%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL726^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n012.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 08:14:12 AM UTC 2026
% Result : Theorem 2.51s 1.30s
% Output : Refutation 2.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL726^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % 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
% 0.05/0.12 % Computer : n012.cluster.edu
% 0.05/0.12 % Model : x86_64 x86_64
% 0.05/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.12 % Memory : 8046.5625MB
% 0.05/0.12 % OS : Linux 6.8.0-71-generic
% 0.05/0.12 % CPULimit : 300
% 0.05/0.12 % WCLimit : 300
% 0.05/0.12 % DateTime : Tue Sep 29 09:57:18 UTC 2026
% 0.05/0.12 % CPUTime :
% 0.05/0.12 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
% 0.40/0.42 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.55/0.52 % [INFO] Parsing done (92ms).
% 0.55/0.52 % [INFO] Running in sequential loop mode.
% 0.99/0.72 % [INFO] eprover registered as external prover.
% 0.99/0.72 % [INFO] Scanning for conjecture ...
% 0.99/0.77 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 0.99/0.78 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 0.99/0.79 % [INFO] Problem is higher-order (TPTP THF).
% 0.99/0.79 % [INFO] Type checking passed.
% 0.99/0.79 % [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 ...
% 2.51/1.30 % [INFO] Killing All external provers ...
% 2.51/1.30 % Time passed: 1099ms (effective reasoning time: 774ms)
% 2.51/1.30 % 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)>
% 2.51/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1099 ms resp. 774 ms w/o parsing
% 2.51/1.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.51/1.36 thf(a_type, type, a: $tType).
% 2.51/1.36 thf(sk1_decl, type, sk1: (((a > $o) > $o) > (a > $o))).
% 2.51/1.36 thf(sk2_decl, type, sk2: (((a > $o) > $o) > ((a > $o) > a))).
% 2.51/1.36 thf(sk3_decl, type, sk3: (((a > $o) > a) > (a > $o))).
% 2.51/1.36 thf(sk4_decl, type, sk4: (((a > $o) > a) > a)).
% 2.51/1.36 thf(sk1_def, definition, sk1 = (^ [A:((a > $o) > $o)]: (@+ [B:(a > $o)]: ~ ((A @ B) => (? [C:a]: (B @ C))))) ).
% 2.51/1.36 thf(sk2_def, definition, sk2 = (^ [A:((a > $o) > $o)]: (@+ [B:((a > $o) > a)]: ! [C:(a > $o)]: ((A @ C) => (C @ (B @ C))))) ).
% 2.51/1.36 thf(sk3_def, definition, sk3 = (@+ [A:(((a > $o) > a) > (a > $o))]: ~ ((! [B:((a > $o) > a)]: ? [C:a]: (A @ (B) @ C)) => (? [B:((a > $o) > a)]: (A @ (B) @ (B @ (A @ (B))))))) ).
% 2.51/1.36 thf(sk4_def, definition, sk4 = (^ [A:((a > $o) > a)]: (@+ [B:a]: (sk3 @ (A) @ B))) ).
% 2.51/1.36 thf(1,conjecture,(((! [A:((a > $o) > $o)]: ((! [B:(a > $o)]: ((A @ B) => (? [C:a]: (B @ C)))) => (? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((A @ C) => (C @ (B @ C)))))) => (! [A:(((a > $o) > a) > (a > $o))]: ((! [B:((a > $o) > a)]: ? [C:a]: (A @ B @ C)) => (? [B:((a > $o) > a)]: (A @ B @ (B @ (A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM534)).
