%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO540^1 : 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 : n014.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 3.76s 2.21s
% Output : Refutation 3.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO540^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n014.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:13:45 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (186ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 2.04/1.40 % [INFO] eprover registered as external prover.
% 2.04/1.41 % [INFO] Scanning for conjecture ...
% 2.22/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.22/1.54 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.22/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.55 % [INFO] Type checking passed.
% 2.22/1.56 % [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 ...
% 3.76/2.20 % [INFO] Killing All external provers ...
% 3.76/2.21 % Time passed: 1855ms (effective reasoning time: 1203ms)
% 3.76/2.21 % 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)>
% 3.76/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1855 ms resp. 1203 ms w/o parsing
% 3.76/2.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.76/2.28 thf(eps_decl, type, eps: (($i > $o) > $i)).
% 3.76/2.28 thf(if_decl, type, if: ($o > ($i > ($i > $i)))).
% 3.76/2.28 thf(sk1_decl, type, sk1: $o).
% 3.76/2.28 thf(sk2_decl, type, sk2: $i).
% 3.76/2.28 thf(if_def, definition, if = (^ [A:$o,B:$i,C:$i]: (eps @ (^ [D:$i]: (((A) & (D = B)) | (~ (A) & (D = C)))))) ).
% 3.76/2.28 thf(sk1_def, definition, sk1 = (@+ [A:$o]: ~ (! [B:$i]: ((eps @ (^ [C:$i]: (((A) & (C = B)) | (~ (A) & (C = B))))) = B))) ).
% 3.76/2.28 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ ((eps @ (^ [B:$i]: (((sk1) & (B = A)) | (~ (sk1) & (B = A))))) = A)) ).
% 3.76/2.28 thf(10,axiom,((? [A:(($i > $o) > $i)]: ! [B:($i > $o)]: ((? [C:$i]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 3.76/2.28 thf(37,plain,(! [A:$i] : ((~ (A = sk2)) | ((eps @ (^ [B:$i]: (B = sk2))) = sk2))),inference(choice,[status(esa)],[10])).
% 3.76/2.28 thf(38,plain,(! [A:$i] : ((A != sk2) | ((eps @ (^ [B:$i]: (B = sk2))) = sk2))),inference(lifteq,[status(thm)],[37])).
% 3.76/2.28 thf(39,plain,(((eps @ (^ [A:$i]: (A = sk2))) = sk2)),inference(simp,[status(thm)],[38])).
% 3.76/2.28 thf(1,conjecture,((! [A:$o,B:$i]: ((if @ A @ B @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 3.76/2.28 thf(2,negated_conjecture,((~ (! [A:$o,B:$i]: ((if @ A @ B @ B) = B)))),inference(neg_conjecture,[status(cth)],[1])).
% 3.76/2.28 thf(4,plain,((~ (! [A:$o,B:$i]: ((eps @ (^ [C:$i]: (((A) & (C = B)) | (~ (A) & (C = B))))) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 3.76/2.28 thf(5,plain,((~ ((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk2))))) = sk2))),inference(cnf,[status(esa)],[4])).
% 3.76/2.28 thf(6,plain,(((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk2))))) != sk2)),inference(lifteq,[status(thm)],[5])).
% 3.76/2.28 thf(11,plain,(! [A:$i] : ((~ (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk2)))) | (((sk1) & ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2)) | (~ (sk1) & ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2))))),inference(choice,[status(esa)],[10])).
% 3.76/2.28 thf(12,plain,(! [A:$i] : (((~ (sk1) | ~ (A = sk2) | (sk1) | ~ (sk1)) & (~ (sk1) | ~ (A = sk2) | (sk1) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2)) & (~ (sk1) | ~ (A = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2) | ~ (sk1)) & (~ (sk1) | ~ (A = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2)) & ((sk1) | ~ (A = sk2) | (sk1) | ~ (sk1)) & ((sk1) | ~ (A = sk2) | (sk1) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2)) & ((sk1) | ~ (A = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2) | ~ (sk1)) & ((sk1) | ~ (A = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2))))),inference(cnf,[status(esa)],[11])).
% 3.76/2.28 thf(13,plain,(! [A:$i] : (sk1 | (~ (A = sk2)) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2))),inference(cnfConj,[status(thm)],[12])).
% 3.76/2.28 thf(22,plain,(! [A:$i] : ((A != sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk2))))) = sk2) | sk1)),inference(lifteq,[status(thm)],[13])).
% 3.76/2.28 thf(23,plain,(((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk2))))) = sk2) | sk1),inference(simp,[status(thm)],[22])).
% 3.76/2.28 thf(34,plain,(sk1),inference(simplifyReflect,[status(thm)],[23,6])).
% 3.76/2.28 thf(35,plain,(((eps @ (^ [A:$i]: (((($true)) & (A = sk2)) | (~ (($true)) & (A = sk2))))) != sk2)),inference(rewrite,[status(thm)],[6,34])).
% 3.76/2.28 thf(36,plain,(((eps @ (^ [A:$i]: (A = sk2))) != sk2)),inference(simp,[status(thm)],[35])).
% 3.76/2.28 thf(40,plain,(($false)),inference(simplifyReflect,[status(thm)],[39,36])).
% 3.76/2.28 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.76/2.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------