%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% 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 : Mon Sep 7 03:00:04 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.06/0.33 % Computer : n010.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Fri Sep 4 20:40:55 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(is_a_theorem_type, type, (
% 0.12/0.38 is_a_theorem: $i > $o)).
% 0.12/0.38 tff(implies_type, type, (
% 0.12/0.38 implies: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_R_40_type, type, (
% 0.12/0.38 tptp_fun_R_40: $i)).
% 0.12/0.38 tff(tptp_fun_P_42_type, type, (
% 0.12/0.38 tptp_fun_P_42: $i)).
% 0.12/0.38 tff(tptp_fun_Q_41_type, type, (
% 0.12/0.38 tptp_fun_Q_41: $i)).
% 0.12/0.38 tff(cn1_type, type, (
% 0.12/0.38 cn1: $o)).
% 0.12/0.38 tff(implies_3_type, type, (
% 0.12/0.38 implies_3: $o)).
% 0.12/0.38 tff(tptp_fun_Z_12_type, type, (
% 0.12/0.38 tptp_fun_Z_12: $i)).
% 0.12/0.38 tff(tptp_fun_X_14_type, type, (
% 0.12/0.38 tptp_fun_X_14: $i)).
% 0.12/0.38 tff(tptp_fun_Y_13_type, type, (
% 0.12/0.38 tptp_fun_Y_13: $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~cn1) <=> (~cn1)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,axiom,(~cn1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','luka_cn1')).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (~cn1),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (((~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)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 ((((~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)))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[4])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 ((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)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(7,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/sandbox2/benchmark/Axioms/LCL006+0.ax','cn1')).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 6])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (cn1 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(implies(Q, R), implies(P, R))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.12/0.38 tff(12,plain,(
% 0.12/0.38 ((~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))))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (((~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))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (cn1 | (~is_a_theorem(implies(implies(P!42, Q!41), implies(implies(Q!41, R!40), implies(P!42, R!40)))))),
% 0.12/0.38 inference(and_elim,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (~is_a_theorem(implies(implies(P!42, Q!41), implies(implies(Q!41, R!40), implies(P!42, R!40))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[14, 3])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (implies_3 <=> implies_3),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(17,axiom,(implies_3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_implies_3')).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (implies_3),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (((~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)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (((~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)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((((~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)))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((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)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,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/sandbox2/benchmark/Axioms/LCL006+0.ax','implies_3')).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.12/0.38 tff(28,plain,(
% 0.12/0.38 ((~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))))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (((~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))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~implies_3) | ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.12/0.38 inference(and_elim,[status(thm)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~implies_3) | ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 19])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 18])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) | is_a_theorem(implies(implies(P!42, Q!41), implies(implies(Q!41, R!40), implies(P!42, R!40))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[33, 32, 15])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------