%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO539^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : 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 3.57s 2.20s
% Output : Refutation 3.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO539^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:14:03 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.90/0.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.96 % [INFO] Parsing done (189ms).
% 1.22/0.97 % [INFO] Running in sequential loop mode.
% 1.80/1.37 % [INFO] eprover registered as external prover.
% 1.80/1.38 % [INFO] Scanning for conjecture ...
% 1.97/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.14/1.51 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.14/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.52 % [INFO] Type checking passed.
% 2.14/1.52 % [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 ...
% 3.57/2.20 % [INFO] Killing All external provers ...
% 3.57/2.20 % Time passed: 1868ms (effective reasoning time: 1221ms)
% 3.57/2.20 % 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)>
% 3.57/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1868 ms resp. 1221 ms w/o parsing
% 3.57/2.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.57/2.29 thf(eps_decl, type, eps: (($i > $o) > $i)).
% 3.57/2.29 thf(if_decl, type, if: ($o > ($i > ($i > $i)))).
% 3.57/2.29 thf(sk1_decl, type, sk1: $o).
% 3.57/2.29 thf(sk2_decl, type, sk2: $i).
% 3.57/2.29 thf(sk3_decl, type, sk3: $i).
% 3.57/2.29 thf(if_def, definition, if = (^ [A:$o,B:$i,C:$i]: (eps @ (^ [D:$i]: (((A) & (D = B)) | (~ (A) & (D = C)))))) ).
% 3.57/2.29 thf(sk1_def, definition, sk1 = (@+ [A:$o]: ~ (! [B:$i,C:$i]: (((eps @ (^ [D:$i]: (((A) & (D = B)) | (~ (A) & (D = C))))) = B) | ((eps @ (^ [D:$i]: (((A) & (D = B)) | (~ (A) & (D = C))))) = C)))) ).
% 3.57/2.29 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ (! [B:$i]: (((eps @ (^ [C:$i]: (((sk1) & (C = A)) | (~ (sk1) & (C = B))))) = A) | ((eps @ (^ [C:$i]: (((sk1) & (C = A)) | (~ (sk1) & (C = B))))) = B)))) ).
% 3.57/2.29 thf(sk3_def, definition, sk3 = (@+ [A:$i]: ~ (((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = A))))) = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = A))))) = A))) ).
% 3.57/2.29 thf(13,axiom,((? [A:(($i > $o) > $i)]: ! [B:($i > $o)]: ((? [C:$i]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 3.57/2.29 thf(14,plain,(! [A:$i] : ((~ (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk3)))) | (((sk1) & ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk2)) | (~ (sk1) & ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk3))))),inference(choice,[status(esa)],[13])).
% 3.57/2.29 thf(15,plain,(! [A:$i] : (((~ (sk1) | ~ (A = sk2) | (sk1) | ~ (sk1)) & (~ (sk1) | ~ (A = sk2) | (sk1) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk3)) & (~ (sk1) | ~ (A = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk2) | ~ (sk1)) & (~ (sk1) | ~ (A = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk3)) & ((sk1) | ~ (A = sk3) | (sk1) | ~ (sk1)) & ((sk1) | ~ (A = sk3) | (sk1) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk3)) & ((sk1) | ~ (A = sk3) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk2) | ~ (sk1)) & ((sk1) | ~ (A = sk3) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk3))))),inference(cnf,[status(esa)],[14])).
% 3.57/2.29 thf(22,plain,(! [A:$i] : (~ (sk1) | (~ (A = sk2)) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk2) | ~ (sk1))),inference(cnfConj,[status(thm)],[15])).
% 3.57/2.29 thf(30,plain,(! [A:$i] : ((A != sk2) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk2) | ~ (sk1) | ~ (sk1))),inference(lifteq,[status(thm)],[22])).
% 3.57/2.29 thf(31,plain,(((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk3))))) = sk2) | ~ (sk1)),inference(simp,[status(thm)],[30])).
% 3.57/2.29 thf(21,plain,(! [A:$i] : (sk1 | (~ (A = sk3)) | sk1 | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk3))),inference(cnfConj,[status(thm)],[15])).
% 3.57/2.29 thf(26,plain,(! [A:$i] : ((A != sk3) | ((eps @ (^ [B:$i]: (((sk1) & (B = sk2)) | (~ (sk1) & (B = sk3))))) = sk3) | sk1 | sk1)),inference(lifteq,[status(thm)],[21])).
% 3.57/2.29 thf(27,plain,(((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk3))))) = sk3) | sk1),inference(simp,[status(thm)],[26])).
% 3.57/2.29 thf(1,conjecture,((! [A:$o,B:$i,C:$i]: (((if @ A @ B @ C) = B) | ((if @ A @ B @ C) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 3.57/2.29 thf(2,negated_conjecture,((~ (! [A:$o,B:$i,C:$i]: (((if @ A @ B @ C) = B) | ((if @ A @ B @ C) = C))))),inference(neg_conjecture,[status(cth)],[1])).
% 3.57/2.29 thf(4,plain,((~ (! [A:$o,B:$i,C:$i]: (((eps @ (^ [D:$i]: (((A) & (D = B)) | (~ (A) & (D = C))))) = B) | ((eps @ (^ [D:$i]: (((A) & (D = B)) | (~ (A) & (D = C))))) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 3.57/2.29 thf(5,plain,((~ ((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk3))))) = sk2) & ~ ((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk3))))) = sk3))),inference(cnf,[status(esa)],[4])).
% 3.57/2.29 thf(7,plain,((~ ((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk3))))) = sk3))),inference(cnfConj,[status(thm)],[5])).
% 3.57/2.29 thf(9,plain,(((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk3))))) != sk3)),inference(lifteq,[status(thm)],[7])).
% 3.57/2.29 thf(40,plain,(sk1),inference(simplifyReflect,[status(thm)],[27,9])).
% 3.57/2.29 thf(48,plain,(((eps @ (^ [A:$i]: (((($true)) & (A = sk2)) | (~ (($true)) & (A = sk3))))) = sk2) | ~ (($true))),inference(rewrite,[status(thm)],[31,40])).
% 3.57/2.29 thf(49,plain,(((eps @ (^ [A:$i]: (A = sk2))) = sk2)),inference(simp,[status(thm)],[48])).
% 3.57/2.29 thf(6,plain,((~ ((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk3))))) = sk2))),inference(cnfConj,[status(thm)],[5])).
% 3.57/2.29 thf(8,plain,(((eps @ (^ [A:$i]: (((sk1) & (A = sk2)) | (~ (sk1) & (A = sk3))))) != sk2)),inference(lifteq,[status(thm)],[6])).
% 3.57/2.29 thf(41,plain,(((eps @ (^ [A:$i]: (((($true)) & (A = sk2)) | (~ (($true)) & (A = sk3))))) != sk2)),inference(rewrite,[status(thm)],[8,40])).
% 3.57/2.29 thf(42,plain,(((eps @ (^ [A:$i]: (A = sk2))) != sk2)),inference(simp,[status(thm)],[41])).
% 3.57/2.29 thf(50,plain,(($false)),inference(simplifyReflect,[status(thm)],[49,42])).
% 3.57/2.29 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.57/2.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------