%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL544+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 0.33s 0.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL544+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 5 20:16:23 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.33/0.57 % SZS status Theorem
% 0.33/0.57 % SZS output start Proof
% 0.33/0.57 tff(is_a_theorem_type, type, (
% 0.33/0.57 is_a_theorem: $i > $o)).
% 0.33/0.57 tff(implies_type, type, (
% 0.33/0.57 implies: ( $i * $i ) > $i)).
% 0.33/0.57 tff(not_type, type, (
% 0.33/0.57 not: $i > $i)).
% 0.33/0.57 tff(and_type, type, (
% 0.33/0.57 and: ( $i * $i ) > $i)).
% 0.33/0.57 tff(tptp_fun_X_86_type, type, (
% 0.33/0.57 tptp_fun_X_86: $i)).
% 0.33/0.57 tff(op_implies_and_type, type, (
% 0.33/0.57 op_implies_and: $o)).
% 0.33/0.57 tff(implies_2_type, type, (
% 0.33/0.57 implies_2: $o)).
% 0.33/0.57 tff(tptp_fun_Y_11_type, type, (
% 0.33/0.57 tptp_fun_Y_11: $i)).
% 0.33/0.57 tff(tptp_fun_X_12_type, type, (
% 0.33/0.57 tptp_fun_X_12: $i)).
% 0.33/0.57 tff(and_3_type, type, (
% 0.33/0.57 and_3: $o)).
% 0.33/0.57 tff(tptp_fun_Y_20_type, type, (
% 0.33/0.57 tptp_fun_Y_20: $i)).
% 0.33/0.57 tff(tptp_fun_X_21_type, type, (
% 0.33/0.57 tptp_fun_X_21: $i)).
% 0.33/0.57 tff(necessarily_type, type, (
% 0.33/0.57 necessarily: $i > $i)).
% 0.33/0.57 tff(strict_implies_type, type, (
% 0.33/0.57 strict_implies: ( $i * $i ) > $i)).
% 0.33/0.57 tff(op_strict_implies_type, type, (
% 0.33/0.57 op_strict_implies: $o)).
% 0.33/0.57 tff(axiom_m4_type, type, (
% 0.33/0.57 axiom_m4: $o)).
% 0.33/0.57 tff(necessitation_type, type, (
% 0.33/0.57 necessitation: $o)).
% 0.33/0.57 tff(tptp_fun_X_58_type, type, (
% 0.33/0.57 tptp_fun_X_58: $i)).
% 0.33/0.57 tff(modus_ponens_type, type, (
% 0.33/0.57 modus_ponens: $o)).
% 0.33/0.57 tff(tptp_fun_Y_3_type, type, (
% 0.33/0.57 tptp_fun_Y_3: $i)).
% 0.33/0.57 tff(tptp_fun_X_4_type, type, (
% 0.33/0.57 tptp_fun_X_4: $i)).
% 0.33/0.57 tff(1,plain,
% 0.33/0.57 (op_implies_and <=> op_implies_and),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(2,axiom,(op_implies_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_op_implies_and')).
% 0.33/0.57 tff(3,plain,
% 0.33/0.57 (op_implies_and),
% 0.33/0.57 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.33/0.57 tff(4,plain,
% 0.33/0.57 (((~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)))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(5,plain,
% 0.33/0.57 (((~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)))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(6,plain,
% 0.33/0.57 ((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)))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(7,axiom,(op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_implies_and')).
% 0.33/0.57 tff(8,plain,
% 0.33/0.57 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.33/0.57 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.33/0.57 tff(9,plain,
% 0.33/0.57 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.33/0.57 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.33/0.57 tff(10,plain,
% 0.33/0.57 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.33/0.57 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.33/0.57 tff(11,plain,
% 0.33/0.57 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.33/0.57 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.33/0.57 Proof display could not be completed: monotonicity rule is not handled
% 0.33/0.58 % E exiting
%------------------------------------------------------------------------------