%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n003.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 03:00:12 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n003.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 21:51:53 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.14/0.43 % SZS status Theorem
% 0.14/0.43 % SZS output start Proof
% 0.14/0.43 tff(is_a_theorem_type, type, (
% 0.14/0.43 is_a_theorem: $i > $o)).
% 0.14/0.43 tff(necessarily_type, type, (
% 0.14/0.43 necessarily: $i > $i)).
% 0.14/0.43 tff(implies_type, type, (
% 0.14/0.43 implies: ( $i * $i ) > $i)).
% 0.14/0.43 tff(tptp_fun_X_82_type, type, (
% 0.14/0.43 tptp_fun_X_82: $i)).
% 0.14/0.43 tff(and_type, type, (
% 0.14/0.43 and: ( $i * $i ) > $i)).
% 0.14/0.43 tff(tptp_fun_Y_81_type, type, (
% 0.14/0.43 tptp_fun_Y_81: $i)).
% 0.14/0.43 tff(strict_implies_type, type, (
% 0.14/0.43 strict_implies: ( $i * $i ) > $i)).
% 0.14/0.43 tff(op_strict_implies_type, type, (
% 0.14/0.43 op_strict_implies: $o)).
% 0.14/0.43 tff(axiom_m2_type, type, (
% 0.14/0.43 axiom_m2: $o)).
% 0.14/0.43 tff(and_1_type, type, (
% 0.14/0.43 and_1: $o)).
% 0.14/0.43 tff(tptp_fun_X_17_type, type, (
% 0.14/0.43 tptp_fun_X_17: $i)).
% 0.14/0.43 tff(tptp_fun_Y_16_type, type, (
% 0.14/0.43 tptp_fun_Y_16: $i)).
% 0.14/0.43 tff(necessitation_type, type, (
% 0.14/0.43 necessitation: $o)).
% 0.14/0.43 tff(tptp_fun_X_58_type, type, (
% 0.14/0.43 tptp_fun_X_58: $i)).
% 0.14/0.43 tff(1,plain,
% 0.14/0.43 (op_strict_implies <=> op_strict_implies),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(2,axiom,(op_strict_implies), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_0_op_strict_implies')).
% 0.14/0.43 tff(3,plain,
% 0.14/0.43 (op_strict_implies),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.14/0.43 tff(4,plain,
% 0.14/0.43 (((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) <=> ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(5,plain,
% 0.14/0.43 (((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) <=> ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(6,plain,
% 0.14/0.43 ((op_strict_implies => ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) <=> ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(7,axiom,(op_strict_implies => ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax','op_strict_implies')).
% 0.14/0.43 tff(8,plain,
% 0.14/0.43 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.14/0.43 tff(9,plain,
% 0.14/0.43 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.14/0.43 tff(10,plain,
% 0.14/0.43 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.43 tff(11,plain,
% 0.14/0.43 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.14/0.43 Proof display could not be completed: monotonicity rule is not handled
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------