%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET907^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 08:23:08 AM UTC 2026
% Result : Theorem 8.16s 3.40s
% Output : Refutation 8.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET907^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n020.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:41:49 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.14/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.98/1.37 % [INFO] Parsing done (342ms).
% 1.98/1.38 % [INFO] Running in sequential loop mode.
% 3.23/1.75 % [INFO] eprover registered as external prover.
% 3.23/1.76 % [INFO] Scanning for conjecture ...
% 3.71/2.01 % [INFO] Found a conjecture (or negated_conjecture) and 29 axioms. Running axiom selection ...
% 4.06/2.13 % [INFO] Axiom selection finished. Selected 29 axioms (removed 0 axioms).
% 4.30/2.19 % [INFO] Problem is higher-order (TPTP THF).
% 4.44/2.20 % [INFO] Type checking passed.
% 4.44/2.21 % [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 ...
% 7.68/3.39 % External prover 'e' found a proof!
% 7.68/3.39 % [INFO] Killing All external provers ...
% 7.68/3.39 % Time passed: 3002ms (effective reasoning time: 2007ms)
% 7.68/3.39 % 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)>
% 7.68/3.40 % Axioms used in derivation (29): in_substitution_2, existence_of_unordered_pair_ax, empty_substitution_1, set_union2_substitution_2, subset_substitution_2, commutativity_k2_xboole_0, unordered_pair_substitution_2, set_union2_substitution_1, fc3_xboole_0, reflexivity_r1_tarski, t12_xboole_1, fc2_xboole_0, existence_of_set_union2_ax, reflexivity, cumulative_ax, unordered_pair_substitution_1, commutativity_k2_tarski, subset_substitution_1, t38_zfmisc_1, in_substitution_1, a1, nonempty_ax, rc1_xboole_0, idempotence_k2_xboole_0, transitivity, a2, rc2_xboole_0, antisymmetry_r2_hidden, symmetry
% 7.68/3.40 % No. of inferences in proof: 62
% 8.16/3.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3002 ms resp. 2007 ms w/o parsing
% 8.57/3.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.57/3.59 thf(mu_type, type, mu: $tType).
% 8.57/3.59 thf(qmltpeq_decl, type, qmltpeq: (mu > (mu > ($i > $o)))).
% 8.57/3.59 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 8.57/3.59 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 8.57/3.59 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 8.57/3.59 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 8.57/3.59 thf(mequiv_decl, type, mequiv: (($i > $o) > (($i > $o) > ($i > $o)))).
% 8.57/3.59 thf(exists_in_world_decl, type, exists_in_world: (mu > ($i > $o))).
% 8.57/3.59 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 8.57/3.59 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 8.57/3.59 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 8.57/3.59 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 8.57/3.59 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 8.57/3.59 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 8.57/3.59 thf(empty_decl, type, empty: (mu > ($i > $o))).
% 8.57/3.59 thf(subset_decl, type, subset: (mu > (mu > ($i > $o)))).
% 8.57/3.59 thf(in_decl, type, in: (mu > (mu > ($i > $o)))).
% 8.57/3.59 thf(unordered_pair_decl, type, unordered_pair: (mu > (mu > mu))).
% 8.57/3.59 thf(set_union2_decl, type, set_union2: (mu > (mu > mu))).
% 8.57/3.59 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 8.57/3.59 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 8.57/3.59 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 8.57/3.59 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 8.57/3.59 thf(mequiv_def, definition, mequiv = (^ [A:($i > $o),B:($i > $o)]: (mand @ (mimplies @ A @ B) @ (mimplies @ B @ A))) ).
% 8.57/3.59 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: ((exists_in_world @ C @ B) => (A @ C @ B))) ).
% 8.57/3.59 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 8.57/3.59 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 8.57/3.59 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 8.57/3.59 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 8.57/3.59 thf(4,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 8.57/3.59 thf(42,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 8.57/3.59 thf(21,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (qmltpeq @ (set_union2 @ A @ B) @ (set_union2 @ B @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0)).
% 8.57/3.59 thf(84,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (qmltpeq @ (set_union2 @ B @ C) @ (set_union2 @ C @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
% 8.57/3.59 thf(11,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (empty @ A)) @ (empty @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_substitution_1)).
% 8.57/3.59 thf(60,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (empty @ B @ A) | (empty @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 8.57/3.59 thf(26,axiom,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (unordered_pair @ B @ C) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_unordered_pair_ax)).
% 8.57/3.59 thf(97,plain,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (unordered_pair @ B @ C) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
% 8.57/3.59 thf(9,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (in @ C @ A)) @ (in @ C @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_2)).
% 8.57/3.59 thf(53,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (in @ D @ B @ A) | (in @ D @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 8.57/3.59 thf(5,axiom,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax)).
% 8.57/3.59 thf(44,plain,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 8.57/3.59 thf(17,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (set_union2 @ C @ A) @ (set_union2 @ C @ B))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_union2_substitution_2)).
% 8.57/3.59 thf(76,plain,((! [A:$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 @ (set_union2 @ D @ B) @ (set_union2 @ D @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 8.57/3.59 thf(19,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (qmltpeq @ (unordered_pair @ A @ B) @ (unordered_pair @ B @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski)).
% 8.57/3.59 thf(80,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (qmltpeq @ (unordered_pair @ B @ C) @ (unordered_pair @ C @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 8.57/3.59 thf(25,axiom,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (set_union2 @ B @ C) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_set_union2_ax)).
% 8.57/3.59 thf(95,plain,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (set_union2 @ B @ C) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 8.57/3.59 thf(27,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (in @ A @ C)) @ (in @ B @ C)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_1)).
