%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL539+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n013.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 03:00:11 PM UTC 2026
% Result : Theorem 182.89s 183.21s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL539+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 14:55:36 UTC 2026
% 0.01/0.36 % CPUTime :
% 182.89/183.21 % SZS status Theorem
% 182.89/183.21 % SZS output start Proof
% 182.89/183.21 tff(is_a_theorem_type, type, (
% 182.89/183.21 is_a_theorem: $i > $o)).
% 182.89/183.21 tff(implies_type, type, (
% 182.89/183.21 implies: ( $i * $i ) > $i)).
% 182.89/183.21 tff(and_type, type, (
% 182.89/183.21 and: ( $i * $i ) > $i)).
% 182.89/183.21 tff(tptp_fun_X_64_type, type, (
% 182.89/183.21 tptp_fun_X_64: $i)).
% 182.89/183.21 tff(tptp_fun_Y_63_type, type, (
% 182.89/183.21 tptp_fun_Y_63: $i)).
% 182.89/183.21 tff(not_type, type, (
% 182.89/183.21 not: $i > $i)).
% 182.89/183.21 tff(equiv_type, type, (
% 182.89/183.21 equiv: ( $i * $i ) > $i)).
% 182.89/183.21 tff(op_equiv_type, type, (
% 182.89/183.21 op_equiv: $o)).
% 182.89/183.21 tff(op_implies_and_type, type, (
% 182.89/183.21 op_implies_and: $o)).
% 182.89/183.21 tff(necessarily_type, type, (
% 182.89/183.21 necessarily: $i > $i)).
% 182.89/183.21 tff(strict_implies_type, type, (
% 182.89/183.21 strict_implies: ( $i * $i ) > $i)).
% 182.89/183.21 tff(op_strict_implies_type, type, (
% 182.89/183.21 op_strict_implies: $o)).
% 182.89/183.21 tff(and_1_type, type, (
% 182.89/183.21 and_1: $o)).
% 182.89/183.21 tff(tptp_fun_X_17_type, type, (
% 182.89/183.21 tptp_fun_X_17: $i)).
% 182.89/183.21 tff(tptp_fun_Y_16_type, type, (
% 182.89/183.21 tptp_fun_Y_16: $i)).
% 182.89/183.21 tff(strict_equiv_type, type, (
% 182.89/183.21 strict_equiv: ( $i * $i ) > $i)).
% 182.89/183.21 tff(op_strict_equiv_type, type, (
% 182.89/183.21 op_strict_equiv: $o)).
% 182.89/183.21 tff(substitution_strict_equiv_type, type, (
% 182.89/183.21 substitution_strict_equiv: $o)).
% 182.89/183.21 tff(modus_ponens_type, type, (
% 182.89/183.21 modus_ponens: $o)).
% 182.89/183.21 tff(tptp_fun_Y_3_type, type, (
% 182.89/183.21 tptp_fun_Y_3: $i)).
% 182.89/183.21 tff(tptp_fun_X_4_type, type, (
% 182.89/183.21 tptp_fun_X_4: $i)).
% 182.89/183.21 tff(axiom_M_type, type, (
% 182.89/183.21 axiom_M: $o)).
% 182.89/183.21 tff(tptp_fun_X_67_type, type, (
% 182.89/183.21 tptp_fun_X_67: $i)).
% 182.89/183.21 tff(equivalence_3_type, type, (
% 182.89/183.21 equivalence_3: $o)).
% 182.89/183.21 tff(tptp_fun_Y_33_type, type, (
% 182.89/183.21 tptp_fun_Y_33: $i)).
% 182.89/183.21 tff(tptp_fun_X_34_type, type, (
% 182.89/183.21 tptp_fun_X_34: $i)).
% 182.89/183.21 tff(and_2_type, type, (
% 182.89/183.21 and_2: $o)).
% 182.89/183.21 tff(tptp_fun_Y_18_type, type, (
% 182.89/183.21 tptp_fun_Y_18: $i)).
% 182.89/183.21 tff(tptp_fun_X_19_type, type, (
% 182.89/183.21 tptp_fun_X_19: $i)).
% 182.89/183.21 tff(substitution_of_equivalents_type, type, (
% 182.89/183.21 substitution_of_equivalents: $o)).
% 182.89/183.21 tff(tptp_fun_Y_5_type, type, (
% 182.89/183.21 tptp_fun_Y_5: $i)).
% 182.89/183.21 tff(tptp_fun_X_6_type, type, (
% 182.89/183.21 tptp_fun_X_6: $i)).
% 182.89/183.21 tff(1,plain,
% 182.89/183.21 (op_equiv <=> op_equiv),
% 182.89/183.21 inference(rewrite,[status(thm)],[])).
% 182.89/183.21 tff(2,axiom,(op_equiv), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_op_equiv')).
% 182.89/183.21 tff(3,plain,
% 182.89/183.21 (op_equiv),
% 182.89/183.21 inference(modus_ponens,[status(thm)],[2, 1])).
% 182.89/183.21 tff(4,plain,
% 182.89/183.21 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 182.89/183.21 inference(rewrite,[status(thm)],[])).
% 182.89/183.21 tff(5,plain,
% 182.89/183.21 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 182.89/183.21 inference(rewrite,[status(thm)],[])).
% 182.89/183.21 tff(6,plain,
% 182.89/183.21 ((op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 182.89/183.21 inference(rewrite,[status(thm)],[])).
% 182.89/183.21 tff(7,axiom,(op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_equiv')).
% 182.89/183.21 tff(8,plain,
% 182.89/183.21 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 182.89/183.21 inference(modus_ponens,[status(thm)],[7, 6])).
% 182.89/183.21 tff(9,plain,
% 182.89/183.21 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 182.89/183.21 inference(modus_ponens,[status(thm)],[8, 5])).
% 182.89/183.21 tff(10,plain,
% 182.89/183.21 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 182.89/183.21 inference(modus_ponens,[status(thm)],[9, 5])).
% 182.89/183.21 tff(11,plain,
% 182.89/183.21 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 182.89/183.21 inference(modus_ponens,[status(thm)],[10, 5])).
% 182.89/183.21 Proof display could not be completed: monotonicity rule is not handled
% 0.16/184.82 % E exiting
%------------------------------------------------------------------------------