%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL877^2 : TPTP v9.3.1. Released v5.2.0.
% 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 : n003.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 7.58s 3.07s
% Output : Refutation 7.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL877^2 : TPTP v9.3.1. Released v5.2.0.
% 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 : n003.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 10:21:58 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
% 0.90/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/1.04 % [INFO] Parsing done (237ms).
% 1.61/1.05 % [INFO] Running in sequential loop mode.
% 2.23/1.45 % [INFO] eprover registered as external prover.
% 2.23/1.46 % [INFO] Scanning for conjecture ...
% 2.71/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.71/1.68 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.71/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 2.71/1.68 % [INFO] Type checking passed.
% 2.71/1.69 % [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 ...
% 7.58/3.06 % External prover 'e' found a proof!
% 7.58/3.06 % [INFO] Killing All external provers ...
% 7.58/3.06 % Time passed: 2710ms (effective reasoning time: 2006ms)
% 7.58/3.06 % 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)>
% 7.58/3.07 % Axioms used in derivation (0):
% 7.58/3.07 % No. of inferences in proof: 4
% 7.58/3.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2710 ms resp. 2006 ms w/o parsing
% 7.58/3.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.58/3.11 thf(mu_type, type, mu: $tType).
% 7.58/3.11 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 7.58/3.11 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 7.58/3.11 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 7.58/3.11 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 7.58/3.11 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 7.58/3.11 thf(meuclidean_decl, type, meuclidean: (($i > ($i > $o)) > $o)).
% 7.58/3.11 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 7.58/3.11 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 7.58/3.11 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 7.58/3.11 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 7.58/3.11 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 7.58/3.11 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 7.58/3.11 thf(meuclidean_def, definition, meuclidean = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => (A @ C @ D))) ).
% 7.58/3.11 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 7.58/3.11 thf(1,conjecture,((! [A:($i > ($i > $o))]: ((mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mnot @ (mbox @ A @ B)) @ (mbox @ A @ (mnot @ (mbox @ A @ B))))))) = (meuclidean @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 7.58/3.11 thf(2,negated_conjecture,((~ (! [A:($i > ($i > $o))]: ((mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mimplies @ (mnot @ (mbox @ A @ B)) @ (mbox @ A @ (mnot @ (mbox @ A @ B))))))) = (meuclidean @ A))))),inference(neg_conjecture,[status(cth)],[1])).
% 7.58/3.11 thf(3,plain,((~ (! [A:($i > ($i > $o))]: ((! [B:$i,C:($i > $o)]: (! [D:$i]: (~ (A @ B @ D) | (C @ D)) | ! [D:$i]: (~ (A @ B @ D) | ~ (! [E:$i]: (~ (A @ D @ E) | (C @ E)))))) = (! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => (A @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 7.58/3.11 thf(284,plain,(($false)),inference(e,[status(thm)],[3])).
% 7.58/3.11 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.58/3.11 % [INFO] Killing All external provers ...
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