%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO255^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n005.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 08:45:29 AM UTC 2026
% Result : Theorem 3.56s 2.23s
% Output : Refutation 3.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO255^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.11/0.20 % Computer : n005.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % 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 16:41:31 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.84/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.97 % [INFO] Parsing done (180ms).
% 1.17/0.98 % [INFO] Running in sequential loop mode.
% 1.73/1.37 % [INFO] eprover registered as external prover.
% 1.73/1.38 % [INFO] Scanning for conjecture ...
% 1.92/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.92/1.48 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.92/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 1.92/1.49 % [INFO] Type checking passed.
% 2.06/1.50 % [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 ...
% 3.56/2.22 % [INFO] Killing All external provers ...
% 3.56/2.23 % Time passed: 1880ms (effective reasoning time: 1237ms)
% 3.56/2.23 % 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)>
% 3.56/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1880 ms resp. 1237 ms w/o parsing
% 3.56/2.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.56/2.27 thf(cP_decl, type, cP: ($i > $o)).
% 3.56/2.27 thf(a_decl, type, a: $i).
% 3.56/2.27 thf(sk1_decl, type, sk1: (($i > $o) > $i)).
% 3.56/2.27 thf(sk1_def, definition, sk1 = (^ [A:($i > $o)]: (@+ [B:$i]: ~ ((A @ B) => (cP @ B)))) ).
% 3.56/2.27 thf(1,conjecture,(((cP @ a) => (? [A:($i > $o)]: (! [B:$i]: ((A @ B) => (cP @ B)) & ? [B:$i]: (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE3)).
% 3.56/2.27 thf(2,negated_conjecture,((~ ((cP @ a) => (? [A:($i > $o)]: (! [B:$i]: ((A @ B) => (cP @ B)) & ? [B:$i]: (A @ B)))))),inference(neg_conjecture,[status(cth)],[1])).
% 3.56/2.27 thf(3,plain,((~ ((cP @ a) => (? [A:($i > $o)]: (! [B:$i]: ((A @ B) => (cP @ B)) & ? [B:$i]: (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 3.56/2.27 thf(4,plain,(! [B:$i,A:($i > $o)] : (((cP @ a) & ((A @ (sk1 @ (A))) | ~ (A @ B)) & (~ (cP @ (sk1 @ (A))) | ~ (A @ B))))),inference(cnf,[status(esa)],[3])).
% 3.56/2.27 thf(5,plain,((cP @ a)),inference(cnfConj,[status(thm)],[4])).
% 3.56/2.27 thf(19,axiom,((? [A:(($i > $o) > $i)]: ! [B:($i > $o)]: ((? [C:$i]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 3.56/2.27 thf(37,plain,(! [A:$i] : ((~ (cP @ A)) | (cP @ (sk1 @ (cP))))),inference(choice,[status(esa)],[19])).
% 3.56/2.27 thf(7,plain,(! [B:$i,A:($i > $o)] : ((~ (cP @ (sk1 @ (A)))) | (~ (A @ B)))),inference(cnfConj,[status(thm)],[4])).
% 3.56/2.27 thf(12,plain,(! [B:$i,A:($i > $o)] : ((~ (cP @ (sk1 @ (A)))) | ((A @ B) != (cP @ (sk1 @ (A)))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[7])).
% 3.56/2.27 thf(22,plain,((~ (cP @ (sk1 @ (cP))))),inference(pre_uni,[status(thm)],[12:[bind(A, $thf(cP)),bind(B, $thf(sk1 @ (cP)))]])).
% 3.56/2.27 thf(44,plain,(! [A:$i] : ((~ (cP @ A)) | ($false))),inference(rewrite,[status(thm)],[37,22])).
% 3.56/2.27 thf(45,plain,(! [A:$i] : ((~ (cP @ A)))),inference(simp,[status(thm)],[44])).
% 3.56/2.27 thf(47,plain,(($false)),inference(rewrite,[status(thm)],[5,45])).
% 3.56/2.27 thf(48,plain,(($false)),inference(simp,[status(thm)],[47])).
% 3.56/2.27 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.56/2.27 % [INFO] Killing All external provers ...
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