%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO543^1 : 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 : 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 08:46:05 AM UTC 2026
% Result : Theorem 3.98s 2.31s
% Output : Refutation 3.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO543^1 : 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
% 0.11/0.20 % Computer : n010.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
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 17:14:18 UTC 2026
% 0.11/0.20 % 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.97 % [INFO] Parsing done (191ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 1.87/1.39 % [INFO] eprover registered as external prover.
% 1.87/1.40 % [INFO] Scanning for conjecture ...
% 2.06/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.23/1.53 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.23/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.54 % [INFO] Type checking passed.
% 2.23/1.54 % [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 ...
% 3.98/2.30 % [INFO] Killing All external provers ...
% 3.98/2.31 % Time passed: 1964ms (effective reasoning time: 1310ms)
% 3.98/2.31 % 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)>
% 3.98/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1964 ms resp. 1310 ms w/o parsing
% 3.98/2.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.98/2.39 thf(epsii_decl, type, epsii: ((($i > $i) > $o) > ($i > $i))).
% 3.98/2.39 thf(if_decl, type, if: ($o > (($i > $i) > (($i > $i) > ($i > $i))))).
% 3.98/2.39 thf(sk1_decl, type, sk1: $o).
% 3.98/2.39 thf(sk2_decl, type, sk2: ($i > $i)).
% 3.98/2.39 thf(if_def, definition, if = (^ [A:$o,B:($i > $i),C:($i > $i)]: (epsii @ (^ [D:($i > $i)]: (((A) & (D = B)) | (~ (A) & (D = C)))))) ).
% 3.98/2.39 thf(sk1_def, definition, sk1 = (@+ [A:$o]: ~ (! [B:($i > $i)]: ((epsii @ (^ [C:($i > $i)]: (((A) & (C = B)) | (~ (A) & (C = B))))) = (B)))) ).
% 3.98/2.39 thf(sk2_def, definition, sk2 = (@+ [A:($i > $i)]: ~ ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = A)) | (~ (sk1) & (B = A))))) = (A))) ).
% 3.98/2.39 thf(11,axiom,((? [A:((($i > $i) > $o) > ($i > $i))]: ! [B:(($i > $i) > $o)]: ((? [C:($i > $i)]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 3.98/2.39 thf(41,plain,(! [A:($i > $i)] : ((~ ((A) = (sk2))) | ((epsii @ (^ [B:($i > $i)]: (B = sk2))) = (sk2)))),inference(choice,[status(esa)],[11])).
% 3.98/2.39 thf(42,plain,(! [A:($i > $i)] : (((A) != (sk2)) | ((epsii @ (^ [B:($i > $i)]: (B = sk2))) = (sk2)))),inference(lifteq,[status(thm)],[41])).
% 3.98/2.39 thf(43,plain,(((epsii @ (^ [A:($i > $i)]: (A = sk2))) = (sk2))),inference(simp,[status(thm)],[42])).
% 3.98/2.39 thf(1,conjecture,((! [A:$o,B:($i > $i)]: ((if @ A @ B @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 3.98/2.39 thf(2,negated_conjecture,((~ (! [A:$o,B:($i > $i)]: ((if @ A @ B @ B) = B)))),inference(neg_conjecture,[status(cth)],[1])).
% 3.98/2.39 thf(4,plain,((~ (! [A:$o,B:($i > $i)]: ((epsii @ (^ [C:($i > $i)]: (((A) & (C = B)) | (~ (A) & (C = B))))) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 3.98/2.39 thf(5,plain,((~ ((epsii @ (^ [A:($i > $i)]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk2))))) = (sk2)))),inference(cnf,[status(esa)],[4])).
% 3.98/2.39 thf(6,plain,(((epsii @ (^ [A:($i > $i)]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk2))))) != (sk2))),inference(lifteq,[status(thm)],[5])).
% 3.98/2.39 thf(12,plain,(! [A:($i > $i)] : ((~ (((sk1) & ((A) = (sk2))) | (~ (sk1) & ((A) = (sk2))))) | (((sk1) & ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2))) | (~ (sk1) & ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2)))))),inference(choice,[status(esa)],[11])).
% 3.98/2.39 thf(13,plain,(! [A:($i > $i)] : (((~ (sk1) | ~ ((A) = (sk2)) | (sk1) | ~ (sk1)) & (~ (sk1) | ~ ((A) = (sk2)) | (sk1) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2))) & (~ (sk1) | ~ ((A) = (sk2)) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2)) | ~ (sk1)) & (~ (sk1) | ~ ((A) = (sk2)) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2)) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2))) & ((sk1) | ~ ((A) = (sk2)) | (sk1) | ~ (sk1)) & ((sk1) | ~ ((A) = (sk2)) | (sk1) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2))) & ((sk1) | ~ ((A) = (sk2)) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2)) | ~ (sk1)) & ((sk1) | ~ ((A) = (sk2)) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2)) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2)))))),inference(cnf,[status(esa)],[12])).
% 3.98/2.39 thf(14,plain,(! [A:($i > $i)] : (~ (sk1) | (~ ((A) = (sk2))) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2)) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2)))),inference(cnfConj,[status(thm)],[13])).
% 3.98/2.39 thf(21,plain,(! [A:($i > $i)] : (((A) != (sk2)) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2)) | ((epsii @ (^ [B:($i > $i)]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = (sk2)) | ~ (sk1))),inference(lifteq,[status(thm)],[14])).
% 3.98/2.39 thf(22,plain,(((epsii @ (^ [A:($i > $i)]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk2))))) = (sk2)) | ~ (sk1)),inference(simp,[status(thm)],[21])).
% 3.98/2.39 thf(35,plain,(~ (sk1)),inference(simplifyReflect,[status(thm)],[22,6])).
% 3.98/2.39 thf(36,plain,(((epsii @ (^ [A:($i > $i)]: (((($false)) & (A = sk2)) | (~ (($false)) & (A = sk2))))) != (sk2))),inference(rewrite,[status(thm)],[6,35])).
% 3.98/2.39 thf(37,plain,(((epsii @ (^ [A:($i > $i)]: (A = sk2))) != (sk2))),inference(simp,[status(thm)],[36])).
% 3.98/2.39 thf(44,plain,(($false)),inference(simplifyReflect,[status(thm)],[43,37])).
% 3.98/2.39 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.98/2.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------