% 8.57/3.59 thf(99,plain,((! [A:$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) | ~ (in @ B @ D @ A) | (in @ C @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
% 8.57/3.59 thf(20,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/sandbox/benchmark/theBenchmark.p',unordered_pair_substitution_2)).
% 8.57/3.59 thf(82,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (unordered_pair @ D @ B) @ (unordered_pair @ D @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 8.57/3.59 thf(8,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (in @ A @ B) @ (mnot @ (in @ B @ A))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden)).
% 8.57/3.59 thf(51,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (in @ B @ C @ A) | ~ (in @ C @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 8.57/3.59 thf(31,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (qmltpeq @ A @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity)).
% 8.57/3.59 thf(107,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (qmltpeq @ B @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 8.57/3.59 thf(24,axiom,((mvalid @ (mexists_ind @ (empty)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0)).
% 8.57/3.59 thf(90,plain,((! [A:$i]: ~ (! [B:mu]: ((exists_in_world @ B @ A) => (~ (empty @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 8.57/3.59 thf(28,axiom,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',cumulative_ax)).
% 8.57/3.59 thf(101,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)],[28])).
% 8.57/3.59 thf(23,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/sandbox/benchmark/theBenchmark.p',unordered_pair_substitution_1)).
% 8.57/3.59 thf(88,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (unordered_pair @ B @ D) @ (unordered_pair @ C @ D) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 8.57/3.59 thf(6,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (subset @ A @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski)).
% 8.57/3.59 thf(46,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (subset @ B @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 8.57/3.59 thf(18,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/sandbox/benchmark/theBenchmark.p',subset_substitution_1)).
% 8.57/3.59 thf(78,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (subset @ B @ D @ A) | (subset @ C @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 8.57/3.59 thf(16,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (qmltpeq @ (set_union2 @ A @ A) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0)).
% 8.57/3.59 thf(73,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (qmltpeq @ (set_union2 @ B @ B) @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 8.57/3.59 thf(30,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/sandbox/benchmark/theBenchmark.p',transitivity)).
% 8.57/3.59 thf(105,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (qmltpeq @ C @ D @ A) | (qmltpeq @ B @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
% 8.57/3.59 thf(1,conjecture,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (in @ A @ B) @ (in @ C @ B)) @ (qmltpeq @ (set_union2 @ (unordered_pair @ A @ C) @ B) @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1)).
% 8.57/3.59 thf(2,negated_conjecture,((~ (mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (in @ A @ B) @ (in @ C @ B)) @ (qmltpeq @ (set_union2 @ (unordered_pair @ A @ C) @ B) @ B))))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 8.57/3.59 thf(32,plain,((~ (! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (in @ B @ C @ A) | ~ (in @ D @ C @ A) | (qmltpeq @ (set_union2 @ (unordered_pair @ B @ D) @ C) @ C @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 8.57/3.59 thf(13,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (set_union2 @ A @ C) @ (set_union2 @ B @ C))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_union2_substitution_1)).
% 8.57/3.59 thf(64,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (set_union2 @ B @ D) @ (set_union2 @ C @ D) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 8.57/3.59 thf(7,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mnot @ (empty @ A)) @ (mnot @ (empty @ (set_union2 @ A @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0)).
% 8.57/3.59 thf(49,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => ((empty @ B @ A) | ~ (empty @ (set_union2 @ B @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 8.57/3.59 thf(22,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ B @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry)).
% 8.57/3.59 thf(86,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ C @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 8.57/3.59 thf(29,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (subset @ A @ B) @ (qmltpeq @ (set_union2 @ A @ B) @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1)).
% 8.57/3.59 thf(103,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (subset @ B @ C @ A) | (qmltpeq @ (set_union2 @ B @ C) @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
% 8.57/3.59 thf(14,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mnot @ (empty @ A)) @ (mnot @ (empty @ (set_union2 @ B @ A)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0)).
% 8.57/3.59 thf(66,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => ((empty @ B @ A) | ~ (empty @ (set_union2 @ C @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 8.57/3.59 thf(3,axiom,((mtransitive @ rel_s4)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 8.57/3.59 thf(40,plain,((! [A:$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])).
% 8.57/3.59 thf(10,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mequiv @ (subset @ (unordered_pair @ A @ B) @ C) @ (mand @ (in @ A @ C) @ (in @ B @ C))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1)).
% 8.57/3.59 thf(55,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (~ (~ (subset @ (unordered_pair @ B @ C) @ D @ A) | ~ (~ (in @ B @ D @ A) | ~ (in @ C @ D @ A))) | ~ (~ (in @ B @ D @ A) | ~ (in @ C @ D @ A) | (subset @ (unordered_pair @ B @ C) @ D @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 8.57/3.59 thf(15,axiom,((mvalid @ (mexists_ind @ (^ [A:mu]: (mnot @ (empty @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0)).
% 8.57/3.59 thf(68,plain,((! [A:$i]: ~ (! [B:mu]: ((exists_in_world @ B @ A) => (empty @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 8.57/3.59 thf(12,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/sandbox/benchmark/theBenchmark.p',subset_substitution_2)).
% 8.57/3.59 thf(62,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (subset @ D @ B @ A) | (subset @ D @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 8.57/3.59 thf(109,plain,(($false)),inference(e,[status(thm)],[42,84,60,97,53,44,76,80,95,99,82,51,107,90,101,88,46,78,73,105,32,64,49,86,103,66,40,55,68,62])).
% 8.57/3.59 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.57/3.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------