%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET914^7 : 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 : n008.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 16.56s 4.75s
% Output : Refutation 15.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET914^7 : 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 : n008.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 13:41:39 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 1.04/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.12 % [INFO] Parsing done (308ms).
% 2.05/1.13 % [INFO] Running in sequential loop mode.
% 2.69/1.53 % [INFO] eprover registered as external prover.
% 2.69/1.54 % [INFO] Scanning for conjecture ...
% 3.12/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 31 axioms. Running axiom selection ...
% 3.31/1.82 % [INFO] Axiom selection finished. Selected 31 axioms (removed 0 axioms).
% 3.31/1.86 % [INFO] Problem is higher-order (TPTP THF).
% 3.31/1.86 % [INFO] Type checking passed.
% 3.31/1.87 % [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 ...
% 16.56/4.75 % External prover 'e' found a proof!
% 16.56/4.75 % [INFO] Killing All external provers ...
% 16.56/4.75 % Time passed: 4389ms (effective reasoning time: 3608ms)
% 16.56/4.75 % 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)>
% 16.56/4.75 % Axioms used in derivation (31): in_substitution_2, idempotence_k3_xboole_0, existence_of_empty_set_ax, disjoint_substitution_2, commutativity_k3_xboole_0, d2_tarski, d1_xboole_0, unordered_pair_substitution_2, d7_xboole_0, set_intersection2_substitution_1, symmetry_r1_xboole_0, transitivity, fc1_xboole_0, existence_of_unordered_pair_ax, empty_substitution_1, existence_of_set_intersection2_ax, disjoint_substitution_1, set_intersection2_substitution_2, reflexivity, cumulative_ax, unordered_pair_substitution_1, commutativity_k2_tarski, in_substitution_1, a1, nonempty_ax, rc1_xboole_0, a2, rc2_xboole_0, d3_xboole_0, antisymmetry_r2_hidden, symmetry
% 16.56/4.75 % No. of inferences in proof: 146
% 16.56/4.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4389 ms resp. 3608 ms w/o parsing
% 15.19/4.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.19/4.82 thf(mu_type, type, mu: $tType).
% 15.19/4.82 thf(qmltpeq_decl, type, qmltpeq: (mu > (mu > ($i > $o)))).
% 15.19/4.82 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 15.19/4.82 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 15.19/4.82 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 15.19/4.82 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 15.19/4.82 thf(mequiv_decl, type, mequiv: (($i > $o) > (($i > $o) > ($i > $o)))).
% 15.19/4.82 thf(exists_in_world_decl, type, exists_in_world: (mu > ($i > $o))).
% 15.19/4.82 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 15.19/4.82 thf(mexists_ind_decl, type, mexists_ind: ((mu > ($i > $o)) > ($i > $o))).
% 15.19/4.82 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 15.19/4.82 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 15.19/4.82 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 15.19/4.82 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 15.19/4.82 thf(empty_decl, type, empty: (mu > ($i > $o))).
% 15.19/4.82 thf(in_decl, type, in: (mu > (mu > ($i > $o)))).
% 15.19/4.82 thf(disjoint_decl, type, disjoint: (mu > (mu > ($i > $o)))).
% 15.19/4.82 thf(empty_set_decl, type, empty_set: mu).
% 15.19/4.82 thf(set_intersection2_decl, type, set_intersection2: (mu > (mu > mu))).
% 15.19/4.82 thf(unordered_pair_decl, type, unordered_pair: (mu > (mu > mu))).
% 15.19/4.82 thf(sk1_decl, type, sk1: $i).
% 15.19/4.82 thf(sk2_decl, type, sk2: mu).
% 15.19/4.82 thf(sk3_decl, type, sk3: mu).
% 15.19/4.82 thf(sk4_decl, type, sk4: mu).
% 15.19/4.82 thf(sk5_decl, type, sk5: (mu > ($i > mu))).
% 15.19/4.82 thf(sk8_decl, type, sk8: ($i > mu)).
% 15.19/4.82 thf(sk9_decl, type, sk9: ($i > mu)).
% 15.19/4.82 thf(sk12_decl, type, sk12: ($i > mu)).
% 15.19/4.82 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 15.19/4.82 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 15.19/4.82 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 15.19/4.82 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 15.19/4.82 thf(mequiv_def, definition, mequiv = (^ [A:($i > $o),B:($i > $o)]: (mand @ (mimplies @ A @ B) @ (mimplies @ B @ A))) ).
% 15.19/4.82 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: ((exists_in_world @ C @ B) => (A @ C @ B))) ).
% 15.19/4.82 thf(mexists_ind_def, definition, mexists_ind = (^ [A:(mu > ($i > $o))]: (mnot @ (mforall_ind @ (^ [B:mu]: (mnot @ (A @ B)))))) ).
