%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL674+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 03:00:35 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL674+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n010.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 02:05:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(r1_type, type, (
% 0.13/0.40 r1: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_X_1_type, type, (
% 0.13/0.40 tptp_fun_X_1: $i > $i)).
% 0.13/0.40 tff(tptp_fun_X_0_type, type, (
% 0.13/0.40 tptp_fun_X_0: $i)).
% 0.13/0.40 tff(p2_type, type, (
% 0.13/0.40 p2: $i > $o)).
% 0.13/0.40 tff(p102_type, type, (
% 0.13/0.40 p102: $i > $o)).
% 0.13/0.40 tff(tptp_fun_X_2_type, type, (
% 0.13/0.40 tptp_fun_X_2: $i > $i)).
% 0.13/0.40 tff(p101_type, type, (
% 0.13/0.40 p101: $i > $o)).
% 0.13/0.40 tff(p100_type, type, (
% 0.13/0.40 p100: $i > $o)).
% 0.13/0.40 tff(p1_type, type, (
% 0.13/0.40 p1: $i > $o)).
% 0.13/0.40 tff(1,assumption,(~r1(X!0, X!0)), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.13/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (![X: $i] : r1(X, X)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.40 tff(7,plain,(
% 0.13/0.40 ![X: $i] : r1(X, X)),
% 0.13/0.40 inference(skolemize,[status(sab)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![X: $i] : r1(X, X)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.13/0.40 tff(11,plain,(r1(X!0, X!0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) <=> ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 ((![Y: $i] : ((~r1(X!0, Y)) | ((((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0)) <=> (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | ((((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0)))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[22])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & (![Y: $i] : ((~r1(X!0, Y)) | ((((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0))),
% 0.13/0.41 inference(transitivity,[status(thm)],[23, 21])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X))))) <=> ?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 ((~(~?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X))))))) <=> ?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 ((~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~((![Y: $i] : ((~r1(X, Y)) | (((((((~![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p102(X))) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p2(X) & (~p102(X))) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p2(X))) | (~p101(X))) | p2(Y)) & (![X: $i] : (((~r1(Y, X)) | p2(X)) | (~p101(X))) | (~p2(Y)))) | (~p101(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p1(X))) | (~p100(X))) | p1(Y)) & (![X: $i] : (((~r1(Y, X)) | p1(X)) | (~p100(X))) | (~p1(Y)))) | (~p100(Y)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (~p101(X))) & p100(X)))))) <=> (~?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~((![Y: $i] : ((~r1(X, Y)) | (((((((~![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p102(X))) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p2(X) & (~p102(X))) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p2(X))) | (~p101(X))) | p2(Y)) & (![X: $i] : (((~r1(Y, X)) | p2(X)) | (~p101(X))) | (~p2(Y)))) | (~p101(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p1(X))) | (~p100(X))) | p1(Y)) & (![X: $i] : (((~r1(Y, X)) | p1(X)) | (~p100(X))) | (~p1(Y)))) | (~p100(Y)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (~p101(X))) & p100(X))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~((![Y: $i] : ((~r1(X, Y)) | (((((((~![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p102(X))) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p2(X) & (~p102(X))) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p2(X))) | (~p101(X))) | p2(Y)) & (![X: $i] : (((~r1(Y, X)) | p2(X)) | (~p101(X))) | (~p2(Y)))) | (~p101(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p1(X))) | (~p100(X))) | p1(Y)) & (![X: $i] : (((~r1(Y, X)) | p1(X)) | (~p100(X))) | (~p1(Y)))) | (~p100(Y)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (~p101(X))) & p100(X))))))) <=> ?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[28, 26])).
