%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL727^5 : 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 : n007.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 08:14:13 AM UTC 2026
% Result : Theorem 4.41s 2.40s
% Output : Refutation 4.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL727^5 : 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
% 0.10/0.21 % Computer : n007.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 09:56:40 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (188ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 2.03/1.41 % [INFO] eprover registered as external prover.
% 2.03/1.41 % [INFO] Scanning for conjecture ...
% 2.22/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.55 % [INFO] Type checking passed.
% 2.22/1.55 % [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 ...
% 4.41/2.40 % External prover 'e' found a proof!
% 4.41/2.40 % [INFO] Killing All external provers ...
% 4.41/2.40 % Time passed: 2052ms (effective reasoning time: 1397ms)
% 4.41/2.40 % 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)>
% 4.41/2.40 % Axioms used in derivation (0):
% 4.41/2.40 % No. of inferences in proof: 9
% 4.41/2.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2052 ms resp. 1397 ms w/o parsing
% 4.41/2.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.41/2.46 thf(a_type, type, a: $tType).
% 4.41/2.46 thf(sk1_decl, type, sk1: (((a > $o) > (a > $o)) > ((a > $o) > a))).
% 4.41/2.46 thf(sk2_decl, type, sk2: ((a > $o) > $o)).
% 4.41/2.46 thf(sk3_decl, type, sk3: ((a > $o) > a)).
% 4.41/2.46 thf(sk4_decl, type, sk4: (((a > $o) > a) > (a > $o))).
% 4.41/2.46 thf(sk1_def, definition, sk1 = (^ [A:((a > $o) > (a > $o))]: (@+ [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ (C) @ D)) => (A @ C @ (B @ C))))) ).
% 4.41/2.46 thf(sk2_def, definition, sk2 = (@+ [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))))))) ).
% 4.41/2.46 thf(sk3_def, definition, sk3 = ((@+) @ a) ).
% 4.41/2.46 thf(sk4_def, definition, sk4 = (^ [A:((a > $o) > a)]: (@+ [B:(a > $o)]: ~ ((sk2 @ B) => (B @ (A @ B))))) ).
% 4.41/2.46 thf(1,conjecture,(((! [A:((a > $o) > (a > $o))]: ? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ C @ D)) => (A @ C @ (B @ C)))) => (! [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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM533)).
% 4.41/2.46 thf(2,negated_conjecture,((~ ((! [A:((a > $o) > (a > $o))]: ? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ C @ D)) => (A @ C @ (B @ C)))) => (! [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))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.41/2.46 thf(3,plain,((~ ((! [A:((a > $o) > (a > $o))]: ? [B:((a > $o) > a)]: ! [C:(a > $o)]: ((? [D:a]: (A @ (C) @ D)) => (A @ (C) @ (B @ (C))))) => (! [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)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.41/2.46 thf(4,plain,(! [E:((a > $o) > a),D:(a > $o),C:a,B:(a > $o),A:((a > $o) > (a > $o))] : (((~ (A @ (B) @ C) | (A @ (B) @ (sk1 @ (A) @ (B)))) & (~ (sk2 @ (D)) | (D @ (sk3 @ (D)))) & (sk2 @ (sk4 @ (E))) & ~ (sk4 @ (E) @ (E @ (sk4 @ (E))))))),inference(cnf,[status(esa)],[3])).
% 4.41/2.46 thf(7,plain,(! [A:((a > $o) > a)] : ((sk2 @ (sk4 @ (A))))),inference(cnfConj,[status(thm)],[4])).
% 4.41/2.46 thf(10,plain,(! [A:((a > $o) > a)] : ((sk2 @ (sk4 @ (A))))),inference(simp,[status(thm)],[7])).
% 4.41/2.46 thf(8,plain,(! [A:((a > $o) > a)] : ((~ (sk4 @ (A) @ (A @ (sk4 @ (A))))))),inference(cnfConj,[status(thm)],[4])).
% 4.41/2.46 thf(11,plain,(! [A:((a > $o) > a)] : ((~ (sk4 @ (A) @ (A @ (sk4 @ (A))))))),inference(simp,[status(thm)],[8])).
% 4.41/2.46 thf(37,plain,(($false)),inference(e,[status(thm)],[3,10,11])).
% 4.41/2.46 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.41/2.46 % [INFO] Killing All external provers ...
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