% 2.51/1.37 thf(2,negated_conjecture,((~ ((! [A:((a > $o) > $o)]: ((! [B:(a > $o)]: ((A @ B) => (? [C:a]: (B @ C)))) => (? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((A @ C) => (C @ (B @ C)))))) => (! [A:(((a > $o) > a) > (a > $o))]: ((! [B:((a > $o) > a)]: ? [C:a]: (A @ B @ C)) => (? [B:((a > $o) > a)]: (A @ B @ (B @ (A @ B))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 2.51/1.37 thf(3,plain,((~ ((! [A:((a > $o) > $o)]: ((! [B:(a > $o)]: ((A @ (B)) => (? [C:a]: (B @ C)))) => (? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((A @ (C)) => (C @ (B @ (C))))))) => (! [A:(((a > $o) > a) > (a > $o))]: ((! [B:((a > $o) > a)]: ? [C:a]: (A @ (B) @ C)) => (? [B:((a > $o) > a)]: (A @ (B) @ (B @ (A @ (B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 2.51/1.37 thf(4,plain,(! [E:((a > $o) > a),D:((a > $o) > a),C:(a > $o),B:a,A:((a > $o) > $o)] : ((((A @ (sk1 @ (A))) | ~ (A @ (C)) | (C @ (sk2 @ (A) @ (C)))) & (~ (sk1 @ (A) @ B) | ~ (A @ (C)) | (C @ (sk2 @ (A) @ (C)))) & (sk3 @ (D) @ (sk4 @ (D))) & ~ (sk3 @ (E) @ (E @ (sk3 @ (E))))))),inference(cnf,[status(esa)],[3])).
% 2.51/1.37 thf(7,plain,(! [A:((a > $o) > a)] : ((sk3 @ (A) @ (sk4 @ (A))))),inference(cnfConj,[status(thm)],[4])).
% 2.51/1.37 thf(13,plain,(! [A:((a > $o) > a)] : ((sk3 @ (A) @ (sk4 @ (A))))),inference(simp,[status(thm)],[7])).
% 2.51/1.37 thf(17,axiom,((? [A:((a > $o) > a)]: ! [B:(a > $o)]: ((? [C:a]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 2.51/1.37 thf(18,plain,(! [B:a,A:((a > $o) > a)] : ((~ (sk3 @ (A) @ B)) | (sk3 @ (A) @ (@+ [C:a]: (sk3 @ (A) @ C))))),inference(choice,[status(esa)],[17])).
% 2.51/1.37 thf(8,plain,(! [A:((a > $o) > a)] : ((~ (sk3 @ (A) @ (A @ (sk3 @ (A))))))),inference(cnfConj,[status(thm)],[4])).
% 2.51/1.37 thf(14,plain,(! [A:((a > $o) > a)] : ((~ (sk3 @ (A) @ (A @ (sk3 @ (A))))))),inference(simp,[status(thm)],[8])).
% 2.51/1.37 thf(27,plain,(! [C:((a > $o) > a),B:a,A:((a > $o) > a)] : ((~ (sk3 @ (A) @ B)) | ~ (($true)) | ((sk3 @ (A) @ (@+ [D:a]: (sk3 @ (A) @ D))) != (sk3 @ (C) @ (C @ (sk3 @ (C))))))),inference(paramod_ordered,[status(thm)],[18,14])).
% 2.51/1.37 thf(28,plain,(! [C:((a > $o) > a),B:a,A:((a > $o) > a)] : ((~ (sk3 @ (A) @ B)) | ((sk3 @ (A) @ (@+ [D:a]: (sk3 @ (A) @ D))) != (sk3 @ (C) @ (C @ (sk3 @ (C))))))),inference(simp,[status(thm)],[27])).
% 2.51/1.37 thf(29,plain,(! [A:a] : ((~ (sk3 @ ((@+) @ a) @ A)))),inference(pre_uni,[status(thm)],[28:[bind(A, $thf((@+) @ a)),bind(B, $thf(B)),bind(C, $thf((@+) @ a))]])).
% 2.51/1.37 thf(31,plain,(! [A:a] : ((~ (sk3 @ ((@+) @ a) @ A)))),inference(simp,[status(thm)],[29])).
% 2.51/1.37 thf(32,plain,(! [B:a,A:((a > $o) > a)] : (~ (($true)) | ((sk3 @ (A) @ (sk4 @ (A))) != (sk3 @ ((@+) @ a) @ B)))),inference(paramod_ordered,[status(thm)],[13,31])).
% 2.51/1.37 thf(33,plain,(! [B:a,A:((a > $o) > a)] : (((sk3 @ (A) @ (sk4 @ (A))) != (sk3 @ ((@+) @ a) @ B)))),inference(simp,[status(thm)],[32])).
% 2.51/1.37 thf(34,plain,(($false)),inference(pattern_uni,[status(thm)],[33:[bind(A, $thf((@+) @ a)),bind(B, $thf(sk4 @ ((@+) @ a)))]])).
% 2.51/1.37 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.51/1.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------