) (waiting_unless formula-decl nil tournamentUnity1 nil) (= const-decl "[T, T -> boolean]" equalities nil) (cup const-decl "bool" ownpred nil) (leq const-decl "bool" bdUnity nil) (savf const-decl "int" tournamentUnity1 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (neg const-decl "bool" ownpred nil) (mubot const-decl "bool" tournamentUnity0 nil) (atlev const-decl "bool" tournamentUnity0 nil) (cap const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (W const-decl "posnat" tournamentUnity0 nil) (Thread type-eq-decl nil tournamentUnity0 nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (below type-eq-decl nil nat_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil)) shostak)) (waiting_progress 0 (waiting_progress-2 nil 3678791392 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - W "cap(leq(z!1, savf), only_some_waiting)" _ "leq(z!1 + W, savf)" E1) (("" (assert) (("" (hide 1) (("" (name ppset "{pp: pred[state] | EXISTS q, k: pp = cap(leq(z!1, savf), cap(atlev(q, 15, k), mubot(path(q, k)))) }") (("" (inst - "Union(ppset)") (("" (hide -1) (("" (split) (("1" (expand "<=") (("1" (expand "Union") (("1" (expand "cap") (("1" (expand "only_some_waiting") (("1" (skosimp*) (("1" (expand "E1") (("1" (hide -5) (("1" (name km "min({k | EXISTS q: s!1`pc(q) = 15 AND k = s!1`level(q) })") (("1" (typepred km) (("1" (hide -3) (("1" (skosimp) (("1" (hide -6) (("1" (inst + "cap(leq(z!1, savf), cap(atlev(q!2, 15, km), mubot(path(q!2, km))))") (("1" (expand "cap") (("1" (expand "atlev") (("1" (assert) (("1" (expand "mubot") (("1" (name-replace nn1 "path(q!2, km)" nil) (("1" (case "kq1(nn1, s!1)") (("1" (expand "kq1") (("1" (assert) (("1" (flatten) (("1" (name-replace rr "s!1`occ(nn1)") (("1" (assert) (("1" (inst -9 rr) (("1" (split) (("1" (case "iq4(rr, s!1)") (("1" (expand "iq4") (("1" (assert) nil nil)) nil) ("2" (hide-all-but (-10 1)) (("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (inst - "s!1`level(rr)") (("1" (split) (("1" (lemma depth_path) (("1" (inst - km q!2) (("1" (lift-if) (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (inst + rr) nil nil)) nil) ("2" (case "iq1(rr, s!1)") (("1" (expand "iq1") (("1" (assert) nil nil)) nil) ("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "globinv") (("2" (expand "kqall") (("2" (flatten) (("2" (inst? -9) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "ppset") (("2" (inst? +) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (expand "nonempty?") (("2" (expand "empty?") 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(("2" (replaceh -1) (("2" (use waiting_progress_lev_mu) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil) (sub_leto formula-decl nil bdUnity nil) (= const-decl "[T, T -> boolean]" equalities nil) (Thread type-eq-decl nil tournamentUnity0 nil) (atlev const-decl "bool" tournamentUnity0 nil) (mubot const-decl "bool" tournamentUnity0 nil) (path const-decl "node" ctrees nil) (leto_union formula-decl nil bdUnity nil) (waiting_progress_lev_mu formula-decl nil tournamentUnity1 nil) (Union_surjective name-judgement "(surjective?[setofsets[T], set[T]])" sets_lemmas nil) (<= const-decl "bool" mucalculus nil) (empty? 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const-decl "bool" sets nil) (setof type-eq-decl nil defined_types nil) (setofsets type-eq-decl nil sets nil) (Union const-decl "set" sets nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (only_some_waiting const-decl "bool" tournamentUnity1 nil) (savf const-decl "int" tournamentUnity1 nil) (leq const-decl "bool" bdUnity nil) (cap const-decl "bool" ownpred nil) (pred type-eq-decl nil defined_types nil) (W const-decl "posnat" tournamentUnity0 nil) (int_plus_int_is_int application-judgement "int" integers nil)) nil) (waiting_progress-1 nil 3670857837 ("" (skosimp) (("" (lemma sub_leto) (("" (inst - W "cap(leq(z!1, savf), only_some_waiting)" _ "leq(z!1 + W, savf)" E1) (("" (assert) (("" (hide 1) (("" (name ppset "{pp: pred[state] | EXISTS q, k: pp = cap(leq(z!1, savf), cap(atlev(q, 15, k), mubot(take(k, q)))) }") (("1" (inst - "Union(ppset)") (("1" (hide -1) (("1" (split) (("1" (expand "<=") (("1" (expand "Union") (("1" (expand "cap") (("1" (expand "only_some_waiting") (("1" (skosimp*) (("1" (expand "E1") (("1" (hide -5) (("1" (name km "min({k | EXISTS q: s!1`pc(q) = 15 AND k = s!1`level(q) })") (("1" (typepred km) (("1" (hide -3) (("1" (skosimp) (("1" (hide -6) (("1" (inst + "cap(leq(z!1, savf), cap(atlev(q!2, 15, km), mubot(take(km, q!2))))") (("1" (expand "cap") (("1" (expand "atlev") (("1" (assert) (("1" (expand "mubot") (("1" (name-replace nn1 "take(km, q!2)" nil) (("1" (case "kq1(nn1, s!1)") (("1" (expand "kq1") (("1" (assert) (("1" (flatten) (("1" (name-replace rr "s!1`occ(nn1)") (("1" (use level_at14_15 (q q!2)) (("1" (assert) (("1" (split) (("1" (expand "curnode") (("1" (inst -10 rr) (("1" (case "iq4(rr, s!1)") (("1" (expand "iq4") (("1" (flatten) (("1" (assert) (("1" (inst - "s!1`level(rr)") (("1" (assert) (("1" (inst + rr) nil nil)) nil) ("2" (case "iq1(rr, s!1)") (("1" (expand "iq1") (("1" (assert) nil nil)) nil) ("2" (expand "globinv") (("2" (expand "iqall") (("2" (flatten) (("2" (inst?) 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tournamentUnity1 nil) (posint_max application-judgement "{k: posint | i <= k AND j <= k}" real_defs nil) (posrat_max application-judgement "{s: posrat | s >= q AND s >= r}" real_defs nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil)) nil)) (eventual_growth_savf 0 (eventual_growth_savf-1 nil 3670997073 ("" (skosimp) (("" (use disgrowth_cover) (("" (assert) (("" (lemma distributed_progress) (("" (inst?) 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(("2" (expand "weight") (("2" (expand "maxDWE") (("2" (expand "max") (("2" (smash) nil nil)) nil)) nil)) nil)) nil)) nil) ("3" (hide - 2) (("3" (skosimp) (("3" (expand "E1") (("3" (use covering) (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((disgrowth_cover formula-decl nil tournamentUnity1 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil) (distributed_progress formula-decl nil bdUnity nil) (maxDWE const-decl "posnat" tournamentUnity1 nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil) (covering formula-decl nil tournamentUnity1 nil) (weight const-decl "posnat" tournamentUnity1 nil) (savf const-decl "int" tournamentUnity1 nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (cover const-decl "set[state]" tournamentUnity1 nil) (pred type-eq-decl nil defined_types nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (int_plus_int_is_int application-judgement "int" integers nil)) shostak)) (eventual_growth_sinc_TCC1 0 (eventual_growth_sinc_TCC1-1 nil 3671006711 ("" (subtype-tcc) nil nil) ((NOT const-decl "[bool -> bool]" booleans nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (N const-decl "posnat" tournamentSafe0 nil) (enum_thread const-decl "(bijective?[below[N], (thread)])" tournamentSafe0 nil) (inverse const-decl "D" function_inverse nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (next11 const-decl "state" tournamentSafe0 nil) (/= const-decl "boolean" notequal nil) (step11 const-decl "bool" tournamentSafe0 nil) (goto const-decl "state" tournamentSafe0 nil) (step12 const-decl "bool" tournamentSafe0 nil) (curnode const-decl "node" tournamentSafe0 nil) (curbranch const-decl "digit" tournamentSafe0 nil) (next13 const-decl "state" tournamentSafe0 nil) (step13 const-decl "bool" tournamentSafe0 nil) (next14 const-decl "state" tournamentSafe0 nil) (step14 const-decl "bool" tournamentSafe0 nil) (next15 const-decl "state" tournamentSafe0 nil) (member const-decl "bool" sets nil) (empty? const-decl "bool" sets nil) (step15F const-decl "bool" tournamentSafe0 nil) (step15G const-decl "bool" tournamentSafe0 nil) (step16 const-decl "bool" tournamentSafe0 nil) (step17 const-decl "bool" tournamentSafe0 nil) (next18 const-decl "state" tournamentSafe0 nil) (step18 const-decl "bool" tournamentSafe0 nil) (next19 const-decl "state" tournamentSafe0 nil) (step19 const-decl "bool" tournamentSafe0 nil) (step const-decl "bool" tournamentSafe0 nil) (step const-decl "bool" tournamentUnity0 nil) (iq0 const-decl "bool" tournamentSafe0 nil) (iq1 const-decl "bool" tournamentSafe0 nil) (iq2 const-decl "bool" tournamentSafe0 nil) (iq3 const-decl "bool" tournamentSafe0 nil) (iq4 const-decl "bool" tournamentSafe0 nil) (iq5 const-decl "bool" tournamentSafe0 nil) (iqall const-decl "bool" tournamentSafe0 nil) (kq0 const-decl "bool" tournamentSafe0 nil) (kq5 const-decl "bool" tournamentSafe0 nil) (kq1 const-decl "bool" tournamentSafe0 nil) (kq4 const-decl "bool" tournamentSafe0 nil) (kqall const-decl "bool" tournamentSafe0 nil) (lq2 const-decl "bool" tournamentSafe1 nil) (lq1 const-decl "bool" tournamentSafe1 nil) (lq0 const-decl "bool" tournamentSafe1 nil) (lqall const-decl "bool" tournamentSafe1 nil) (globinv const-decl "bool" tournamentSafe1 nil) (state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (exec const-decl "bool" bdUnity nil) (fullset const-decl "set" sets nil) (at const-decl "bool" tournamentUnity0 nil) (neg const-decl "bool" ownpred nil) (leto const-decl "bool" bdUnity nil) (ass_exit const-decl "bool" tournamentUnity0 nil) (ass_cs const-decl "bool" tournamentUnity0 nil) (atlev const-decl "bool" tournamentUnity0 nil) (mubot const-decl "bool" tournamentUnity0 nil) (ass_waiting const-decl "bool" tournamentUnity0 nil) (between const-decl "bool" tournamentUnity0 nil) (ass_doorway const-decl "bool" tournamentUnity0 nil) (depthnode const-decl "nat" ctrees nil) (DW1 const-decl "posnat" tournamentUnity1 nil) (exi1 const-decl "posnat" tournamentUnity0 nil) (AA const-decl "posnat" tournamentUnity1 nil) (maxDWE const-decl "posnat" tournamentUnity1 nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (even_times_int_is_even application-judgement "even_int" integers nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (posint_max application-judgement "{k: posint | i <= k AND j <= k}" real_defs nil) (posrat_max application-judgement "{s: posrat | s >= q AND s >= r}" real_defs nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil)) nil)) (eventual_growth_sinc 0 (eventual_growth_sinc-1 nil 3671006732 ("" (skosimp) (("" (lemma proportional_progress) (("" (inst - allidle "kk!1 * (AA - 1)" "neg(competing_leq(kk!1))" AA i!1 "maxDWE - 1" E1 sinc savf z!1) (("1" (assert) (("1" (hide 2) (("1" (split) (("1" (skosimp) (("1" (use eventual_growth_savf (n k!1)) (("1" (assert) nil nil)) nil)) nil) ("2" (skosimp) (("2" (expand "E1") (("2" (use savf_LWB) (("2" (assert) nil nil)) nil)) nil)) nil) ("3" (skosimp) (("3" (expand "E1") (("3" (expand "neg") (("3" (use savf_UPB) (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil) ("3" (lemma pos_times_le) (("3" (inst - "AA-1" kk!1) (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((state type-eq-decl nil tournamentSafe0 nil) (edigit type-eq-decl nil tournamentSafe0 nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (thread const-decl "finite_set[node]" tournamentSafe0 nil) (finite_set type-eq-decl nil finite_sets nil) (is_finite const-decl "bool" finite_sets nil) (set type-eq-decl nil sets nil) (digit type-eq-decl nil ctrees nil) (degree formal-const-decl "posnat" tournamentUnity1 nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (node formal-nonempty-type-decl nil tournamentUnity1 nil) (proportional_progress formula-decl nil bdUnity nil) (pos_times_le formula-decl nil real_props nil) (int_plus_int_is_int application-judgement "int" integers nil) (eventual_growth_savf formula-decl nil tournamentUnity1 nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (savf_LWB formula-decl nil tournamentUnity1 nil) (savf_UPB formula-decl nil tournamentUnity1 nil) (savf const-decl "int" tournamentUnity1 nil) (sinc const-decl "int" tournamentUnity0 nil) (E1 const-decl "specification[state]" tournamentUnity0 nil) (specification type-eq-decl nil bdUnity nil) (competing_leq const-decl "bool" tournamentUnity0 nil) (neg const-decl "bool" ownpred nil) (allidle const-decl "bool" tournamentUnity1 nil) (pred type-eq-decl nil defined_types nil) (maxDWE const-decl "posnat" tournamentUnity1 nil) (kk!1 skolem-const-decl "nat" tournamentUnity1 nil) (AA const-decl "posnat" tournamentUnity1 nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil)) shostak)))