% 15.19/4.82 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 15.19/4.82 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 15.19/4.82 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 15.19/4.82 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ~ (! [B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (disjoint @ (unordered_pair @ B @ C) @ D @ A) | ~ (in @ B @ D @ A))))))))) ).
% 15.19/4.82 thf(sk2_def, definition, sk2 = (@+ [A:mu]: ~ ((exists_in_world @ A @ sk1) => (! [B:mu]: ((exists_in_world @ B @ sk1) => (! [C:mu]: ((exists_in_world @ C @ sk1) => (~ (disjoint @ (unordered_pair @ A @ B) @ C @ sk1) | ~ (in @ A @ C @ sk1)))))))) ).
% 15.19/4.82 thf(sk3_def, definition, sk3 = (@+ [A:mu]: ~ ((exists_in_world @ A @ sk1) => (! [B:mu]: ((exists_in_world @ B @ sk1) => (~ (disjoint @ (unordered_pair @ sk2 @ A) @ B @ sk1) | ~ (in @ sk2 @ B @ sk1)))))) ).
% 15.19/4.82 thf(sk4_def, definition, sk4 = (@+ [A:mu]: ~ ((exists_in_world @ A @ sk1) => (~ (disjoint @ (unordered_pair @ sk2 @ sk3) @ A @ sk1) | ~ (in @ sk2 @ A @ sk1)))) ).
% 15.19/4.82 thf(sk5_def, definition, sk5 = (^ [A:mu,B:$i]: (@+ [C:mu]: ~ ((exists_in_world @ C @ B) => (~ (in @ C @ A @ B))))) ).
% 15.19/4.82 thf(sk8_def, definition, sk8 = (^ [A:$i]: (@+ [B:mu]: ~ ((exists_in_world @ B @ A) => (~ (empty @ B @ A))))) ).
% 15.19/4.82 thf(sk9_def, definition, sk9 = (^ [A:$i]: (@+ [B:mu]: (exists_in_world @ B @ A))) ).
% 15.19/4.82 thf(sk12_def, definition, sk12 = (^ [A:$i]: (@+ [B:mu]: ~ ((exists_in_world @ B @ A) => (empty @ B @ A)))) ).
% 15.19/4.82 thf(26,axiom,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax)).
% 15.19/4.82 thf(103,plain,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
% 15.19/4.82 thf(104,plain,(! [A:$i] : ((exists_in_world @ (sk9 @ A) @ A))),inference(cnf,[status(esa)],[103])).
% 15.19/4.82 thf(1,conjecture,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mnot @ (mand @ (disjoint @ (unordered_pair @ A @ B) @ C) @ (in @ A @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1)).
% 15.19/4.82 thf(2,negated_conjecture,((~ (mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mnot @ (mand @ (disjoint @ (unordered_pair @ A @ B) @ C) @ (in @ A @ C)))))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 15.19/4.82 thf(34,plain,((~ (! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (disjoint @ (unordered_pair @ B @ C) @ D @ A) | ~ (in @ B @ D @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 15.19/4.82 thf(35,plain,(((exists_in_world @ sk2 @ sk1) & (exists_in_world @ sk3 @ sk1) & (exists_in_world @ sk4 @ sk1) & (disjoint @ (unordered_pair @ sk2 @ sk3) @ sk4 @ sk1) & (in @ sk2 @ sk4 @ sk1))),inference(cnf,[status(esa)],[34])).
% 15.19/4.82 thf(40,plain,((exists_in_world @ sk2 @ sk1)),inference(cnfConj,[status(thm)],[35])).
% 15.19/4.82 thf(9,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mequiv @ (qmltpeq @ A @ empty_set) @ (mforall_ind @ (^ [B:mu]: (mnot @ (in @ B @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0)).
% 15.19/4.82 thf(53,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (~ (~ (~ (qmltpeq @ B @ empty_set @ A) | ! [C:mu]: ((exists_in_world @ C @ A) => (~ (in @ C @ B @ A)))) | ~ (~ (! [C:mu]: ((exists_in_world @ C @ A) => (~ (in @ C @ B @ A)))) | (qmltpeq @ B @ empty_set @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 15.19/4.82 thf(54,plain,(! [C:mu,B:mu,A:$i] : (((~ (exists_in_world @ B @ A) | ~ (qmltpeq @ B @ empty_set @ A) | ~ (exists_in_world @ C @ A) | ~ (in @ C @ B @ A)) & (~ (exists_in_world @ B @ A) | (exists_in_world @ (sk5 @ B @ A) @ A) | (qmltpeq @ B @ empty_set @ A)) & (~ (exists_in_world @ B @ A) | (in @ (sk5 @ B @ A) @ B @ A) | (qmltpeq @ B @ empty_set @ A))))),inference(cnf,[status(esa)],[53])).
