%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL666+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n010.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 03:00:31 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL666+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 21:19:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 % SZS output start Proof
% 0.12/0.41 tff(r1_type, type, (
% 0.12/0.41 r1: ( $i * $i ) > $o)).
% 0.12/0.41 tff(tptp_fun_X_0_type, type, (
% 0.12/0.41 tptp_fun_X_0: $i)).
% 0.12/0.41 tff(p101_type, type, (
% 0.12/0.41 p101: $i > $o)).
% 0.12/0.41 tff(p201_type, type, (
% 0.12/0.41 p201: $i > $o)).
% 0.12/0.41 tff(1,plain,
% 0.12/0.41 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y))) <=> ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(2,plain,
% 0.12/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.41 tff(3,plain,
% 0.12/0.41 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((p201(Y) & p101(Y)) <=> (~((~p201(Y)) | (~p101(Y))))), ((~(p201(Y) & p101(Y))) <=> (~(~((~p201(Y)) | (~p101(Y))))))), rewrite((~(~((~p201(Y)) | (~p101(Y))))) <=> ((~p201(Y)) | (~p101(Y)))), ((~(p201(Y) & p101(Y))) <=> ((~p201(Y)) | (~p101(Y))))), (((~r1(X!0, Y)) | (~(p201(Y) & p101(Y)))) <=> ((~r1(X!0, Y)) | ((~p201(Y)) | (~p101(Y)))))), rewrite(((~r1(X!0, Y)) | ((~p201(Y)) | (~p101(Y)))) <=> ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))), (((~r1(X!0, Y)) | (~(p201(Y) & p101(Y)))) <=> ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(4,plain,
% 0.12/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.41 tff(5,plain,
% 0.12/0.41 (((p201(X!0) & p101(X!0)) & ![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y))))) <=> (p201(X!0) & p101(X!0) & ![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(6,plain,
% 0.12/0.41 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(7,plain,
% 0.12/0.41 ((~(~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(8,plain,
% 0.12/0.41 ((~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))) | (~(p201(X) & p101(X)))))) <=> (~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(9,plain,
% 0.12/0.41 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))) | (~(p201(X) & p101(X))))))) <=> (~(~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[8])).
% 0.12/0.41 tff(10,plain,
% 0.12/0.41 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))) | (~(p201(X) & p101(X))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[9, 7])).
% 0.12/0.41 tff(11,axiom,(~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))) | (~(p201(X) & p101(X))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.12/0.41 tff(12,plain,
% 0.12/0.41 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.41 tff(13,plain,
% 0.12/0.41 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.12/0.41 tff(14,plain,
% 0.12/0.41 (p201(X!0) & p101(X!0) & ![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.12/0.41 tff(15,plain,
% 0.12/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y))))),
% 0.12/0.41 inference(and_elim,[status(thm)],[14])).
% 0.12/0.41 tff(16,plain,
% 0.12/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.12/0.41 tff(17,plain,
% 0.12/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[16, 2])).
% 0.12/0.41 tff(18,plain,
% 0.12/0.41 (p101(X!0)),
% 0.12/0.41 inference(and_elim,[status(thm)],[14])).
% 0.12/0.41 tff(19,plain,
% 0.12/0.41 (p201(X!0)),
% 0.12/0.41 inference(and_elim,[status(thm)],[14])).
% 0.12/0.41 tff(20,plain,
% 0.12/0.41 (((~![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))) | ((~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))) | (~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(21,plain,
% 0.12/0.41 ((~![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))) | ((~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(22,plain,
% 0.12/0.41 ((~![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))) | (~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.41 tff(23,plain,
% 0.12/0.41 (~r1(X!0, X!0)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[22, 19, 18, 17])).
% 0.12/0.41 tff(24,plain,
% 0.12/0.41 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(25,plain,
% 0.12/0.41 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.12/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.41 tff(26,plain,
% 0.12/0.41 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(27,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.12/0.42 tff(28,plain,
% 0.12/0.42 (![X: $i] : r1(X, X)),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.42 tff(29,plain,(
% 0.12/0.42 ![X: $i] : r1(X, X)),
% 0.12/0.42 inference(skolemize,[status(sab)],[28])).
% 0.12/0.42 tff(30,plain,
% 0.12/0.42 (![X: $i] : r1(X, X)),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.42 tff(31,plain,
% 0.12/0.42 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(32,plain,
% 0.12/0.42 ($false),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.12/0.42 % SZS output end Proof
% 0.12/0.42 % E exiting
%------------------------------------------------------------------------------