%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 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 : n026.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 08:14:09 AM UTC 2026
% Result : Theorem 3.90s 2.29s
% Output : Refutation 4.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 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
% 0.09/0.20 % Computer : n026.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
% 0.09/0.21 % DateTime : Tue Sep 29 09:35:07 UTC 2026
% 0.09/0.21 % 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.08 % [INFO] Parsing done (282ms).
% 1.54/1.10 % [INFO] Running in sequential loop mode.
% 2.24/1.50 % [INFO] eprover registered as external prover.
% 2.44/1.50 % [INFO] Scanning for conjecture ...
% 2.63/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.86/1.72 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.86/1.72 % [INFO] Problem is higher-order (TPTP THF).
% 2.86/1.72 % [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 ...
% 3.90/2.29 % External prover 'e' found a proof!
% 3.90/2.29 % [INFO] Killing All external provers ...
% 3.90/2.29 % Time passed: 1938ms (effective reasoning time: 1185ms)
% 3.90/2.29 % 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)>
% 3.90/2.29 % Axioms used in derivation (1): upwf_trans
% 3.90/2.29 % No. of inferences in proof: 6
% 3.90/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1938 ms resp. 1185 ms w/o parsing
% 4.17/2.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.17/2.35 thf(individuals_type, type, individuals: $tType).
% 4.17/2.35 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.17/2.35 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.17/2.35 thf(mimpl_decl, type, mimpl: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.17/2.35 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 4.17/2.35 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 4.17/2.35 thf(transitive_decl, type, transitive: (($i > ($i > $o)) > $o)).
% 4.17/2.35 thf(upwards_well_founded_decl, type, upwards_well_founded: (($i > ($i > $o)) > $o)).
% 4.17/2.35 thf(r_decl, type, r: ($i > ($i > $o))).
% 4.17/2.35 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.17/2.35 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.17/2.35 thf(mimpl_def, definition, mimpl = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.17/2.35 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: ((A @ C @ D) => (B @ D))) ).
% 4.17/2.35 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 4.17/2.35 thf(transitive_def, definition, transitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ).
% 4.17/2.35 thf(upwards_well_founded_def, definition, upwards_well_founded = (^ [A:($i > ($i > $o))]: ! [B:($i > $o),C:$i]: ((B @ C) => (? [D:$i]: ((B @ D) & ! [E:$i]: ((A @ D @ D) => (~ (B @ E))))))) ).
% 4.17/2.35 thf(1,conjecture,((! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ r @ A) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k4)).
% 4.17/2.35 thf(2,negated_conjecture,((~ (! [A:($i > $o)]: (mvalid @ (mimpl @ (mbox @ r @ A) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ A)))))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.17/2.35 thf(4,plain,((~ (! [A:($i > $o),B:$i]: (~ (! [C:$i]: ((r @ B @ C) => (A @ C))) | ! [C:$i]: ((r @ B @ C) => (! [D:$i]: ((r @ C @ D) => (! [E:$i]: ((r @ D @ E) => (A @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.17/2.35 thf(3,axiom,(((transitive @ r) & (upwards_well_founded @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upwf_trans)).
% 4.17/2.35 thf(11,plain,((! [A:$i,B:$i,C:$i]: (((r @ A @ B) & (r @ B @ C)) => (r @ A @ C)) & ! [A:($i > $o),B:$i]: ((A @ B) => (? [C:$i]: ((A @ C) & ! [D:$i]: ((r @ C @ C) => (~ (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.17/2.35 thf(18,plain,(($false)),inference(e,[status(thm)],[4,11])).
% 4.17/2.35 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.17/2.35 % [INFO] Killing All external provers ...
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