%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n012.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 03:00:36 PM UTC 2026
% Result : Theorem 0.03s 0.32s
% Output : Proof 0.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.01 % Command : run_E %s %d THM
% 0.03/0.28 % Computer : n012.cluster.edu
% 0.03/0.28 % Model : x86_64 x86_64
% 0.03/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.28 % Memory : 8046.5625MB
% 0.03/0.28 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 5 23:57:14 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.32 % SZS status Theorem
% 0.03/0.32 % SZS output start Proof
% 0.03/0.32 tff(r1_type, type, (
% 0.03/0.32 r1: ( $i * $i ) > $o)).
% 0.03/0.32 tff(tptp_fun_X_0_type, type, (
% 0.03/0.32 tptp_fun_X_0: $i)).
% 0.03/0.32 tff(p1_type, type, (
% 0.03/0.32 p1: $i > $o)).
% 0.03/0.32 tff(1,plain,
% 0.03/0.32 (^[Y: $i] : refl((~r1(X!0, Y)) <=> (~r1(X!0, Y)))),
% 0.03/0.32 inference(bind,[status(th)],[])).
% 0.03/0.32 tff(2,plain,
% 0.03/0.32 (![Y: $i] : (~r1(X!0, Y)) <=> ![Y: $i] : (~r1(X!0, Y))),
% 0.03/0.32 inference(quant_intro,[status(thm)],[1])).
% 0.03/0.32 tff(3,plain,
% 0.03/0.32 (?[X: $i] : ![Y: $i] : (~r1(X, Y)) <=> ?[X: $i] : ![Y: $i] : (~r1(X, Y))),
% 0.03/0.32 inference(rewrite,[status(thm)],[])).
% 0.03/0.32 tff(4,plain,
% 0.03/0.32 ((~(~?[X: $i] : ![Y: $i] : (~r1(X, Y)))) <=> ?[X: $i] : ![Y: $i] : (~r1(X, Y))),
% 0.03/0.32 inference(rewrite,[status(thm)],[])).
% 0.03/0.32 tff(5,plain,
% 0.03/0.32 ((~?[X: $i] : (~($false | (~![Y: $i] : (((~r1(X, Y)) | $false) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) <=> (~?[X: $i] : ![Y: $i] : (~r1(X, Y)))),
% 0.03/0.32 inference(rewrite,[status(thm)],[])).
% 0.03/0.32 tff(6,plain,
% 0.03/0.32 ((~(~?[X: $i] : (~($false | (~![Y: $i] : (((~r1(X, Y)) | $false) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))))) <=> (~(~?[X: $i] : ![Y: $i] : (~r1(X, Y))))),
% 0.03/0.32 inference(monotonicity,[status(thm)],[5])).
% 0.03/0.32 tff(7,plain,
% 0.03/0.32 ((~(~?[X: $i] : (~($false | (~![Y: $i] : (((~r1(X, Y)) | $false) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))))) <=> ?[X: $i] : ![Y: $i] : (~r1(X, Y))),
% 0.03/0.32 inference(transitivity,[status(thm)],[6, 4])).
% 0.03/0.32 tff(8,axiom,(~(~?[X: $i] : (~($false | (~![Y: $i] : (((~r1(X, Y)) | $false) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.03/0.32 tff(9,plain,
% 0.03/0.32 (?[X: $i] : ![Y: $i] : (~r1(X, Y))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.03/0.32 tff(10,plain,
% 0.03/0.32 (?[X: $i] : ![Y: $i] : (~r1(X, Y))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.03/0.32 tff(11,plain,(
% 0.03/0.32 $oeq(![Y: $i] : (~r1(X!0, Y)), ![Y: $i] : (~r1(X!0, Y)))),
% 0.03/0.32 inference(transitivity,[status(sab)],[10])).
% 0.03/0.32 tff(12,plain,
% 0.03/0.32 (![Y: $i] : (~r1(X!0, Y))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.03/0.32 tff(13,plain,
% 0.03/0.32 ((~![Y: $i] : (~r1(X!0, Y))) | (~r1(X!0, X!0))),
% 0.03/0.32 inference(quant_inst,[status(thm)],[])).
% 0.03/0.32 tff(14,plain,
% 0.03/0.32 (~r1(X!0, X!0)),
% 0.03/0.32 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.03/0.32 tff(15,plain,
% 0.03/0.32 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.03/0.32 inference(bind,[status(th)],[])).
% 0.03/0.32 tff(16,plain,
% 0.03/0.32 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.03/0.32 inference(quant_intro,[status(thm)],[15])).
% 0.03/0.32 tff(17,plain,
% 0.03/0.32 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.03/0.32 inference(rewrite,[status(thm)],[])).
% 0.03/0.32 tff(18,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.03/0.32 tff(19,plain,
% 0.03/0.32 (![X: $i] : r1(X, X)),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.03/0.32 tff(20,plain,(
% 0.03/0.32 ![X: $i] : r1(X, X)),
% 0.03/0.32 inference(skolemize,[status(sab)],[19])).
% 0.03/0.32 tff(21,plain,
% 0.03/0.32 (![X: $i] : r1(X, X)),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.03/0.32 tff(22,plain,
% 0.03/0.32 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.03/0.32 inference(quant_inst,[status(thm)],[])).
% 0.03/0.32 tff(23,plain,
% 0.03/0.32 ($false),
% 0.03/0.32 inference(unit_resolution,[status(thm)],[22, 21, 14])).
% 0.03/0.32 % SZS output end Proof
% 0.03/0.32 % E exiting
%------------------------------------------------------------------------------