%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL506+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n011.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 03:00:09 PM UTC 2026
% Result : Theorem 0.12s 0.42s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL506+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 22:27:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.42 % SZS status Theorem
% 0.12/0.42 % SZS output start Proof
% 0.12/0.42 tff(is_a_theorem_type, type, (
% 0.12/0.42 is_a_theorem: $i > $o)).
% 0.12/0.42 tff(implies_type, type, (
% 0.12/0.42 implies: ( $i * $i ) > $i)).
% 0.12/0.42 tff(and_type, type, (
% 0.12/0.42 and: ( $i * $i ) > $i)).
% 0.12/0.42 tff(kn2_type, type, (
% 0.12/0.42 kn2: $o)).
% 0.12/0.42 tff(tptp_fun_P_36_type, type, (
% 0.12/0.42 tptp_fun_P_36: $i)).
% 0.12/0.42 tff(tptp_fun_Q_35_type, type, (
% 0.12/0.42 tptp_fun_Q_35: $i)).
% 0.12/0.42 tff(tptp_fun_X_16_type, type, (
% 0.12/0.42 tptp_fun_X_16: $i)).
% 0.12/0.42 tff(tptp_fun_Y_15_type, type, (
% 0.12/0.42 tptp_fun_Y_15: $i)).
% 0.12/0.42 tff(and_1_type, type, (
% 0.12/0.42 and_1: $o)).
% 0.12/0.42 tff(1,plain,
% 0.12/0.42 (kn2 <=> kn2),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(2,axiom,(kn2), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax','rosser_kn2')).
% 0.12/0.42 tff(3,plain,
% 0.12/0.42 (kn2),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.12/0.42 tff(4,plain,
% 0.12/0.42 (((~kn2) | ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> ((~kn2) | ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(5,plain,
% 0.12/0.42 (((~kn2) | ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> ((~kn2) | ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(6,plain,
% 0.12/0.42 ((((~kn2) | ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) & (kn2 | (~is_a_theorem(implies(and(P!36, Q!35), P!36))))) <=> (((~kn2) | ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) & (kn2 | (~is_a_theorem(implies(and(P!36, Q!35), P!36)))))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[5])).
% 0.12/0.42 tff(7,plain,
% 0.12/0.42 ((kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(8,axiom,(kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','kn2')).
% 0.12/0.42 tff(9,plain,
% 0.12/0.42 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.42 tff(10,plain,
% 0.12/0.42 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[9, 7])).
% 0.12/0.42 tff(11,plain,
% 0.12/0.42 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.12/0.42 tff(12,plain,
% 0.12/0.42 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.12/0.42 tff(13,plain,(
% 0.12/0.42 ((~kn2) | ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) & (kn2 | (~is_a_theorem(implies(and(P!36, Q!35), P!36))))),
% 0.12/0.42 inference(skolemize,[status(sab)],[12])).
% 0.12/0.42 tff(14,plain,
% 0.12/0.42 (((~kn2) | ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) & (kn2 | (~is_a_theorem(implies(and(P!36, Q!35), P!36))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.12/0.42 tff(15,plain,
% 0.12/0.42 ((~kn2) | ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.12/0.42 inference(and_elim,[status(thm)],[14])).
% 0.12/0.42 tff(16,plain,
% 0.12/0.42 ((~kn2) | ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.12/0.42 tff(17,plain,
% 0.12/0.42 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[16, 3])).
% 0.12/0.42 tff(18,plain,
% 0.12/0.42 ((~and_1) <=> (~and_1)),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(19,axiom,(~and_1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hilbert_and_1')).
% 0.12/0.42 tff(20,plain,
% 0.12/0.42 (~and_1),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.42 tff(21,plain,
% 0.12/0.42 (((~and_1) | ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> ((~and_1) | ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(22,plain,
% 0.12/0.42 ((((~and_1) | ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) & (and_1 | (~is_a_theorem(implies(and(X!16, Y!15), X!16))))) <=> (((~and_1) | ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) & (and_1 | (~is_a_theorem(implies(and(X!16, Y!15), X!16)))))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[21])).
% 0.12/0.42 tff(23,plain,
% 0.12/0.42 ((and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(24,axiom,(and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','and_1')).
% 0.12/0.42 tff(25,plain,
% 0.12/0.42 (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.42 tff(26,plain,
% 0.12/0.42 (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.12/0.42 tff(27,plain,
% 0.12/0.42 (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.12/0.42 tff(28,plain,
% 0.12/0.42 (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.42 tff(29,plain,(
% 0.12/0.42 ((~and_1) | ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) & (and_1 | (~is_a_theorem(implies(and(X!16, Y!15), X!16))))),
% 0.12/0.42 inference(skolemize,[status(sab)],[28])).
% 0.12/0.42 tff(30,plain,
% 0.12/0.42 (((~and_1) | ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) & (and_1 | (~is_a_theorem(implies(and(X!16, Y!15), X!16))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.12/0.42 tff(31,plain,
% 0.12/0.42 (and_1 | (~is_a_theorem(implies(and(X!16, Y!15), X!16)))),
% 0.12/0.42 inference(and_elim,[status(thm)],[30])).
% 0.12/0.42 tff(32,plain,
% 0.12/0.42 (~is_a_theorem(implies(and(X!16, Y!15), X!16))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.12/0.42 tff(33,plain,
% 0.12/0.42 ((~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) | is_a_theorem(implies(and(X!16, Y!15), X!16))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(34,plain,
% 0.12/0.42 ($false),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[33, 32, 17])).
% 0.12/0.42 % SZS output end Proof
% 0.12/0.42 % E exiting
%------------------------------------------------------------------------------