%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL873^1 : 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 : n002.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 08:14:16 AM UTC 2026
% Result : Theorem 4.94s 2.50s
% Output : Refutation 4.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL873^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 10:21:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.21 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
% 0.86/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.57/1.05 % [INFO] Parsing done (279ms).
% 1.57/1.07 % [INFO] Running in sequential loop mode.
% 2.27/1.48 % [INFO] eprover registered as external prover.
% 2.27/1.48 % [INFO] Scanning for conjecture ...
% 2.67/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.92/1.71 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.92/1.71 % [INFO] Problem is higher-order (TPTP THF).
% 2.92/1.72 % [INFO] Type checking passed.
% 2.92/1.72 % [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 ...
% 4.94/2.50 % External prover 'e' found a proof!
% 4.94/2.50 % [INFO] Killing All external provers ...
% 4.94/2.50 % Time passed: 2161ms (effective reasoning time: 1425ms)
% 4.94/2.50 % 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)>
% 4.94/2.50 % Axioms used in derivation (6): ax4, ax6, ax1, ax2, ax3, ax5
% 4.94/2.50 % No. of inferences in proof: 16
% 4.94/2.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2161 ms resp. 1425 ms w/o parsing
% 4.94/2.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.94/2.57 thf(mu_type, type, mu: $tType).
% 4.94/2.57 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.94/2.57 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.94/2.57 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.94/2.57 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 4.94/2.57 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 4.94/2.57 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)).
% 4.94/2.57 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)).
% 4.94/2.57 thf(meuclidean_decl, type, meuclidean: (($i > ($i > $o)) > $o)).
% 4.94/2.57 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.94/2.57 thf(ra_decl, type, ra: ($i > ($i > $o))).
% 4.94/2.57 thf(rb_decl, type, rb: ($i > ($i > $o))).
% 4.94/2.57 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.94/2.57 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.94/2.57 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.94/2.57 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 4.94/2.57 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 4.94/2.57 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ).
% 4.94/2.57 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 4.94/2.57 thf(meuclidean_def, definition, meuclidean = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => (A @ C @ D))) ).
% 4.94/2.57 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.94/2.57 thf(4,axiom,((mreflexive @ rb)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2)).
% 4.94/2.57 thf(24,plain,((! [A:$i]: (rb @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.94/2.57 thf(6,axiom,((mtransitive @ rb)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4)).
% 4.94/2.57 thf(28,plain,((! [A:$i,B:$i,C:$i]: (((rb @ A @ B) & (rb @ B @ C)) => (rb @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 4.94/2.57 thf(1,conjecture,(((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mbox @ ra @ (mor @ (mbox @ ra @ A) @ (mbox @ rb @ B))) @ (mor @ (mbox @ ra @ A) @ (mbox @ ra @ B)))))))) & (mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mbox @ rb @ (mor @ (mbox @ ra @ A) @ (mbox @ rb @ B))) @ (mor @ (mbox @ rb @ A) @ (mbox @ rb @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 4.94/2.57 thf(2,negated_conjecture,((~ ((mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mbox @ ra @ (mor @ (mbox @ ra @ A) @ (mbox @ rb @ B))) @ (mor @ (mbox @ ra @ A) @ (mbox @ ra @ B)))))))) & (mvalid @ (mforall_prop @ (^ [A:($i > $o)]: (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mbox @ rb @ (mor @ (mbox @ ra @ A) @ (mbox @ rb @ B))) @ (mor @ (mbox @ rb @ A) @ (mbox @ rb @ B))))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.94/2.57 thf(9,plain,((~ (! [A:$i,B:($i > $o),C:($i > $o)]: (~ (! [D:$i]: (~ (ra @ A @ D) | ! [E:$i]: (~ (ra @ D @ E) | (B @ E)) | ! [E:$i]: (~ (rb @ D @ E) | (C @ E)))) | ! [D:$i]: (~ (ra @ A @ D) | (B @ D)) | ! [D:$i]: (~ (ra @ A @ D) | (C @ D))) & ! [A:$i,B:($i > $o),C:($i > $o)]: (~ (! [D:$i]: (~ (rb @ A @ D) | ! [E:$i]: (~ (ra @ D @ E) | (B @ E)) | ! [E:$i]: (~ (rb @ D @ E) | (C @ E)))) | ! [D:$i]: (~ (rb @ A @ D) | (B @ D)) | ! [D:$i]: (~ (rb @ A @ D) | (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.94/2.57 thf(8,axiom,((meuclidean @ rb)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6)).
% 4.94/2.57 thf(32,plain,((! [A:$i,B:$i,C:$i]: (((rb @ A @ B) & (rb @ A @ C)) => (rb @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 4.94/2.57 thf(3,axiom,((mreflexive @ ra)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1)).
% 4.94/2.57 thf(22,plain,((! [A:$i]: (ra @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.94/2.57 thf(5,axiom,((mtransitive @ ra)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)).
% 4.94/2.57 thf(26,plain,((! [A:$i,B:$i,C:$i]: (((ra @ A @ B) & (ra @ B @ C)) => (ra @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.94/2.57 thf(7,axiom,((meuclidean @ ra)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5)).
% 4.94/2.57 thf(30,plain,((! [A:$i,B:$i,C:$i]: (((ra @ A @ B) & (ra @ A @ C)) => (ra @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 4.94/2.57 thf(34,plain,(($false)),inference(e,[status(thm)],[24,28,9,32,22,26,30])).
% 4.94/2.57 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.94/2.57 % [INFO] Killing All external provers ...
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