%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET062^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:22:53 AM UTC 2026
% Result : Theorem 6.23s 2.84s
% Output : Refutation 6.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET062^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n019.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 13:36:33 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.56/1.08 % [INFO] Parsing done (292ms).
% 1.56/1.09 % [INFO] Running in sequential loop mode.
% 2.41/1.48 % [INFO] eprover registered as external prover.
% 2.41/1.48 % [INFO] Scanning for conjecture ...
% 2.81/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 45 axioms. Running axiom selection ...
% 3.01/1.75 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 3.26/1.80 % [INFO] Problem is higher-order (TPTP THF).
% 3.26/1.81 % [INFO] Type checking passed.
% 3.26/1.82 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.23/2.84 % External prover 'e' found a proof!
% 6.23/2.84 % [INFO] Killing All external provers ...
% 6.23/2.84 % Time passed: 2485ms (effective reasoning time: 1740ms)
% 6.23/2.84 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.23/2.84 % Axioms used in derivation (45): existence_of_unordered_pair_ax, union, intersection, subset_substitution_2, existence_of_singleton_ax, unordered_pair_substitution_2, intersection_substitution_2, existence_of_difference_ax, union_substitution_2, equal_set_substitution_2, singleton, a1, nonempty_ax, member_substitution_1, power_set, sum_substitution_1, unordered_pair, existence_of_product_ax, existence_of_power_set_ax, product_substitution_1, existence_of_empty_set_ax, empty_set, intersection_substitution_1, reflexivity, cumulative_ax, difference_substitution_2, subset, unordered_pair_substitution_1, equal_set, power_set_substitution_1, subset_substitution_1, equal_set_substitution_1, union_substitution_1, difference_substitution_1, existence_of_union_ax, existence_of_sum_ax, existence_of_intersection_ax, transitivity, difference, member_substitution_2, a2, sum, singleton_substitution_1, product, symmetry
% 6.23/2.84 % No. of inferences in proof: 94
% 6.23/2.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2485 ms resp. 1740 ms w/o parsing
% 6.69/2.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.69/2.98 thf(mu_type, type, mu: $tType).
% 6.69/2.98 thf(qmltpeq_decl, type, qmltpeq: (mu > (mu > ($i > $o)))).
% 6.69/2.98 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 6.69/2.98 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 6.69/2.98 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 6.69/2.98 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 6.69/2.98 thf(mequiv_decl, type, mequiv: (($i > $o) > (($i > $o) > ($i > $o)))).
% 6.69/2.98 thf(exists_in_world_decl, type, exists_in_world: (mu > ($i > $o))).
% 6.69/2.98 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 6.69/2.98 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 6.69/2.98 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 6.69/2.98 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 6.69/2.98 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 6.69/2.98 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 6.69/2.98 thf(equal_set_decl, type, equal_set: (mu > (mu > ($i > $o)))).
% 6.69/2.98 thf(member_decl, type, member: (mu > (mu > ($i > $o)))).
% 6.69/2.98 thf(subset_decl, type, subset: (mu > (mu > ($i > $o)))).
% 6.69/2.98 thf(power_set_decl, type, power_set: (mu > mu)).
% 6.69/2.98 thf(intersection_decl, type, intersection: (mu > (mu > mu))).
% 6.69/2.98 thf(union_decl, type, union: (mu > (mu > mu))).
% 6.69/2.98 thf(difference_decl, type, difference: (mu > (mu > mu))).
% 6.69/2.98 thf(singleton_decl, type, singleton: (mu > mu)).
% 6.69/2.98 thf(unordered_pair_decl, type, unordered_pair: (mu > (mu > mu))).
% 6.69/2.98 thf(sum_decl, type, sum: (mu > mu)).
% 6.69/2.98 thf(product_decl, type, product: (mu > mu)).
% 6.69/2.98 thf(empty_set_decl, type, empty_set: mu).
% 6.69/2.98 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 6.69/2.98 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 6.69/2.98 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 6.69/2.98 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 6.69/2.98 thf(mequiv_def, definition, mequiv = (^ [A:($i > $o),B:($i > $o)]: (mand @ (mimplies @ A @ B) @ (mimplies @ B @ A))) ).
% 6.69/2.98 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: ((exists_in_world @ C @ B) => (A @ C @ B))) ).
