%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL707^1 : TPTP v9.3.1. Bugfixed v5.1.0.
% 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 : n010.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 08:14:10 AM UTC 2026
% Result : Theorem 3.94s 2.23s
% Output : Refutation 3.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL707^1 : TPTP v9.3.1. Bugfixed v5.1.0.
% 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
% 0.11/0.22 % Computer : n010.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 09:45:33 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
% 0.86/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/1.03 % [INFO] Parsing done (241ms).
% 1.18/1.04 % [INFO] Running in sequential loop mode.
% 2.17/1.43 % [INFO] eprover registered as external prover.
% 2.17/1.43 % [INFO] Scanning for conjecture ...
% 2.61/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.61/1.64 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.61/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.61/1.65 % [INFO] Type checking passed.
% 2.61/1.65 % [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 ...
% 3.94/2.22 % External prover 'e' found a proof!
% 3.94/2.23 % [INFO] Killing All external provers ...
% 3.94/2.23 % Time passed: 1869ms (effective reasoning time: 1177ms)
% 3.94/2.23 % 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)>
% 3.94/2.23 % Axioms used in derivation (0):
% 3.94/2.23 % No. of inferences in proof: 4
% 3.94/2.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1869 ms resp. 1177 ms w/o parsing
% 3.94/2.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.94/2.28 thf(mu_type, type, mu: $tType).
% 3.94/2.28 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 3.94/2.28 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 3.94/2.28 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 3.94/2.28 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 3.94/2.28 thf(mforall_prop_decl, type, mforall_prop: ((($i > $o) > ($i > $o)) > ($i > $o))).
% 3.94/2.28 thf(mbox_decl, type, mbox: (($i > ($i > $o)) > (($i > $o) > ($i > $o)))).
% 3.94/2.28 thf(mweakly_connected_decl, type, mweakly_connected: (($i > ($i > $o)) > $o)).
% 3.94/2.28 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)).
% 3.94/2.28 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 3.94/2.28 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 3.94/2.28 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o)]: (mnot @ (mor @ (mnot @ A) @ (mnot @ B)))) ).
% 3.94/2.28 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 3.94/2.28 thf(mforall_prop_def, definition, mforall_prop = (^ [A:(($i > $o) > ($i > $o)),B:$i]: ! [C:($i > $o)]: (A @ C @ B)) ).
% 3.94/2.28 thf(mbox_def, definition, mbox = (^ [A:($i > ($i > $o)),B:($i > $o),C:$i]: ! [D:$i]: (~ (A @ C @ D) | (B @ D))) ).
% 3.94/2.28 thf(mweakly_connected_def, definition, mweakly_connected = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => ((A @ C @ D) | (C = D) | (A @ D @ C)))) ).
% 3.94/2.28 thf(mvalid_def, definition, mvalid = ((!) @ $i) ).
% 3.94/2.28 thf(1,conjecture,((! [A:($i > ($i > $o))]: ((mweakly_connected @ A) => (mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mforall_prop @ (^ [C:($i > $o)]: (mor @ (mbox @ A @ (mimplies @ (mand @ B @ (mbox @ A @ B)) @ C)) @ (mbox @ A @ (mimplies @ (mand @ C @ (mbox @ A @ C)) @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 3.94/2.28 thf(2,negated_conjecture,((~ (! [A:($i > ($i > $o))]: ((mweakly_connected @ A) => (mvalid @ (mforall_prop @ (^ [B:($i > $o)]: (mforall_prop @ (^ [C:($i > $o)]: (mor @ (mbox @ A @ (mimplies @ (mand @ B @ (mbox @ A @ B)) @ C)) @ (mbox @ A @ (mimplies @ (mand @ C @ (mbox @ A @ C)) @ B)))))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 3.94/2.28 thf(3,plain,((~ (! [A:($i > ($i > $o))]: ((! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ B @ D)) => ((A @ C @ D) | (C = D) | (A @ D @ C)))) => (! [B:$i,C:($i > $o),D:($i > $o)]: (! [E:$i]: (~ (A @ B @ E) | ~ (C @ E) | ~ (! [F:$i]: (~ (A @ E @ F) | (C @ F))) | (D @ E)) | ! [E:$i]: (~ (A @ B @ E) | ~ (D @ E) | ~ (! [F:$i]: (~ (A @ E @ F) | (D @ F))) | (C @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 3.94/2.28 thf(17,plain,(($false)),inference(e,[status(thm)],[3])).
% 3.94/2.28 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.94/2.28 % [INFO] Killing All external provers ...
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