% 15.19/4.82 thf(55,plain,(! [C:mu,B:mu,A:$i] : ((~ (exists_in_world @ B @ A)) | (~ (qmltpeq @ B @ empty_set @ A)) | (~ (exists_in_world @ C @ A)) | (~ (in @ C @ B @ A)))),inference(cnfConj,[status(thm)],[54])).
% 15.19/4.82 thf(148,plain,(! [C:mu,B:mu,A:$i] : (~ (($true)) | (~ (qmltpeq @ B @ empty_set @ A)) | (~ (exists_in_world @ C @ A)) | (~ (in @ C @ B @ A)) | ((exists_in_world @ sk2 @ sk1) != (exists_in_world @ B @ A)))),inference(paramod_ordered,[status(thm)],[40,55])).
% 15.19/4.82 thf(149,plain,(! [C:mu,B:mu,A:$i] : ((~ (qmltpeq @ B @ empty_set @ A)) | (~ (exists_in_world @ C @ A)) | (~ (in @ C @ B @ A)) | ((exists_in_world @ sk2 @ sk1) != (exists_in_world @ B @ A)))),inference(simp,[status(thm)],[148])).
% 15.19/4.82 thf(150,plain,(! [A:mu] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (exists_in_world @ A @ sk1)) | (~ (in @ A @ sk2 @ sk1)))),inference(pattern_uni,[status(thm)],[149:[bind(A, $thf(sk1)),bind(B, $thf(sk2))]])).
% 15.19/4.82 thf(155,plain,(! [A:mu] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (exists_in_world @ A @ sk1)) | (~ (in @ A @ sk2 @ sk1)))),inference(simp,[status(thm)],[150])).
% 15.19/4.82 thf(245,plain,(! [B:mu,A:$i] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | ~ (($true)) | (~ (in @ B @ sk2 @ sk1)) | ((exists_in_world @ (sk9 @ A) @ A) != (exists_in_world @ B @ sk1)))),inference(paramod_ordered,[status(thm)],[104,155])).
% 15.19/4.82 thf(246,plain,(! [B:mu,A:$i] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ B @ sk2 @ sk1)) | ((exists_in_world @ (sk9 @ A) @ A) != (exists_in_world @ B @ sk1)))),inference(simp,[status(thm)],[245])).
% 15.19/4.82 thf(247,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ (sk9 @ sk1) @ sk2 @ sk1))),inference(pattern_uni,[status(thm)],[246:[bind(A, $thf(sk1)),bind(B, $thf(sk9 @ sk1))]])).
% 15.19/4.82 thf(56,plain,(! [B:mu,A:$i] : ((~ (exists_in_world @ B @ A)) | (exists_in_world @ (sk5 @ B @ A) @ A) | (qmltpeq @ B @ empty_set @ A))),inference(cnfConj,[status(thm)],[54])).
% 15.19/4.82 thf(5,axiom,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (set_intersection2 @ B @ C) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_set_intersection2_ax)).
% 15.19/4.82 thf(45,plain,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (set_intersection2 @ B @ C) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 15.19/4.82 thf(46,plain,(! [C:mu,B:mu,A:$i] : ((exists_in_world @ (set_intersection2 @ B @ C) @ A))),inference(cnf,[status(esa)],[45])).
% 15.19/4.82 thf(11,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (qmltpeq @ (set_intersection2 @ A @ B) @ (set_intersection2 @ B @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0)).
% 15.19/4.82 thf(60,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (qmltpeq @ (set_intersection2 @ B @ C) @ (set_intersection2 @ C @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 15.19/4.82 thf(38,plain,((disjoint @ (unordered_pair @ sk2 @ sk3) @ sk4 @ sk1)),inference(cnfConj,[status(thm)],[35])).
% 15.19/4.82 thf(22,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)).
% 15.19/4.82 thf(92,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ C @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 15.19/4.82 thf(39,plain,((exists_in_world @ sk3 @ sk1)),inference(cnfConj,[status(thm)],[35])).
% 15.19/4.82 thf(165,plain,(! [A:mu] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | ~ (($true)) | (~ (in @ A @ sk2 @ sk1)) | ((exists_in_world @ sk3 @ sk1) != (exists_in_world @ A @ sk1)))),inference(paramod_ordered,[status(thm)],[39,155])).
% 15.19/4.82 thf(166,plain,(! [A:mu] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ A @ sk2 @ sk1)) | ((exists_in_world @ sk3 @ sk1) != (exists_in_world @ A @ sk1)))),inference(simp,[status(thm)],[165])).
% 15.19/4.82 thf(167,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ sk3 @ sk2 @ sk1))),inference(pattern_uni,[status(thm)],[166:[bind(A, $thf(sk3))]])).
