%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL465+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n006.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 : Mon Sep 7 03:00:06 PM UTC 2026
% Result : Theorem 0.13s 0.46s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL465+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.13/0.38 % Computer : n006.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 4 21:21:18 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.46 % SZS status Theorem
% 0.13/0.46 % SZS output start Proof
% 0.13/0.46 tff(is_a_theorem_type, type, (
% 0.13/0.46 is_a_theorem: $i > $o)).
% 0.13/0.46 tff(implies_type, type, (
% 0.13/0.46 implies: ( $i * $i ) > $i)).
% 0.13/0.46 tff(cn1_type, type, (
% 0.13/0.46 cn1: $o)).
% 0.13/0.46 tff(tptp_fun_R_40_type, type, (
% 0.13/0.46 tptp_fun_R_40: $i)).
% 0.13/0.46 tff(tptp_fun_P_42_type, type, (
% 0.13/0.46 tptp_fun_P_42: $i)).
% 0.13/0.46 tff(tptp_fun_Q_41_type, type, (
% 0.13/0.46 tptp_fun_Q_41: $i)).
% 0.13/0.46 tff(tptp_fun_Z_12_type, type, (
% 0.13/0.46 tptp_fun_Z_12: $i)).
% 0.13/0.46 tff(tptp_fun_X_14_type, type, (
% 0.13/0.46 tptp_fun_X_14: $i)).
% 0.13/0.46 tff(tptp_fun_Y_13_type, type, (
% 0.13/0.46 tptp_fun_Y_13: $i)).
% 0.13/0.46 tff(implies_3_type, type, (
% 0.13/0.46 implies_3: $o)).
% 0.13/0.46 tff(1,plain,
% 0.13/0.46 (cn1 <=> cn1),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(2,axiom,(cn1), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax','luka_cn1')).
% 0.13/0.46 tff(3,plain,
% 0.13/0.46 (cn1),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.13/0.46 tff(4,plain,
% 0.13/0.46 (((~cn1) | ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))) <=> ((~cn1) | ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R)))))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(5,plain,
% 0.13/0.46 (((~cn1) | ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))) <=> ((~cn1) | ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R)))))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(6,plain,
% 0.13/0.46 ((((~cn1) | ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))) & (cn1 | (~is_a_theorem(implies(implies(P!42, Q!41), implies(implies(Q!41, R!40), implies(P!42, R!40))))))) <=> (((~cn1) | ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))) & (cn1 | (~is_a_theorem(implies(implies(P!42, Q!41), implies(implies(Q!41, R!40), implies(P!42, R!40)))))))),
% 0.13/0.46 inference(monotonicity,[status(thm)],[5])).
% 0.13/0.46 tff(7,plain,
% 0.13/0.46 ((cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))) <=> (cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R)))))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(8,axiom,(cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','cn1')).
% 0.13/0.46 tff(9,plain,
% 0.13/0.46 (cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.46 tff(10,plain,
% 0.13/0.46 (cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[9, 7])).
% 0.13/0.46 tff(11,plain,
% 0.13/0.46 (cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.13/0.46 tff(12,plain,
% 0.13/0.46 (cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.13/0.46 tff(13,plain,(
% 0.13/0.46 ((~cn1) | ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))) & (cn1 | (~is_a_theorem(implies(implies(P!42, Q!41), implies(implies(Q!41, R!40), implies(P!42, R!40))))))),
% 0.13/0.46 inference(skolemize,[status(sab)],[12])).
% 0.13/0.46 tff(14,plain,
% 0.13/0.46 (((~cn1) | ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))) & (cn1 | (~is_a_theorem(implies(implies(P!42, Q!41), implies(implies(Q!41, R!40), implies(P!42, R!40))))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.13/0.46 tff(15,plain,
% 0.13/0.46 ((~cn1) | ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.13/0.46 inference(and_elim,[status(thm)],[14])).
% 0.13/0.46 tff(16,plain,
% 0.13/0.46 ((~cn1) | ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.13/0.46 tff(17,plain,
% 0.13/0.46 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[16, 3])).
% 0.13/0.47 tff(18,plain,
% 0.13/0.47 ((~implies_3) <=> (~implies_3)),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(19,axiom,(~implies_3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hilbert_implies_3')).
% 0.13/0.47 tff(20,plain,
% 0.13/0.47 (~implies_3),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.47 tff(21,plain,
% 0.13/0.47 (((~implies_3) | ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> ((~implies_3) | ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(22,plain,
% 0.13/0.47 ((((~implies_3) | ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) & (implies_3 | (~is_a_theorem(implies(implies(X!14, Y!13), implies(implies(Y!13, Z!12), implies(X!14, Z!12))))))) <=> (((~implies_3) | ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) & (implies_3 | (~is_a_theorem(implies(implies(X!14, Y!13), implies(implies(Y!13, Z!12), implies(X!14, Z!12)))))))),
% 0.13/0.47 inference(monotonicity,[status(thm)],[21])).
% 0.13/0.47 tff(23,plain,
% 0.13/0.47 ((implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))))),
% 0.13/0.47 inference(rewrite,[status(thm)],[])).
% 0.13/0.47 tff(24,axiom,(implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','implies_3')).
% 0.13/0.47 tff(25,plain,
% 0.13/0.47 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.47 tff(26,plain,
% 0.13/0.47 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.13/0.47 tff(27,plain,
% 0.13/0.47 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.13/0.47 tff(28,plain,
% 0.13/0.47 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.13/0.47 tff(29,plain,(
% 0.13/0.47 ((~implies_3) | ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) & (implies_3 | (~is_a_theorem(implies(implies(X!14, Y!13), implies(implies(Y!13, Z!12), implies(X!14, Z!12))))))),
% 0.13/0.47 inference(skolemize,[status(sab)],[28])).
% 0.13/0.47 tff(30,plain,
% 0.13/0.47 (((~implies_3) | ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) & (implies_3 | (~is_a_theorem(implies(implies(X!14, Y!13), implies(implies(Y!13, Z!12), implies(X!14, Z!12))))))),
% 0.13/0.47 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.13/0.47 tff(31,plain,
% 0.13/0.47 (implies_3 | (~is_a_theorem(implies(implies(X!14, Y!13), implies(implies(Y!13, Z!12), implies(X!14, Z!12)))))),
% 0.13/0.47 inference(and_elim,[status(thm)],[30])).
% 0.13/0.47 tff(32,plain,
% 0.13/0.47 (~is_a_theorem(implies(implies(X!14, Y!13), implies(implies(Y!13, Z!12), implies(X!14, Z!12))))),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.13/0.47 tff(33,plain,
% 0.13/0.47 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))) | is_a_theorem(implies(implies(X!14, Y!13), implies(implies(Y!13, Z!12), implies(X!14, Z!12))))),
% 0.13/0.47 inference(quant_inst,[status(thm)],[])).
% 0.13/0.47 tff(34,plain,
% 0.13/0.47 ($false),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[33, 32, 17])).
% 0.13/0.47 % SZS output end Proof
% 0.13/0.47 % E exiting
%------------------------------------------------------------------------------