% 6.69/2.98 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 6.69/2.98 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 6.69/2.98 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 6.69/2.98 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 6.69/2.98 thf(27,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mequiv @ (equal_set @ A @ B) @ (mand @ (subset @ A @ B) @ (subset @ B @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set)).
% 6.69/2.98 thf(120,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (~ (~ (equal_set @ B @ C @ A) | ~ (~ (subset @ B @ C @ A) | ~ (subset @ C @ B @ A))) | ~ (~ (subset @ B @ C @ A) | ~ (subset @ C @ B @ A) | (equal_set @ B @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
% 6.69/2.98 thf(39,axiom,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax)).
% 6.69/2.98 thf(152,plain,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
% 6.69/2.98 thf(20,axiom,((! [A:$i]: (exists_in_world @ empty_set @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_empty_set_ax)).
% 6.69/2.98 thf(102,plain,((! [A:$i]: (exists_in_world @ empty_set @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 6.69/2.98 thf(44,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (qmltpeq @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity)).
% 6.69/2.98 thf(165,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (qmltpeq @ B @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
% 6.69/2.98 thf(8,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (difference @ A @ C) @ (difference @ B @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_substitution_1)).
% 6.69/2.98 thf(65,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (difference @ B @ D) @ (difference @ C @ D) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 6.69/2.98 thf(30,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mequiv @ (member @ A @ (unordered_pair @ B @ C)) @ (mor @ (qmltpeq @ A @ B) @ (qmltpeq @ A @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair)).
% 6.69/2.98 thf(129,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (~ (~ (member @ B @ (unordered_pair @ C @ D) @ A) | (qmltpeq @ B @ C @ A) | (qmltpeq @ B @ D @ A)) | ~ (~ ((qmltpeq @ B @ C @ A) | (qmltpeq @ B @ D @ A)) | (member @ B @ (unordered_pair @ C @ D) @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
% 6.69/2.98 thf(31,axiom,((! [A:$i,B:mu]: (exists_in_world @ (sum @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_sum_ax)).
% 6.69/2.98 thf(134,plain,((! [A:$i,B:mu]: (exists_in_world @ (sum @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 6.69/2.98 thf(26,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mnot @ (member @ A @ empty_set)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set)).
% 6.69/2.98 thf(118,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (~ (member @ B @ empty_set @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
% 6.69/2.98 thf(23,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (union @ C @ A) @ (union @ C @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2)).
% 6.69/2.98 thf(108,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (union @ D @ B) @ (union @ D @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 6.69/2.98 thf(45,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (singleton @ A) @ (singleton @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_substitution_1)).
% 6.69/2.98 thf(167,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (singleton @ B) @ (singleton @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
% 6.69/2.98 thf(25,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mequiv @ (member @ A @ (product @ B)) @ (mforall_ind @ (^ [C:mu]: (mimplies @ (member @ C @ B) @ (member @ A @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product)).
% 6.69/2.98 thf(112,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (~ (~ (member @ B @ (product @ C) @ A) | ! [D:mu]: ((exists_in_world @ D @ A) => (~ (member @ D @ C @ A) | (member @ B @ D @ A)))) | ~ (~ (! [D:mu]: ((exists_in_world @ D @ A) => (~ (member @ D @ C @ A) | (member @ B @ D @ A)))) | (member @ B @ (product @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 6.69/2.98 thf(40,axiom,((! [A:$i,B:mu]: (exists_in_world @ (product @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_product_ax)).
% 6.69/2.98 thf(154,plain,((! [A:$i,B:mu]: (exists_in_world @ (product @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
% 6.69/2.98 thf(21,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (intersection @ C @ A) @ (intersection @ C @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_2)).
% 6.69/2.98 thf(104,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (intersection @ D @ B) @ (intersection @ D @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
% 6.69/2.98 thf(47,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (difference @ C @ A) @ (difference @ C @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_substitution_2)).
% 6.69/2.98 thf(171,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (difference @ D @ B) @ (difference @ D @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
% 6.69/2.98 thf(36,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (unordered_pair @ A @ C) @ (unordered_pair @ B @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_1)).
% 6.69/2.98 thf(146,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (unordered_pair @ B @ D) @ (unordered_pair @ C @ D) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
% 6.69/2.98 thf(43,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (qmltpeq @ B @ C)) @ (qmltpeq @ A @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity)).