% 15.19/4.82 thf(36,plain,((in @ sk2 @ sk4 @ sk1)),inference(cnfConj,[status(thm)],[35])).
% 15.19/4.82 thf(37,plain,((exists_in_world @ sk4 @ sk1)),inference(cnfConj,[status(thm)],[35])).
% 15.19/4.82 thf(162,plain,(! [A:mu] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | ~ (($true)) | (~ (in @ A @ sk2 @ sk1)) | ((exists_in_world @ sk4 @ sk1) != (exists_in_world @ A @ sk1)))),inference(paramod_ordered,[status(thm)],[37,155])).
% 15.19/4.82 thf(163,plain,(! [A:mu] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ A @ sk2 @ sk1)) | ((exists_in_world @ sk4 @ sk1) != (exists_in_world @ A @ sk1)))),inference(simp,[status(thm)],[162])).
% 15.19/4.82 thf(164,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ sk4 @ sk2 @ sk1))),inference(pattern_uni,[status(thm)],[163:[bind(A, $thf(sk4))]])).
% 15.19/4.82 thf(206,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | ~ (($true)) | ((in @ sk4 @ sk2 @ sk1) != (in @ sk2 @ sk4 @ sk1))),inference(paramod_ordered,[status(thm)],[36,164])).
% 15.19/4.82 thf(207,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | ((in @ sk4 @ sk2 @ sk1) != (in @ sk2 @ sk4 @ sk1))),inference(simp,[status(thm)],[206])).
% 15.19/4.82 thf(208,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (sk4 != sk2) | (sk4 != sk2) | (sk1 != sk1)),inference(simp,[status(thm)],[207])).
% 15.19/4.82 thf(209,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (sk4 != sk2)),inference(simp,[status(thm)],[208])).
% 15.19/4.82 thf(6,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (set_intersection2 @ A @ C) @ (set_intersection2 @ B @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_intersection2_substitution_1)).
% 15.19/4.82 thf(47,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (set_intersection2 @ B @ D) @ (set_intersection2 @ C @ D) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 15.19/4.82 thf(48,plain,(! [D:mu,C:mu,B:mu,A:$i] : ((~ (exists_in_world @ B @ A)) | (~ (exists_in_world @ C @ A)) | (~ (exists_in_world @ D @ A)) | (~ (qmltpeq @ B @ C @ A)) | (qmltpeq @ (set_intersection2 @ B @ D) @ (set_intersection2 @ C @ D) @ A))),inference(cnf,[status(esa)],[47])).
% 15.19/4.82 thf(4,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 15.19/4.82 thf(43,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 15.19/4.82 thf(23,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (unordered_pair @ A @ C) @ (unordered_pair @ B @ C))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_1)).
% 15.19/4.82 thf(94,plain,((! [A:$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])).
% 15.19/4.82 thf(25,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/sandbox2/benchmark/theBenchmark.p',in_substitution_1)).
% 15.19/4.82 thf(101,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (in @ B @ D @ A) | (in @ C @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 15.19/4.82 thf(20,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (disjoint @ C @ A)) @ (disjoint @ C @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_substitution_2)).
% 15.19/4.82 thf(88,plain,((! [A:$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) | ~ (disjoint @ D @ B @ A) | (disjoint @ D @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 15.19/4.82 thf(3,axiom,((mtransitive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 15.19/4.82 thf(41,plain,((! [A:$i,B:$i,C:$i]: (((rel_s4 @ A @ B) & (rel_s4 @ B @ C)) => (rel_s4 @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 15.19/4.82 thf(42,plain,(! [C:$i,B:$i,A:$i] : ((~ (rel_s4 @ A @ B)) | (~ (rel_s4 @ B @ C)) | (rel_s4 @ A @ C))),inference(cnf,[status(esa)],[41])).
% 15.19/4.82 thf(8,axiom,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (unordered_pair @ B @ C) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_unordered_pair_ax)).
% 15.19/4.82 thf(51,plain,((! [A:$i,B:mu,C:mu]: (exists_in_world @ (unordered_pair @ B @ C) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 15.19/4.82 thf(52,plain,(! [C:mu,B:mu,A:$i] : ((exists_in_world @ (unordered_pair @ B @ C) @ A))),inference(cnf,[status(esa)],[51])).
% 15.19/4.82 thf(28,axiom,((! [A:$i]: (exists_in_world @ empty_set @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_empty_set_ax)).
% 15.19/4.82 thf(109,plain,((! [A:$i]: (exists_in_world @ empty_set @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
% 15.19/4.82 thf(110,plain,(! [A:$i] : ((exists_in_world @ empty_set @ A))),inference(cnf,[status(esa)],[109])).
