%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET027^7 : 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 : n011.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 08:22:52 AM UTC 2026
% Result : Theorem 5.07s 2.44s
% Output : Refutation 5.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027^7 : 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
% 0.10/0.27 % Computer : n011.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 13:36:01 UTC 2026
% 0.10/0.28 % CPUTime :
% 0.10/0.28 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
% 1.18/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.75/1.17 % [INFO] Parsing done (262ms).
% 1.75/1.19 % [INFO] Running in sequential loop mode.
% 2.67/1.55 % [INFO] eprover registered as external prover.
% 2.67/1.56 % [INFO] Scanning for conjecture ...
% 3.23/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 3.23/1.77 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 3.23/1.78 % [INFO] Problem is higher-order (TPTP THF).
% 3.23/1.78 % [INFO] Type checking passed.
% 3.23/1.79 % [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 ...
% 5.07/2.44 % External prover 'e' found a proof!
% 5.07/2.44 % [INFO] Killing All external provers ...
% 5.07/2.44 % Time passed: 2006ms (effective reasoning time: 1248ms)
% 5.07/2.44 % 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)>
% 5.07/2.44 % Axioms used in derivation (6): reflexivity_of_subset, cumulative_ax, a1, nonempty_ax, subset_defn, a2
% 5.07/2.44 % No. of inferences in proof: 16
% 5.07/2.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2006 ms resp. 1248 ms w/o parsing
% 5.50/2.50 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.50/2.50 thf(mu_type, type, mu: $tType).
% 5.50/2.50 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 5.50/2.50 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.50/2.50 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.50/2.50 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.50/2.50 thf(mequiv_decl, type, mequiv: (($i > $o) > (($i > $o) > ($i > $o)))).
% 5.50/2.50 thf(exists_in_world_decl, type, exists_in_world: (mu > ($i > $o))).
% 5.50/2.50 thf(mforall_ind_decl, type, mforall_ind: ((mu > ($i > $o)) > ($i > $o))).
% 5.50/2.50 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 5.50/2.50 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 5.50/2.50 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 5.50/2.50 thf(rel_s4_decl, type, rel_s4: ($i > ($i > $o))).
% 5.50/2.50 thf(member_decl, type, member: (mu > (mu > ($i > $o)))).
% 5.50/2.50 thf(subset_decl, type, subset: (mu > (mu > ($i > $o)))).
% 5.50/2.50 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 5.50/2.50 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 5.50/2.50 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 5.50/2.50 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 5.50/2.50 thf(mequiv_def, definition, mequiv = (^ [A:($i > $o),B:($i > $o)]: (mand @ (mimplies @ A @ B) @ (mimplies @ B @ A))) ).
% 5.50/2.50 thf(mforall_ind_def, definition, mforall_ind = (^ [A:(mu > ($i > $o)),B:$i]: ! [C:mu]: ((exists_in_world @ C @ B) => (A @ C @ B))) ).
% 5.50/2.50 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 5.50/2.50 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 5.50/2.50 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 5.50/2.50 thf(7,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mequiv @ (subset @ A @ B) @ (mforall_ind @ (^ [C:mu]: (mimplies @ (member @ C @ A) @ (member @ C @ B))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn)).
% 5.50/2.50 thf(25,plain,((! [A:$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)],[7])).
% 5.50/2.50 thf(5,axiom,((mtransitive @ rel_s4)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 5.50/2.50 thf(21,plain,((! [A:$i,B:$i,C:$i]: (((rel_s4 @ A @ B) & (rel_s4 @ B @ C)) => (rel_s4 @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 5.50/2.50 thf(1,conjecture,((mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (subset @ A @ B) @ (subset @ B @ C)) @ (subset @ A @ C)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset)).
% 5.50/2.50 thf(2,negated_conjecture,((~ (mvalid @ (mforall_ind @ (^ [A:mu]: (mforall_ind @ (^ [B:mu]: (mforall_ind @ (^ [C:mu]: (mimplies @ (mand @ (subset @ A @ B) @ (subset @ B @ C)) @ (subset @ A @ C))))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 5.50/2.50 thf(9,plain,((~ (! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (! [C:mu]: ((exists_in_world @ C @ A) => (! [D:mu]: ((exists_in_world @ D @ A) => (~ (subset @ B @ C @ A) | ~ (subset @ C @ D @ A) | (subset @ B @ D @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 5.50/2.50 thf(3,axiom,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax)).
% 5.50/2.50 thf(17,plain,((! [A:$i]: ? [B:mu]: (exists_in_world @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 5.50/2.50 thf(8,axiom,((mvalid @ (mforall_ind @ (^ [A:mu]: (subset @ A @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset)).
% 5.50/2.50 thf(31,plain,((! [A:$i,B:mu]: ((exists_in_world @ B @ A) => (subset @ B @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 5.50/2.50 thf(6,axiom,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',cumulative_ax)).
% 5.50/2.50 thf(23,plain,((! [A:mu,B:$i,C:$i]: (((exists_in_world @ A @ B) & (rel_s4 @ B @ C)) => (exists_in_world @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 5.50/2.50 thf(4,axiom,((mreflexive @ rel_s4)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 5.50/2.50 thf(19,plain,((! [A:$i]: (rel_s4 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 5.50/2.50 thf(33,plain,(($false)),inference(e,[status(thm)],[25,21,9,17,31,23,19])).
% 5.50/2.50 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.50/2.50 % [INFO] Killing All external provers ...
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