%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET583^7 : 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 : n016.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 08:22:57 AM UTC 2026
% Result : Theorem 4.48s 2.46s
% Output : Refutation 4.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET583^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.07 % 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 : n016.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 13:42:49 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
% 0.86/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/1.07 % [INFO] Parsing done (290ms).
% 1.51/1.09 % [INFO] Running in sequential loop mode.
% 2.24/1.48 % [INFO] eprover registered as external prover.
% 2.24/1.49 % [INFO] Scanning for conjecture ...
% 2.64/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.86/1.70 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.86/1.72 % [INFO] Problem is higher-order (TPTP THF).
% 2.86/1.73 % [INFO] Type checking passed.
% 2.86/1.73 % [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 ...
% 4.48/2.45 % External prover 'e' found a proof!
% 4.48/2.45 % [INFO] Killing All external provers ...
% 4.48/2.45 % Time passed: 2102ms (effective reasoning time: 1359ms)
% 4.48/2.45 % 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)>
% 4.48/2.45 % Axioms used in derivation (14): member_substitution_1, reflexivity_of_subset, subset_substitution_2, subset_substitution_1, equal_defn, a1, nonempty_ax, symmetry, reflexivity, cumulative_ax, transitivity, subset_defn, a2, member_substitution_2
% 4.48/2.45 % No. of inferences in proof: 32
% 4.48/2.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2102 ms resp. 1359 ms w/o parsing
% 4.78/2.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.78/2.55 thf(mu_type, type, mu: $tType).
% 4.78/2.55 thf(qmltpeq_decl, type, qmltpeq: (mu > (mu > ($i > $o)))).
% 4.78/2.55 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.78/2.55 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.78/2.55 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.78/2.55 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.78/2.55 thf(mequiv_decl, type, mequiv: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.78/2.55 thf(exists_in_world_decl, type, exists_in_world: (mu > ($i > $o))).
% 4.78/2.55 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 4.78/2.55 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 4.78/2.55 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 4.78/2.55 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.78/2.55 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 4.78/2.55 thf(member_decl, type, member: (mu > (mu > ($i > $o)))).
% 4.78/2.55 thf(subset_decl, type, subset: (mu > (mu > ($i > $o)))).
% 4.78/2.55 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.78/2.55 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.78/2.55 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 4.78/2.55 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.78/2.55 thf(mequiv_def, definition, mequiv = (^ [A:($i > $o),B:($i > $o)]: (mand @ (mimplies @ A @ B) @ (mimplies @ B @ A))) ).
% 4.78/2.55 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: ((exists_in_world @ C @ B) => (A @ C @ B))) ).
% 4.78/2.55 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 4.78/2.55 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 4.78/2.55 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.78/2.55 thf(13,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (qmltpeq @ A @ B) @ (subset @ C @ A)) @ (subset @ C @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_2)).
% 4.78/2.55 thf(44,plain,((! [A:$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)],[13])).
% 4.78/2.55 thf(12,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)).
% 4.78/2.55 thf(42,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (subset @ B @ D @ A) | (subset @ C @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 4.78/2.55 thf(3,axiom,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax)).
% 4.78/2.55 thf(24,plain,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.78/2.55 thf(14,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mequiv @ (qmltpeq @ A @ B) @ (mand @ (subset @ A @ B) @ (subset @ B @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn)).
% 4.78/2.55 thf(46,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (~ (~ (qmltpeq @ B @ C @ A) | ~ (~ (subset @ B @ C @ A) | ~ (subset @ C @ B @ A))) | ~ (~ (subset @ B @ C @ A) | ~ (subset @ C @ B @ A) | (qmltpeq @ B @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 4.78/2.55 thf(16,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (subset @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset)).
% 4.78/2.55 thf(57,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (subset @ B @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 4.78/2.55 thf(5,axiom,((mtransitive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 4.78/2.55 thf(28,plain,((! [A:$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)],[5])).
% 4.78/2.55 thf(10,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)).
% 4.78/2.55 thf(38,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (member @ B @ D @ A) | (member @ C @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 4.78/2.55 thf(1,conjecture,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mand @ (subset @ A @ B) @ (subset @ B @ A)) @ (qmltpeq @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_extensionality)).
% 4.78/2.55 thf(2,negated_conjecture,((~ (mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (mand @ (subset @ A @ B) @ (subset @ B @ A)) @ (qmltpeq @ A @ B))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.78/2.55 thf(17,plain,((~ (! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (~ (subset @ B @ C @ A) | ~ (subset @ C @ B @ A) | (qmltpeq @ B @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.78/2.55 thf(7,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (qmltpeq @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity)).
% 4.78/2.55 thf(32,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (qmltpeq @ B @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 4.78/2.55 thf(8,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mimplies @ (qmltpeq @ A @ B) @ (qmltpeq @ B @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry)).
% 4.78/2.55 thf(34,plain,((! [A:$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)],[8])).
% 4.78/2.55 thf(11,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)).
% 4.78/2.55 thf(40,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (member @ D @ B @ A) | (member @ D @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 4.78/2.55 thf(4,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 4.78/2.55 thf(26,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.78/2.55 thf(9,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)).
% 4.78/2.55 thf(36,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (qmltpeq @ B @ C @ A) | ~ (qmltpeq @ C @ D @ A) | (qmltpeq @ B @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 4.78/2.55 thf(6,axiom,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax)).
% 4.78/2.55 thf(30,plain,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 4.78/2.55 thf(15,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mequiv @ (subset @ A @ B) @ (mforall_ind @ (^ [C:mu]: (mimplies @ (member @ C @ A) @ (member @ C @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn)).
% 4.78/2.55 thf(51,plain,((! [A:$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)],[15])).
% 4.78/2.55 thf(59,plain,(($false)),inference(e,[status(thm)],[44,42,24,46,57,28,38,17,32,34,40,26,36,30,51])).
% 4.78/2.55 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.78/2.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------