% 15.19/4.82 thf(229,plain,(! [D:mu,C:mu,B:mu,A:$i] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | ~ (($true)) | (~ (in @ D @ sk2 @ sk1)) | ((exists_in_world @ (set_intersection2 @ B @ C) @ A) != (exists_in_world @ D @ sk1)))),inference(paramod_ordered,[status(thm)],[46,155])).
% 15.19/4.82 thf(230,plain,(! [D:mu,C:mu,B:mu,A:$i] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ D @ sk2 @ sk1)) | ((exists_in_world @ (set_intersection2 @ B @ C) @ A) != (exists_in_world @ D @ sk1)))),inference(simp,[status(thm)],[229])).
% 15.19/4.82 thf(231,plain,(! [B:mu,A:mu] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ (set_intersection2 @ A @ B) @ sk2 @ sk1)))),inference(pattern_uni,[status(thm)],[230:[bind(A, $thf(sk1)),bind(B, $thf(E)),bind(C, $thf(F)),bind(D, $thf(set_intersection2 @ E @ F))]])).
% 15.19/4.82 thf(238,plain,(! [B:mu,A:mu] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ (set_intersection2 @ A @ B) @ sk2 @ sk1)))),inference(simp,[status(thm)],[231])).
% 15.19/4.82 thf(14,axiom,((mvalid @ (empty @ empty_set))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0)).
% 15.19/4.82 thf(66,plain,((! [A:$i]: (empty @ empty_set @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 15.19/4.82 thf(67,plain,(! [A:$i] : ((empty @ empty_set @ A))),inference(cnf,[status(esa)],[66])).
% 15.19/4.82 thf(31,axiom,((mvalid @ (mexists_ind @ (^ [A:mu]: (mnot @ (empty @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0)).
% 15.19/4.82 thf(124,plain,((! [A:$i]: ~ (! [B:mu]: ((exists_in_world @ B @ A) => (empty @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 15.19/4.82 thf(125,plain,((~ (? [A:$i]: ! [B:mu]: ((exists_in_world @ B @ A) => (empty @ B @ A))))),inference(miniscope,[status(thm)],[124])).
% 15.19/4.82 thf(126,plain,(! [A:$i] : (((exists_in_world @ (sk12 @ A) @ A) & ~ (empty @ (sk12 @ A) @ A)))),inference(cnf,[status(esa)],[125])).
% 15.19/4.82 thf(128,plain,(! [A:$i] : ((~ (empty @ (sk12 @ A) @ A)))),inference(cnfConj,[status(thm)],[126])).
% 15.19/4.82 thf(185,plain,(! [B:$i,A:$i] : (~ (($true)) | ((empty @ empty_set @ A) != (empty @ (sk12 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[67,128])).
% 15.19/4.82 thf(186,plain,(! [B:$i,A:$i] : (((empty @ empty_set @ A) != (empty @ (sk12 @ B) @ B)))),inference(simp,[status(thm)],[185])).
% 15.19/4.82 thf(187,plain,(! [B:$i,A:$i] : (((sk12 @ B) != empty_set) | (A != B))),inference(simp,[status(thm)],[186])).
% 15.19/4.82 thf(188,plain,(! [A:$i] : (((sk12 @ A) != empty_set))),inference(simp,[status(thm)],[187])).
% 15.19/4.82 thf(19,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mequiv @ (qmltpeq @ C @ (set_intersection2 @ A @ B)) @ (mforall_ind @ (^ [D:mu]: (mequiv @ (in @ D @ C) @ (mand @ (in @ D @ A) @ (in @ D @ B)))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0)).
% 15.19/4.82 thf(77,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (~ (~ (qmltpeq @ D @ (set_intersection2 @ B @ C) @ A) | ! [E:mu]: ((exists_in_world @ E @ A) => (~ (~ (~ (in @ E @ D @ A) | ~ (~ (in @ E @ B @ A) | ~ (in @ E @ C @ A))) | ~ (~ (in @ E @ B @ A) | ~ (in @ E @ C @ A) | (in @ E @ D @ A)))))) | ~ (~ (! [E:mu]: ((exists_in_world @ E @ A) => (~ (~ (~ (in @ E @ D @ A) | ~ (~ (in @ E @ B @ A) | ~ (in @ E @ C @ A))) | ~ (~ (in @ E @ B @ A) | ~ (in @ E @ C @ A) | (in @ E @ D @ A)))))) | (qmltpeq @ D @ (set_intersection2 @ B @ C) @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 15.19/4.82 thf(145,plain,(! [C:mu,B:mu,A:$i] : ((~ (exists_in_world @ B @ A)) | (~ (qmltpeq @ B @ empty_set @ A)) | (~ (exists_in_world @ C @ A)) | ~ (($true)) | ((in @ sk2 @ sk4 @ sk1) != (in @ C @ B @ A)))),inference(paramod_ordered,[status(thm)],[36,55])).
