%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n004.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 0.34s 0.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n004.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 18:28:31 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.34/0.58 % SZS status Theorem
% 0.34/0.58 % SZS output start Proof
% 0.34/0.58 tff(is_a_theorem_type, type, (
% 0.34/0.58 is_a_theorem: $i > $o)).
% 0.34/0.58 tff(implies_type, type, (
% 0.34/0.58 implies: ( $i * $i ) > $i)).
% 0.34/0.58 tff(not_type, type, (
% 0.34/0.58 not: $i > $i)).
% 0.34/0.58 tff(and_type, type, (
% 0.34/0.58 and: ( $i * $i ) > $i)).
% 0.34/0.58 tff(tptp_fun_X_86_type, type, (
% 0.34/0.58 tptp_fun_X_86: $i)).
% 0.34/0.58 tff(op_implies_and_type, type, (
% 0.34/0.58 op_implies_and: $o)).
% 0.34/0.58 tff(implies_2_type, type, (
% 0.34/0.58 implies_2: $o)).
% 0.34/0.58 tff(tptp_fun_Y_11_type, type, (
% 0.34/0.58 tptp_fun_Y_11: $i)).
% 0.34/0.58 tff(tptp_fun_X_12_type, type, (
% 0.34/0.58 tptp_fun_X_12: $i)).
% 0.34/0.58 tff(and_3_type, type, (
% 0.34/0.58 and_3: $o)).
% 0.34/0.58 tff(tptp_fun_Y_20_type, type, (
% 0.34/0.58 tptp_fun_Y_20: $i)).
% 0.34/0.58 tff(tptp_fun_X_21_type, type, (
% 0.34/0.58 tptp_fun_X_21: $i)).
% 0.34/0.58 tff(necessarily_type, type, (
% 0.34/0.58 necessarily: $i > $i)).
% 0.34/0.58 tff(strict_implies_type, type, (
% 0.34/0.58 strict_implies: ( $i * $i ) > $i)).
% 0.34/0.58 tff(op_strict_implies_type, type, (
% 0.34/0.58 op_strict_implies: $o)).
% 0.34/0.58 tff(axiom_m4_type, type, (
% 0.34/0.58 axiom_m4: $o)).
% 0.34/0.58 tff(necessitation_type, type, (
% 0.34/0.58 necessitation: $o)).
% 0.34/0.58 tff(tptp_fun_X_58_type, type, (
% 0.34/0.58 tptp_fun_X_58: $i)).
% 0.34/0.58 tff(modus_ponens_type, type, (
% 0.34/0.58 modus_ponens: $o)).
% 0.34/0.58 tff(tptp_fun_Y_3_type, type, (
% 0.34/0.58 tptp_fun_Y_3: $i)).
% 0.34/0.58 tff(tptp_fun_X_4_type, type, (
% 0.34/0.58 tptp_fun_X_4: $i)).
% 0.34/0.58 tff(1,plain,
% 0.34/0.58 (op_implies_and <=> op_implies_and),
% 0.34/0.58 inference(rewrite,[status(thm)],[])).
% 0.34/0.58 tff(2,axiom,(op_implies_and), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_op_implies_and')).
% 0.34/0.58 tff(3,plain,
% 0.34/0.58 (op_implies_and),
% 0.34/0.58 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.34/0.58 tff(4,plain,
% 0.34/0.58 (((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))))),
% 0.34/0.58 inference(rewrite,[status(thm)],[])).
% 0.34/0.58 tff(5,plain,
% 0.34/0.58 (((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))))),
% 0.34/0.58 inference(rewrite,[status(thm)],[])).
% 0.34/0.58 tff(6,plain,
% 0.34/0.58 ((op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))))),
% 0.34/0.58 inference(rewrite,[status(thm)],[])).
% 0.34/0.58 tff(7,axiom,(op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_implies_and')).
% 0.34/0.58 tff(8,plain,
% 0.34/0.58 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.34/0.58 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.34/0.58 tff(9,plain,
% 0.34/0.58 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.34/0.58 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.34/0.58 tff(10,plain,
% 0.34/0.58 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.34/0.58 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.34/0.58 tff(11,plain,
% 0.34/0.58 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.34/0.58 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.34/0.58 Proof display could not be completed: monotonicity rule is not handled
% 0.34/0.59 % E exiting
%------------------------------------------------------------------------------