%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n019.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 03:00:39 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 16:34:26 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(p101_type, type, (
% 0.14/0.40 p101: $i > $o)).
% 0.14/0.40 tff(p201_type, type, (
% 0.14/0.40 p201: $i > $o)).
% 0.14/0.40 tff(r1_type, type, (
% 0.14/0.40 r1: ( $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_X_0_type, type, (
% 0.14/0.40 tptp_fun_X_0: $i)).
% 0.14/0.40 tff(1,assumption,(~r1(X!0, X!0)), introduced(assumption)).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.14/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(5,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity')).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (![X: $i] : r1(X, X)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.40 tff(7,plain,(
% 0.14/0.40 ![X: $i] : r1(X, X)),
% 0.14/0.40 inference(skolemize,[status(sab)],[6])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (![X: $i] : r1(X, X)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.14/0.40 tff(11,plain,(r1(X!0, X!0)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[15, 13])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (((p201(X!0) & p101(X!0)) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) <=> (p201(X!0) & p101(X!0) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 ((~(~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 ((~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) | (~(p201(X) & p101(X)))))) <=> (~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) | (~(p201(X) & p101(X))))))) <=> (~(~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[22])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) | (~(p201(X) & p101(X))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[23, 21])).
% 0.14/0.40 tff(25,axiom,(~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) | (~(p201(X) & p101(X))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (p201(X!0) & p101(X!0) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))),
% 0.14/0.40 inference(and_elim,[status(thm)],[28])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[29, 18])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[30, 16])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))) | ((~r1(X!0, X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))) | (~r1(X!0, X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))) | ((~r1(X!0, X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))) | (~r1(X!0, X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 ((~r1(X!0, X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[35, 11])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (p101(X!0)),
% 0.14/0.40 inference(and_elim,[status(thm)],[28])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (p201(X!0)),
% 0.14/0.40 inference(and_elim,[status(thm)],[28])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 (((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | ((~p101(X!0)) | (~r1(X!0, X!0)) | (~p201(X!0)))) <=> ((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | (~p101(X!0)) | (~r1(X!0, X!0)) | (~p201(X!0)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (((~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0))) <=> ((~p101(X!0)) | (~r1(X!0, X!0)) | (~p201(X!0)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | ((~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))) <=> ((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | ((~p101(X!0)) | (~r1(X!0, X!0)) | (~p201(X!0))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | ((~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))) <=> ((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | (~p101(X!0)) | (~r1(X!0, X!0)) | (~p201(X!0)))),
% 0.14/0.40 inference(transitivity,[status(thm)],[41, 39])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 ((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | ((~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 ((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | (~p101(X!0)) | (~r1(X!0, X!0)) | (~p201(X!0))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[44, 38, 37, 11, 36])).
% 0.14/0.40 % SZS output end Proof
% 0.14/0.41 % E exiting
%------------------------------------------------------------------------------