% 15.19/4.82 thf(146,plain,(! [C:mu,B:mu,A:$i] : ((~ (exists_in_world @ B @ A)) | (~ (qmltpeq @ B @ empty_set @ A)) | (~ (exists_in_world @ C @ A)) | ((in @ sk2 @ sk4 @ sk1) != (in @ C @ B @ A)))),inference(simp,[status(thm)],[145])).
% 15.19/4.82 thf(147,plain,((~ (exists_in_world @ sk4 @ sk1)) | (~ (qmltpeq @ sk4 @ empty_set @ sk1)) | (~ (exists_in_world @ sk2 @ sk1))),inference(pattern_uni,[status(thm)],[146:[bind(A, $thf(sk1)),bind(B, $thf(sk4)),bind(C, $thf(sk2))]])).
% 15.19/4.82 thf(160,plain,(~ (($true)) | (~ (qmltpeq @ sk4 @ empty_set @ sk1)) | ~ (($true))),inference(rewrite,[status(thm)],[147,37,40])).
% 15.19/4.82 thf(161,plain,((~ (qmltpeq @ sk4 @ empty_set @ sk1))),inference(simp,[status(thm)],[160])).
% 15.19/4.82 thf(470,plain,(! [B:mu,A:$i] : ((~ (exists_in_world @ B @ A)) | (exists_in_world @ (sk5 @ B @ A) @ A) | ~ (($true)) | ((qmltpeq @ B @ empty_set @ A) != (qmltpeq @ sk4 @ empty_set @ sk1)))),inference(paramod_ordered,[status(thm)],[56,161])).
% 15.19/4.82 thf(471,plain,(! [B:mu,A:$i] : ((~ (exists_in_world @ B @ A)) | (exists_in_world @ (sk5 @ B @ A) @ A) | ((qmltpeq @ B @ empty_set @ A) != (qmltpeq @ sk4 @ empty_set @ sk1)))),inference(simp,[status(thm)],[470])).
% 15.19/4.82 thf(472,plain,((~ (exists_in_world @ sk4 @ sk1)) | (exists_in_world @ (sk5 @ sk4 @ sk1) @ sk1)),inference(pattern_uni,[status(thm)],[471:[bind(A, $thf(sk1)),bind(B, $thf(sk4))]])).
% 15.19/4.82 thf(536,plain,(~ (($true)) | (exists_in_world @ (sk5 @ sk4 @ sk1) @ sk1)),inference(rewrite,[status(thm)],[472,37])).
% 15.19/4.82 thf(537,plain,((exists_in_world @ (sk5 @ sk4 @ sk1) @ sk1)),inference(simp,[status(thm)],[536])).
% 15.19/4.82 thf(24,axiom,((mvalid @ (mexists_ind @ (empty)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0)).
% 15.19/4.82 thf(96,plain,((! [A:$i]: ~ (! [B:mu]: ((exists_in_world @ B @ A) => (~ (empty @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 15.19/4.82 thf(97,plain,((~ (? [A:$i]: ! [B:mu]: ((exists_in_world @ B @ A) => (~ (empty @ B @ A)))))),inference(miniscope,[status(thm)],[96])).
% 15.19/4.82 thf(98,plain,(! [A:$i] : (((exists_in_world @ (sk8 @ A) @ A) & (empty @ (sk8 @ A) @ A)))),inference(cnf,[status(esa)],[97])).
% 15.19/4.82 thf(99,plain,(! [A:$i] : ((exists_in_world @ (sk8 @ A) @ A))),inference(cnfConj,[status(thm)],[98])).
% 15.19/4.82 thf(210,plain,(! [B:mu,A:$i] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | ~ (($true)) | (~ (in @ B @ sk2 @ sk1)) | ((exists_in_world @ (sk8 @ A) @ A) != (exists_in_world @ B @ sk1)))),inference(paramod_ordered,[status(thm)],[99,155])).
% 15.19/4.82 thf(211,plain,(! [B:mu,A:$i] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ B @ sk2 @ sk1)) | ((exists_in_world @ (sk8 @ A) @ A) != (exists_in_world @ B @ sk1)))),inference(simp,[status(thm)],[210])).
% 15.19/4.82 thf(212,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ (sk8 @ sk1) @ sk2 @ sk1))),inference(pattern_uni,[status(thm)],[211:[bind(A, $thf(sk1)),bind(B, $thf(sk8 @ sk1))]])).
% 15.19/4.82 thf(32,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ (set_intersection2 @ C @ A) @ (set_intersection2 @ C @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_intersection2_substitution_2)).
% 15.19/4.82 thf(129,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (set_intersection2 @ D @ B) @ (set_intersection2 @ D @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
% 15.19/4.82 thf(17,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)).