% 6.69/2.98 thf(163,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (qmltpeq @ C @ D @ A) | (qmltpeq @ B @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
% 6.69/2.98 thf(17,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mequiv @ (member @ A @ (singleton @ B)) @ (qmltpeq @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
% 6.69/2.98 thf(90,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (~ (~ (member @ B @ (singleton @ C) @ A) | (qmltpeq @ B @ C @ A)) | ~ (~ (qmltpeq @ B @ C @ A) | (member @ B @ (singleton @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 6.69/2.98 thf(10,axiom,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (unordered_pair @ B @ C) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_unordered_pair_ax)).
% 6.69/2.98 thf(69,plain,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (unordered_pair @ B @ C) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 6.69/2.98 thf(33,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mequiv @ (member @ A @ (power_set @ B)) @ (subset @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set)).
% 6.69/2.98 thf(138,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (~ (~ (member @ B @ (power_set @ C) @ A) | (subset @ B @ C @ A)) | ~ (~ (subset @ B @ C @ A) | (member @ B @ (power_set @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
% 6.69/2.98 thf(16,axiom,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (union @ B @ C) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_union_ax)).
% 6.69/2.98 thf(88,plain,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (union @ B @ C) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 6.69/2.98 thf(5,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (power_set @ A) @ (power_set @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set_substitution_1)).
% 6.69/2.98 thf(56,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (power_set @ B) @ (power_set @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 6.69/2.98 thf(34,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ B @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry)).
% 6.69/2.98 thf(142,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ C @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
% 6.69/2.98 thf(3,axiom,((mtransitive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 6.69/2.98 thf(52,plain,((! [A:$i,B:$i,C:$i]: (((rel_s4 @ A @ B) & (rel_s4 @ B @ C)) => (rel_s4 @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 6.69/2.98 thf(24,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (intersection @ A @ C) @ (intersection @ B @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_1)).
% 6.69/2.98 thf(110,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (intersection @ B @ D) @ (intersection @ C @ D) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 6.69/2.98 thf(28,axiom,((! [A:$i,B:mu]: (exists_in_world @ (power_set @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_power_set_ax)).
% 6.69/2.98 thf(125,plain,((! [A:$i,B:mu]: (exists_in_world @ (power_set @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
% 6.69/2.98 thf(22,axiom,((! [A:$i,B:mu]: (exists_in_world @ (singleton @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_singleton_ax)).
% 6.69/2.98 thf(106,plain,((! [A:$i,B:mu]: (exists_in_world @ (singleton @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 6.69/2.98 thf(14,axiom,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax)).
% 6.69/2.98 thf(84,plain,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 6.69/2.98 thf(41,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mequiv @ (member @ A @ (union @ B @ C)) @ (mor @ (member @ A @ B) @ (member @ A @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union)).
% 6.69/2.98 thf(156,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (~ (~ (member @ B @ (union @ C @ D) @ A) | (member @ B @ C @ A) | (member @ B @ D @ A)) | ~ (~ ((member @ B @ C @ A) | (member @ B @ D @ A)) | (member @ B @ (union @ C @ D) @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
% 6.69/2.98 thf(46,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (unordered_pair @ C @ A) @ (unordered_pair @ C @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_2)).
% 6.69/2.98 thf(169,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (unordered_pair @ D @ B) @ (unordered_pair @ D @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
% 6.69/2.98 thf(12,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mequiv @ (member @ A @ (difference @ C @ B)) @ (mand @ (member @ A @ C) @ (mnot @ (member @ A @ B)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference)).
% 6.69/2.98 thf(77,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (~ (~ (member @ B @ (difference @ D @ C) @ A) | ~ (~ (member @ B @ D @ A) | (member @ B @ C @ A))) | ~ (~ (member @ B @ D @ A) | (member @ B @ C @ A) | (member @ B @ (difference @ D @ C) @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 6.69/2.98 thf(19,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mequiv @ (subset @ A @ B) @ (mforall_ind @ (^ [C:mu]: (mimplies @ (member @ C @ A) @ (member @ C @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset)).
