%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL494+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n007.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 03:00:08 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL494+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.34 % Computer : n007.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 4 18:59:56 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.13/0.43 % SZS status Theorem
% 0.13/0.43 % SZS output start Proof
% 0.13/0.43 tff(is_a_theorem_type, type, (
% 0.13/0.43 is_a_theorem: $i > $o)).
% 0.13/0.43 tff(implies_type, type, (
% 0.13/0.43 implies: ( $i * $i ) > $i)).
% 0.13/0.43 tff(or_type, type, (
% 0.13/0.43 or: ( $i * $i ) > $i)).
% 0.13/0.43 tff(not_type, type, (
% 0.13/0.43 not: $i > $i)).
% 0.13/0.43 tff(tptp_fun_X_29_type, type, (
% 0.13/0.43 tptp_fun_X_29: $i)).
% 0.13/0.43 tff(tptp_fun_Y_28_type, type, (
% 0.13/0.43 tptp_fun_Y_28: $i)).
% 0.13/0.43 tff(equiv_type, type, (
% 0.13/0.43 equiv: ( $i * $i ) > $i)).
% 0.13/0.43 tff(and_type, type, (
% 0.13/0.43 and: ( $i * $i ) > $i)).
% 0.13/0.43 tff(op_and_type, type, (
% 0.13/0.43 op_and: $o)).
% 0.13/0.43 tff(op_implies_or_type, type, (
% 0.13/0.43 op_implies_or: $o)).
% 0.13/0.43 tff(op_equiv_type, type, (
% 0.13/0.43 op_equiv: $o)).
% 0.13/0.43 tff(op_implies_and_type, type, (
% 0.13/0.43 op_implies_and: $o)).
% 0.13/0.43 tff(r3_type, type, (
% 0.13/0.43 r3: $o)).
% 0.13/0.43 tff(tptp_fun_P_48_type, type, (
% 0.13/0.43 tptp_fun_P_48: $i)).
% 0.13/0.43 tff(tptp_fun_Q_47_type, type, (
% 0.13/0.43 tptp_fun_Q_47: $i)).
% 0.13/0.43 tff(equivalence_2_type, type, (
% 0.13/0.43 equivalence_2: $o)).
% 0.13/0.43 tff(modus_ponens_type, type, (
% 0.13/0.43 modus_ponens: $o)).
% 0.13/0.43 tff(tptp_fun_Y_0_type, type, (
% 0.13/0.43 tptp_fun_Y_0: $i)).
% 0.13/0.43 tff(tptp_fun_X_1_type, type, (
% 0.13/0.43 tptp_fun_X_1: $i)).
% 0.13/0.43 tff(r2_type, type, (
% 0.13/0.43 r2: $o)).
% 0.13/0.43 tff(tptp_fun_Q_45_type, type, (
% 0.13/0.43 tptp_fun_Q_45: $i)).
% 0.13/0.43 tff(tptp_fun_P_46_type, type, (
% 0.13/0.43 tptp_fun_P_46: $i)).
% 0.13/0.43 tff(1,plain,
% 0.13/0.43 (op_and <=> op_and),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(2,axiom,(op_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_and')).
% 0.13/0.43 tff(3,plain,
% 0.13/0.43 (op_and),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.13/0.43 tff(4,plain,
% 0.13/0.43 (((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(5,plain,
% 0.13/0.43 (((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(6,plain,
% 0.13/0.43 ((op_and => ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(7,axiom,(op_and => ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_and')).
% 0.13/0.43 tff(8,plain,
% 0.13/0.43 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.43 tff(9,plain,
% 0.13/0.43 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.13/0.43 tff(10,plain,
% 0.13/0.43 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.43 tff(11,plain,
% 0.13/0.43 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.13/0.43 Proof display could not be completed: monotonicity rule is not handled
% 0.13/0.44 % E exiting
%------------------------------------------------------------------------------