% 15.19/4.82 thf(73,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (qmltpeq @ C @ D @ A) | (qmltpeq @ B @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 15.19/4.82 thf(506,plain,(! [B:mu,A:$i] : (~ (($true)) | (exists_in_world @ (sk5 @ B @ A) @ A) | (qmltpeq @ B @ empty_set @ A) | ((exists_in_world @ sk3 @ sk1) != (exists_in_world @ B @ A)))),inference(paramod_ordered,[status(thm)],[39,56])).
% 15.19/4.82 thf(507,plain,(! [B:mu,A:$i] : ((exists_in_world @ (sk5 @ B @ A) @ A) | (qmltpeq @ B @ empty_set @ A) | ((exists_in_world @ sk3 @ sk1) != (exists_in_world @ B @ A)))),inference(simp,[status(thm)],[506])).
% 15.19/4.82 thf(508,plain,((exists_in_world @ (sk5 @ sk3 @ sk1) @ sk1) | (qmltpeq @ sk3 @ empty_set @ sk1)),inference(pattern_uni,[status(thm)],[507:[bind(A, $thf(sk1)),bind(B, $thf(sk3))]])).
% 15.19/4.82 thf(27,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mequiv @ (disjoint @ A @ B) @ (qmltpeq @ (set_intersection2 @ A @ B) @ empty_set)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0)).
% 15.19/4.82 thf(105,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (~ (~ (disjoint @ B @ C @ A) | (qmltpeq @ (set_intersection2 @ B @ C) @ empty_set @ A)) | ~ (~ (qmltpeq @ (set_intersection2 @ B @ C) @ empty_set @ A) | (disjoint @ B @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
% 15.19/4.82 thf(100,plain,(! [A:$i] : ((empty @ (sk8 @ A) @ A))),inference(cnfConj,[status(thm)],[98])).
% 15.19/4.82 thf(241,plain,(! [B:$i,A:$i] : (~ (($true)) | ((empty @ (sk8 @ A) @ A) != (empty @ (sk12 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[100,128])).
% 15.19/4.82 thf(242,plain,(! [B:$i,A:$i] : (((empty @ (sk8 @ A) @ A) != (empty @ (sk12 @ B) @ B)))),inference(simp,[status(thm)],[241])).
% 15.19/4.82 thf(243,plain,(! [B:$i,A:$i] : (((sk8 @ A) != (sk12 @ B)) | (A != B))),inference(simp,[status(thm)],[242])).
% 15.19/4.82 thf(244,plain,(! [A:$i] : (((sk12 @ A) != (sk8 @ A)))),inference(simp,[status(thm)],[243])).
% 15.19/4.82 thf(13,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (in @ C @ A)) @ (in @ C @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_substitution_2)).
% 15.19/4.82 thf(64,plain,((! [A:$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) | ~ (in @ D @ B @ A) | (in @ D @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 15.19/4.82 thf(189,plain,(! [B:mu,A:$i] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | ~ (($true)) | (~ (in @ B @ sk2 @ sk1)) | ((exists_in_world @ empty_set @ A) != (exists_in_world @ B @ sk1)))),inference(paramod_ordered,[status(thm)],[110,155])).
% 15.19/4.82 thf(190,plain,(! [B:mu,A:$i] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ B @ sk2 @ sk1)) | ((exists_in_world @ empty_set @ A) != (exists_in_world @ B @ sk1)))),inference(simp,[status(thm)],[189])).
% 15.19/4.82 thf(191,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ empty_set @ sk2 @ sk1))),inference(pattern_uni,[status(thm)],[190:[bind(A, $thf(sk1)),bind(B, $thf(empty_set))]])).
% 15.19/4.82 thf(44,plain,(! [A:$i] : ((rel_s4 @ A @ A))),inference(cnf,[status(esa)],[43])).
% 15.19/4.82 thf(16,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (disjoint @ A @ B) @ (disjoint @ B @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0)).
% 15.19/4.82 thf(71,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (disjoint @ B @ C @ A) | (disjoint @ C @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 15.19/4.82 thf(7,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (disjoint @ A @ C)) @ (disjoint @ B @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_substitution_1)).
% 15.19/4.82 thf(49,plain,((! [A:$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) | ~ (disjoint @ B @ D @ A) | (disjoint @ C @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 15.19/4.82 thf(170,plain,(! [A:mu] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | ~ (($true)) | (~ (in @ A @ sk2 @ sk1)) | ((exists_in_world @ sk2 @ sk1) != (exists_in_world @ A @ sk1)))),inference(paramod_ordered,[status(thm)],[40,155])).
% 15.19/4.82 thf(171,plain,(! [A:mu] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ A @ sk2 @ sk1)) | ((exists_in_world @ sk2 @ sk1) != (exists_in_world @ A @ sk1)))),inference(simp,[status(thm)],[170])).
