%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL725^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 : n015.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 08:14:12 AM UTC 2026
% Result : Theorem 4.00s 2.30s
% Output : Refutation 4.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL725^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 : n015.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 10:47:17 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
% 0.85/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.04 % [INFO] Parsing done (255ms).
% 1.54/1.05 % [INFO] Running in sequential loop mode.
% 2.07/1.48 % [INFO] eprover registered as external prover.
% 2.07/1.49 % [INFO] Scanning for conjecture ...
% 2.47/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.69/1.70 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.69/1.71 % [INFO] Problem is higher-order (TPTP THF).
% 2.69/1.71 % [INFO] Type checking passed.
% 2.69/1.71 % [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 ...
% 4.00/2.30 % External prover 'e' found a proof!
% 4.00/2.30 % [INFO] Killing All external provers ...
% 4.00/2.30 % Time passed: 1952ms (effective reasoning time: 1242ms)
% 4.00/2.30 % 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)>
% 4.00/2.30 % Axioms used in derivation (3): a1, a2, a3
% 4.00/2.30 % No. of inferences in proof: 10
% 4.00/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1952 ms resp. 1242 ms w/o parsing
% 4.00/2.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.00/2.36 thf(mu_type, type, mu: $tType).
% 4.00/2.36 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.00/2.36 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.00/2.36 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.00/2.36 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 4.00/2.36 thf(msymmetric_decl, type, msymmetric: (($i > ($i > $o)) > $o)).
% 4.00/2.36 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 4.00/2.36 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.00/2.36 thf(rel_s5_decl, type, rel_s5: ($i > ($i > $o))).
% 4.00/2.36 thf(mbox_s5_decl, type, mbox_s5: (($i > $o) > ($i > $o))).
% 4.00/2.36 thf(mdia_s5_decl, type, mdia_s5: (($i > $o) > ($i > $o))).
% 4.00/2.36 thf(phi_decl, type, phi: ($i > $o)).
% 4.00/2.36 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.00/2.36 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.00/2.36 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.00/2.36 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 4.00/2.36 thf(msymmetric_def, definition, msymmetric = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i]: ((A @ B @ C) => (A @ C @ B))) ).
% 4.00/2.36 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 4.00/2.36 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.00/2.36 thf(mbox_s5_def, definition, mbox_s5 = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_s5 @ B @ C) | (A @ C))) ).
% 4.00/2.36 thf(mdia_s5_def, definition, mdia_s5 = (^ [A:($i > $o)]: (mnot @ (mbox_s5 @ (mnot @ A)))) ).
% 4.00/2.36 thf(1,conjecture,(((mvalid @ (mimplies @ (mbox_s5 @ phi) @ phi)) & (mvalid @ (mimplies @ (mbox_s5 @ phi) @ (mbox_s5 @ (mbox_s5 @ phi)))) & (mvalid @ (mimplies @ phi @ (mbox_s5 @ (mdia_s5 @ phi)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 4.00/2.36 thf(2,negated_conjecture,((~ ((mvalid @ (mimplies @ (mbox_s5 @ phi) @ phi)) & (mvalid @ (mimplies @ (mbox_s5 @ phi) @ (mbox_s5 @ (mbox_s5 @ phi)))) & (mvalid @ (mimplies @ phi @ (mbox_s5 @ (mdia_s5 @ phi))))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.00/2.36 thf(6,plain,((~ (! [A:$i]: (~ (! [B:$i]: (~ (rel_s5 @ A @ B) | (phi @ B))) | (phi @ A)) & ! [A:$i]: (~ (! [B:$i]: (~ (rel_s5 @ A @ B) | (phi @ B))) | ! [B:$i]: (~ (rel_s5 @ A @ B) | ! [C:$i]: (~ (rel_s5 @ B @ C) | (phi @ C)))) & ! [A:$i]: (~ (phi @ A) | ! [B:$i]: (~ (rel_s5 @ A @ B) | ~ (! [C:$i]: (~ (rel_s5 @ B @ C) | ~ (phi @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.00/2.36 thf(3,axiom,((mreflexive @ rel_s5)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 4.00/2.36 thf(19,plain,((! [A:$i]: (rel_s5 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.00/2.36 thf(4,axiom,((mtransitive @ rel_s5)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 4.00/2.36 thf(21,plain,((! [A:$i,B:$i,C:$i]: (((rel_s5 @ A @ B) & (rel_s5 @ B @ C)) => (rel_s5 @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.00/2.36 thf(5,axiom,((msymmetric @ rel_s5)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3)).
% 4.00/2.36 thf(23,plain,((! [A:$i,B:$i]: ((rel_s5 @ A @ B) => (rel_s5 @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.00/2.36 thf(25,plain,(($false)),inference(e,[status(thm)],[6,19,21,23])).
% 4.00/2.36 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.00/2.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------