%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO271^5 : 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 : n016.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 08:45:31 AM UTC 2026
% Result : Theorem 3.71s 2.20s
% Output : Refutation 3.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO271^5 : 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
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:47:04 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.89/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.91 % [INFO] Parsing done (181ms).
% 1.24/0.92 % [INFO] Running in sequential loop mode.
% 1.80/1.32 % [INFO] eprover registered as external prover.
% 1.80/1.33 % [INFO] Scanning for conjecture ...
% 1.96/1.42 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.96/1.45 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.96/1.45 % [INFO] Problem is higher-order (TPTP THF).
% 1.96/1.46 % [INFO] Type checking passed.
% 1.96/1.46 % [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 ...
% 3.71/2.19 % [INFO] Killing All external provers ...
% 3.71/2.19 % Time passed: 1903ms (effective reasoning time: 1263ms)
% 3.71/2.19 % 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)>
% 3.71/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1903 ms resp. 1263 ms w/o parsing
% 3.66/2.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.66/2.27 thf(b_type, type, b: $tType).
% 3.66/2.27 thf(a_type, type, a: $tType).
% 3.66/2.27 thf(cJ_decl, type, cJ: ((b > $o) > b)).
% 3.66/2.27 thf(sk1_decl, type, sk1: (b > a)).
% 3.66/2.27 thf(sk2_decl, type, sk2: (b > a)).
% 3.66/2.27 thf(sk1_def, definition, sk1 = (@+ [A:(b > a)]: ~ (! [B:(b > a)]: (((A @ (cJ @ (^ [C:b]: ~ ((A @ C) = (B @ C))))) = (B @ (cJ @ (^ [C:b]: ~ ((A @ C) = (B @ C)))))) => ((A) = (B))))) ).
% 3.66/2.27 thf(sk2_def, definition, sk2 = (@+ [A:(b > a)]: ~ (((sk1 @ (cJ @ (^ [B:b]: ~ ((sk1 @ B) = (A @ B))))) = (A @ (cJ @ (^ [B:b]: ~ ((sk1 @ B) = (A @ B)))))) => ((sk1) = (A)))) ).
% 3.66/2.27 thf(1,conjecture,(((! [A:(b > $o)]: ((? [B:b]: (A @ B)) => (A @ (cJ @ A)))) => (! [A:(b > a),B:(b > a)]: (((A @ (cJ @ (^ [C:b]: ((A @ C) != (B @ C))))) = (B @ (cJ @ (^ [C:b]: ((A @ C) != (B @ C)))))) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5500)).
% 3.66/2.27 thf(2,negated_conjecture,((~ ((! [A:(b > $o)]: ((? [B:b]: (A @ B)) => (A @ (cJ @ A)))) => (! [A:(b > a),B:(b > a)]: (((A @ (cJ @ (^ [C:b]: ((A @ C) != (B @ C))))) = (B @ (cJ @ (^ [C:b]: ((A @ C) != (B @ C)))))) => (A = B)))))),inference(neg_conjecture,[status(cth)],[1])).
% 3.66/2.27 thf(3,plain,((~ ((! [A:(b > $o)]: ((? [B:b]: (A @ B)) => (A @ (cJ @ (A))))) => (! [A:(b > a),B:(b > a)]: (((A @ (cJ @ (^ [C:b]: ~ ((A @ C) = (B @ C))))) = (B @ (cJ @ (^ [C:b]: ~ ((A @ C) = (B @ C)))))) => ((A) = (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 3.66/2.27 thf(4,plain,(! [B:b,A:(b > $o)] : (((~ (A @ B) | (A @ (cJ @ (A)))) & ((sk1 @ (cJ @ (^ [C:b]: ~ ((sk1 @ C) = (sk2 @ C))))) = (sk2 @ (cJ @ (^ [C:b]: ~ ((sk1 @ C) = (sk2 @ C)))))) & ~ ((sk1) = (sk2))))),inference(cnf,[status(esa)],[3])).
% 3.66/2.27 thf(7,plain,((~ ((sk1) = (sk2)))),inference(cnfConj,[status(thm)],[4])).
% 3.66/2.27 thf(9,plain,(((sk2) != (sk1))),inference(lifteq,[status(thm)],[7])).
% 3.66/2.27 thf(13,axiom,((? [A:((b > $o) > b)]: ! [B:(b > $o)]: ((? [C:b]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 3.66/2.27 thf(14,plain,(! [A:b] : ((~ (~ ((sk1 @ A) = (sk2 @ A)))) | (~ ((sk1 @ (cJ @ (^ [B:b]: ~ ((sk1 @ B) = (sk2 @ B))))) = (sk2 @ (cJ @ (^ [B:b]: ~ ((sk1 @ B) = (sk2 @ B))))))))),inference(choice,[status(esa)],[13])).
% 3.66/2.27 thf(19,plain,(! [A:b] : (((sk1 @ A) = (sk2 @ A)) | (~ ((sk1 @ (cJ @ (^ [B:b]: ~ ((sk1 @ B) = (sk2 @ B))))) = (sk2 @ (cJ @ (^ [B:b]: ~ ((sk1 @ B) = (sk2 @ B))))))))),inference(cnf,[status(esa)],[14])).
% 3.66/2.27 thf(20,plain,(! [A:b] : (((sk2 @ A) = (sk1 @ A)) | ((sk2 @ (cJ @ (^ [B:b]: ~ ((sk1 @ B) = (sk2 @ B))))) != (sk1 @ (cJ @ (^ [B:b]: ~ ((sk1 @ B) = (sk2 @ B)))))))),inference(lifteq,[status(thm)],[19])).
% 3.66/2.27 thf(6,plain,(((sk1 @ (cJ @ (^ [A:b]: ~ ((sk1 @ A) = (sk2 @ A))))) = (sk2 @ (cJ @ (^ [A:b]: ~ ((sk1 @ A) = (sk2 @ A))))))),inference(cnfConj,[status(thm)],[4])).
% 3.66/2.27 thf(8,plain,(((sk2 @ (cJ @ (^ [A:b]: ~ ((sk1 @ A) = (sk2 @ A))))) = (sk1 @ (cJ @ (^ [A:b]: ~ ((sk1 @ A) = (sk2 @ A))))))),inference(lifteq,[status(thm)],[6])).
% 3.66/2.27 thf(22,plain,(! [A:b] : (((sk2 @ A) = (sk1 @ A)) | ((sk1 @ (cJ @ (^ [B:b]: ~ ((sk1 @ B) = (sk2 @ B))))) != (sk1 @ (cJ @ (^ [B:b]: ~ ((sk1 @ B) = (sk2 @ B)))))))),inference(rewrite,[status(thm)],[20,8])).
% 3.66/2.27 thf(23,plain,(! [A:b] : (((sk2 @ A) = (sk1 @ A)))),inference(simp,[status(thm)],[22])).
% 3.66/2.27 thf(28,plain,(((sk1) != (sk1))),inference(rewrite,[status(thm)],[9,23])).
% 3.66/2.27 thf(29,plain,(($false)),inference(simp,[status(thm)],[28])).
% 3.66/2.27 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.66/2.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------