% 6.69/2.98 thf(96,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (~ (~ (subset @ B @ C @ A) | ! [D:mu]: ((exists_in_world @ D @ A) => (~ (member @ D @ B @ A) | (member @ D @ C @ A)))) | ~ (~ (! [D:mu]: ((exists_in_world @ D @ A) => (~ (member @ D @ B @ A) | (member @ D @ C @ A)))) | (subset @ B @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 6.69/2.98 thf(37,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (member @ C @ A)) @ (member @ C @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2)).
% 6.69/2.98 thf(148,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (member @ D @ B @ A) | (member @ D @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
% 6.69/2.98 thf(42,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (subset @ C @ A)) @ (subset @ C @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_2)).
% 6.69/2.98 thf(161,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (subset @ D @ B @ A) | (subset @ D @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
% 6.69/2.98 thf(11,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mequiv @ (member @ A @ (sum @ B)) @ (mexists_ind @ (^ [C:mu]: (mand @ (member @ C @ B) @ (member @ A @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum)).
% 6.69/2.98 thf(71,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (~ (~ (member @ B @ (sum @ C) @ A) | ~ (! [D:mu]: ((exists_in_world @ D @ A) => (~ (member @ D @ C @ A) | ~ (member @ B @ D @ A))))) | ~ (! [D:mu]: ((exists_in_world @ D @ A) => (~ (member @ D @ C @ A) | ~ (member @ B @ D @ A))) | (member @ B @ (sum @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 6.69/2.98 thf(4,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 6.69/2.98 thf(54,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 6.69/2.98 thf(35,axiom,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (difference @ B @ C) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_difference_ax)).
% 6.69/2.98 thf(144,plain,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (difference @ B @ C) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
% 6.69/2.98 thf(15,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (product @ A) @ (product @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution_1)).
% 6.69/2.98 thf(86,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (product @ B) @ (product @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 6.69/2.98 thf(1,conjecture,((mvalid @ (mforall_ind @ (subset @ empty_set)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI15)).
% 6.69/2.98 thf(2,negated_conjecture,((~ (mvalid @ (mforall_ind @ (subset @ empty_set))))),inference(neg_conjecture,[status(cth)],[1])).
% 6.69/2.98 thf(48,plain,((~ (! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (subset @ empty_set @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 6.69/2.98 thf(7,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (equal_set @ A @ C)) @ (equal_set @ B @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_substitution_1)).
% 6.69/2.98 thf(63,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (equal_set @ B @ D @ A) | (equal_set @ C @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 6.69/2.98 thf(38,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (equal_set @ C @ A)) @ (equal_set @ C @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_substitution_2)).
% 6.69/2.98 thf(150,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (equal_set @ D @ B @ A) | (equal_set @ D @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
% 6.69/2.98 thf(9,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (union @ A @ C) @ (union @ B @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1)).
% 6.69/2.98 thf(67,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (union @ B @ D) @ (union @ C @ D) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 6.69/2.98 thf(29,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (member @ A @ C)) @ (member @ B @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1)).
% 6.69/2.98 thf(127,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (member @ B @ D @ A) | (member @ C @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
% 6.69/2.98 thf(6,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mequiv @ (member @ A @ (intersection @ B @ C)) @ (mand @ (member @ A @ B) @ (member @ A @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection)).
% 6.69/2.98 thf(58,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (~ (~ (member @ B @ (intersection @ C @ D) @ A) | ~ (~ (member @ B @ C @ A) | ~ (member @ B @ D @ A))) | ~ (~ (member @ B @ C @ A) | ~ (member @ B @ D @ A) | (member @ B @ (intersection @ C @ D) @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 6.69/2.98 thf(13,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (sum @ A) @ (sum @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution_1)).
% 6.69/2.98 thf(82,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (sum @ B) @ (sum @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 6.69/2.98 thf(32,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (subset @ A @ C)) @ (subset @ B @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_1)).
% 6.69/2.98 thf(136,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (subset @ B @ D @ A) | (subset @ C @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
% 6.69/2.98 thf(18,axiom,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (intersection @ B @ C) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_intersection_ax)).
% 6.69/2.98 thf(94,plain,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (intersection @ B @ C) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 6.69/2.98 thf(173,plain,(($false)),inference(e,[status(thm)],[120,152,102,165,65,129,134,118,108,167,112,154,104,171,146,163,90,69,138,88,56,142,52,110,125,106,84,156,169,77,96,148,161,71,54,144,86,48,63,150,67,127,58,82,136,94])).
% 6.69/2.98 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.69/2.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------