%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO513^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/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 08:46:03 AM UTC 2026
% Result : Theorem 10.67s 3.61s
% Output : Refutation 10.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO513^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.23 % Computer : n002.cluster.edu
% 0.12/0.23 % Model : x86_64 x86_64
% 0.12/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.23 % Memory : 8046.5625MB
% 0.12/0.23 % OS : Linux 6.8.0-71-generic
% 0.12/0.23 % CPULimit : 300
% 0.12/0.23 % WCLimit : 300
% 0.12/0.23 % DateTime : Tue Sep 29 17:14:37 UTC 2026
% 0.12/0.23 % CPUTime :
% 0.12/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.05/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.00 % [INFO] Parsing done (172ms).
% 1.22/1.01 % [INFO] Running in sequential loop mode.
% 2.02/1.41 % [INFO] eprover registered as external prover.
% 2.02/1.42 % [INFO] Scanning for conjecture ...
% 2.02/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.54 % [INFO] Type checking passed.
% 2.21/1.54 % [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 ...
% 10.67/3.60 % [INFO] Killing All external provers ...
% 10.67/3.61 % Time passed: 3229ms (effective reasoning time: 2587ms)
% 10.67/3.61 % 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)>
% 10.67/3.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3229 ms resp. 2587 ms w/o parsing
% 10.67/3.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.67/3.66 thf(sk1_decl, type, sk1: ((($o > $o) > $o) > ($o > $o))).
% 10.67/3.66 thf(sk2_decl, type, sk2: ((($o > $o) > $o) > $o)).
% 10.67/3.66 thf(sk1_def, definition, sk1 = (^ [A:(($o > $o) > $o)]: (@+ [B:($o > $o)]: ~ ((? [C:$o]: (B @ C)) => (B @ (A @ B))))) ).
% 10.67/3.66 thf(sk2_def, definition, sk2 = (^ [A:(($o > $o) > $o)]: (@+ [B:$o]: (sk1 @ (A) @ B))) ).
% 10.67/3.66 thf(1,conjecture,((? [A:(($o > $o) > $o)]: ! [B:($o > $o)]: ((? [C:$o]: (B @ C)) => (B @ (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceo)).
% 10.67/3.66 thf(2,negated_conjecture,((~ (? [A:(($o > $o) > $o)]: ! [B:($o > $o)]: ((? [C:$o]: (B @ C)) => (B @ (A @ B)))))),inference(neg_conjecture,[status(cth)],[1])).
% 10.67/3.66 thf(3,plain,((~ (? [A:(($o > $o) > $o)]: ! [B:($o > $o)]: ((? [C:$o]: (B @ C)) => (B @ (A @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 10.67/3.66 thf(4,plain,(! [A:(($o > $o) > $o)] : (((sk1 @ (A) @ (sk2 @ (A))) & ~ (sk1 @ (A) @ (A @ (sk1 @ (A))))))),inference(cnf,[status(esa)],[3])).
% 10.67/3.66 thf(5,plain,(! [A:(($o > $o) > $o)] : ((sk1 @ (A) @ (sk2 @ (A))))),inference(cnfConj,[status(thm)],[4])).
% 10.67/3.66 thf(10,axiom,((? [A:(($o > $o) > $o)]: ! [B:($o > $o)]: ((? [C:$o]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 10.67/3.66 thf(11,plain,(! [B:$o,A:(($o > $o) > $o)] : ((~ (sk1 @ (A) @ B)) | (sk1 @ (A) @ (@+ [C:$o]: (sk1 @ (A) @ C))))),inference(choice,[status(esa)],[10])).
% 10.67/3.66 thf(6,plain,(! [A:(($o > $o) > $o)] : ((~ (sk1 @ (A) @ (A @ (sk1 @ (A))))))),inference(cnfConj,[status(thm)],[4])).
% 10.67/3.66 thf(167,plain,(! [C:(($o > $o) > $o),B:$o,A:(($o > $o) > $o)] : ((~ (sk1 @ (A) @ B)) | ~ (($true)) | ((sk1 @ (A) @ (@+ [D:$o]: (sk1 @ (A) @ D))) != (sk1 @ (C) @ (C @ (sk1 @ (C))))))),inference(paramod_ordered,[status(thm)],[11,6])).
% 10.67/3.66 thf(168,plain,(! [C:(($o > $o) > $o),B:$o,A:(($o > $o) > $o)] : ((~ (sk1 @ (A) @ B)) | ((sk1 @ (A) @ (@+ [D:$o]: (sk1 @ (A) @ D))) != (sk1 @ (C) @ (C @ (sk1 @ (C))))))),inference(simp,[status(thm)],[167])).
% 10.67/3.66 thf(197,plain,(! [A:$o] : ((~ (sk1 @ ((@+) @ $o) @ A)))),inference(pre_uni,[status(thm)],[168:[bind(A, $thf((@+) @ $o)),bind(B, $thf(B)),bind(C, $thf((@+) @ $o))]])).
% 10.67/3.66 thf(203,plain,(! [A:$o] : ((~ (sk1 @ ((@+) @ $o) @ A)))),inference(simp,[status(thm)],[197])).
% 10.67/3.66 thf(259,plain,(! [B:$o,A:(($o > $o) > $o)] : (~ (($true)) | ((sk1 @ (A) @ (sk2 @ (A))) != (sk1 @ ((@+) @ $o) @ B)))),inference(paramod_ordered,[status(thm)],[5,203])).
% 10.67/3.66 thf(260,plain,(! [B:$o,A:(($o > $o) > $o)] : (((sk1 @ (A) @ (sk2 @ (A))) != (sk1 @ ((@+) @ $o) @ B)))),inference(simp,[status(thm)],[259])).
% 10.67/3.66 thf(261,plain,(($false)),inference(pattern_uni,[status(thm)],[260:[bind(A, $thf((@+) @ $o)),bind(B, $thf(sk2 @ ((@+) @ $o)))]])).
% 10.67/3.66 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.67/3.66 % [INFO] Killing All external provers ...
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