% 15.19/4.82 thf(172,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ sk2 @ sk2 @ sk1))),inference(pattern_uni,[status(thm)],[171:[bind(A, $thf(sk2))]])).
% 15.19/4.82 thf(30,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mequiv @ (qmltpeq @ C @ (unordered_pair @ A @ B)) @ (mforall_ind @ (^ [D:mu]: (mequiv @ (in @ D @ C) @ (mor @ (qmltpeq @ D @ A) @ (qmltpeq @ D @ B)))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski)).
% 15.19/4.82 thf(113,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (~ (~ (qmltpeq @ D @ (unordered_pair @ B @ C) @ A) | ! [E:mu]: ((exists_in_world @ E @ A) => (~ (~ (~ (in @ E @ D @ A) | (qmltpeq @ E @ B @ A) | (qmltpeq @ E @ C @ A)) | ~ (~ ((qmltpeq @ E @ B @ A) | (qmltpeq @ E @ C @ A)) | (in @ E @ D @ A)))))) | ~ (~ (! [E:mu]: ((exists_in_world @ E @ A) => (~ (~ (~ (in @ E @ D @ A) | (qmltpeq @ E @ B @ A) | (qmltpeq @ E @ C @ A)) | ~ (~ ((qmltpeq @ E @ B @ A) | (qmltpeq @ E @ C @ A)) | (in @ E @ D @ A)))))) | (qmltpeq @ D @ (unordered_pair @ B @ C) @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
% 15.19/4.82 thf(50,plain,(! [D:mu,C:mu,B:mu,A:$i] : ((~ (exists_in_world @ B @ A)) | (~ (exists_in_world @ C @ A)) | (~ (exists_in_world @ D @ A)) | (~ (qmltpeq @ B @ C @ A)) | (~ (disjoint @ B @ D @ A)) | (disjoint @ C @ D @ A))),inference(cnf,[status(esa)],[49])).
% 15.19/4.82 thf(127,plain,(! [A:$i] : ((exists_in_world @ (sk12 @ A) @ A))),inference(cnfConj,[status(thm)],[126])).
% 15.19/4.82 thf(256,plain,(! [B:mu,A:$i] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | ~ (($true)) | (~ (in @ B @ sk2 @ sk1)) | ((exists_in_world @ (sk12 @ A) @ A) != (exists_in_world @ B @ sk1)))),inference(paramod_ordered,[status(thm)],[127,155])).
% 15.19/4.82 thf(257,plain,(! [B:mu,A:$i] : ((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ B @ sk2 @ sk1)) | ((exists_in_world @ (sk12 @ A) @ A) != (exists_in_world @ B @ sk1)))),inference(simp,[status(thm)],[256])).
% 15.19/4.82 thf(258,plain,((~ (qmltpeq @ sk2 @ empty_set @ sk1)) | (~ (in @ (sk12 @ sk1) @ sk2 @ sk1))),inference(pattern_uni,[status(thm)],[257:[bind(A, $thf(sk1)),bind(B, $thf(sk12 @ sk1))]])).
% 15.19/4.82 thf(18,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (qmltpeq @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity)).
% 15.19/4.82 thf(75,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (qmltpeq @ B @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 15.19/4.82 thf(10,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)).
% 15.19/4.82 thf(58,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)],[10])).
% 15.19/4.82 thf(15,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (qmltpeq @ (set_intersection2 @ A @ A) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0)).
% 15.19/4.82 thf(68,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (qmltpeq @ (set_intersection2 @ B @ B) @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 15.19/4.82 thf(12,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (in @ A @ B) @ (mnot @ (in @ B @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden)).
% 15.19/4.82 thf(62,plain,((! [A:$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)],[12])).
% 15.19/4.82 thf(33,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)).
% 15.19/4.82 thf(131,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | (qmltpeq @ (unordered_pair @ D @ B) @ (unordered_pair @ D @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
% 15.19/4.82 thf(21,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (qmltpeq @ (unordered_pair @ A @ B) @ (unordered_pair @ B @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski)).
% 15.19/4.82 thf(90,plain,((! [A:$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)],[21])).
% 15.19/4.82 thf(29,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (empty @ A)) @ (empty @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_substitution_1)).
% 15.19/4.82 thf(111,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (empty @ B @ A) | (empty @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
% 15.19/4.82 thf(2872,plain,(($false)),inference(e,[status(thm)],[247,56,46,60,38,92,167,209,48,43,94,101,88,42,37,52,110,164,238,188,53,109,124,77,537,212,96,129,41,73,128,508,105,244,34,45,161,64,191,44,71,49,172,113,39,103,66,155,50,67,127,99,104,40,258,55,75,58,36,51,68,62,131,47,100,90,111])).
% 15.19/4.82 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.19/4.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------