% 0.13/0.42 tff(30,axiom,(~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~((![Y: $i] : ((~r1(X, Y)) | (((((((~![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p102(X))) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~((p2(X) & (~p102(X))) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p2(X))) | (~p101(X))) | p2(Y)) & (![X: $i] : (((~r1(Y, X)) | p2(X)) | (~p101(X))) | (~p2(Y)))) | (~p101(Y)))) & (((![X: $i] : (((~r1(Y, X)) | (~p1(X))) | (~p100(X))) | p1(Y)) & (![X: $i] : (((~r1(Y, X)) | p1(X)) | (~p100(X))) | (~p1(Y)))) | (~p100(Y)))) & (p101(Y) | (~p102(Y)))) & (p100(Y) | (~p101(Y))))) & (~p101(X))) & p100(X))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.13/0.42 tff(31,plain,
% 0.13/0.42 (?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.42 tff(32,plain,
% 0.13/0.42 (?[X: $i] : (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | ((((~![X: $i] : ((~r1(Y, X)) | (~((~p2(X)) & (~p102(X)) & p101(X))))) & (~![X: $i] : ((~r1(Y, X)) | (~(p2(X) & (~p102(X)) & p101(X)))))) | (~((~p101(Y)) & p100(Y)))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X)) & p100(X)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.13/0.42 tff(33,plain,
% 0.13/0.42 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y))))) & (~p101(X!0)) & p100(X!0)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.13/0.42 tff(34,plain,
% 0.13/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (((~((~p101(Y)) & p100(Y))) | ((~((~r1(Y, tptp_fun_X_1(Y))) | (~((~p2(tptp_fun_X_1(Y))) & (~p102(tptp_fun_X_1(Y))) & p101(tptp_fun_X_1(Y)))))) & (~((~r1(Y, tptp_fun_X_2(Y))) | (~(p2(tptp_fun_X_2(Y)) & (~p102(tptp_fun_X_2(Y))) & p101(tptp_fun_X_2(Y)))))))) & ((~p101(Y)) | ((p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X)))) & ((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X)))))) & ((~p100(Y)) | ((p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X)))) & ((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X)))))) & (p101(Y) | (~p102(Y))) & (p100(Y) | (~p101(Y)))))),
% 0.13/0.42 inference(and_elim,[status(thm)],[33])).
% 0.13/0.42 tff(35,plain,
% 0.13/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[34, 20])).
% 0.13/0.42 tff(36,plain,
% 0.13/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[35, 18])).
% 0.13/0.42 tff(37,plain,
% 0.13/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[36, 13])).
% 0.13/0.42 tff(38,plain,
% 0.13/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, X!0)) | (~((~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p100(X!0) | (~p101(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | (~r1(X!0, X!0)) | (~((~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p100(X!0) | (~p101(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(39,plain,
% 0.13/0.42 (((~r1(X!0, X!0)) | (~((~(p101(X!0) | (~p100(X!0)) | (~((~r1(X!0, tptp_fun_X_1(X!0))) | p2(tptp_fun_X_1(X!0)) | p102(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_2(X!0)) | (~p101(tptp_fun_X_1(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_2(X!0))))))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X)))))))))))) <=> ((~r1(X!0, X!0)) | (~((~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p100(X!0) | (~p101(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(40,plain,
% 0.13/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, X!0)) | (~((~(p101(X!0) | (~p100(X!0)) | (~((~r1(X!0, tptp_fun_X_1(X!0))) | p2(tptp_fun_X_1(X!0)) | p102(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_2(X!0)) | (~p101(tptp_fun_X_1(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_2(X!0))))))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, X!0)) | (~((~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p100(X!0) | (~p101(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0)))))))))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[39])).
% 0.13/0.42 tff(41,plain,
% 0.13/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, X!0)) | (~((~(p101(X!0) | (~p100(X!0)) | (~((~r1(X!0, tptp_fun_X_1(X!0))) | p2(tptp_fun_X_1(X!0)) | p102(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_2(X!0)) | (~p101(tptp_fun_X_1(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_2(X!0))))))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | (~r1(X!0, X!0)) | (~((~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p100(X!0) | (~p101(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[40, 38])).
% 0.13/0.42 tff(42,plain,
% 0.13/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | ((~r1(X!0, X!0)) | (~((~(p101(X!0) | (~p100(X!0)) | (~((~r1(X!0, tptp_fun_X_1(X!0))) | p2(tptp_fun_X_1(X!0)) | p102(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_2(X!0)) | (~p101(tptp_fun_X_1(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_2(X!0))))))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p100(X!0) | (~p101(X!0)))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(43,plain,
% 0.13/0.43 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~(p101(Y) | (~p100(Y)) | (~((~r1(Y, tptp_fun_X_1(Y))) | p2(tptp_fun_X_1(Y)) | p102(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_2(Y))) | p102(tptp_fun_X_2(Y)) | (~p101(tptp_fun_X_1(Y))) | (~p2(tptp_fun_X_2(Y))) | (~p101(tptp_fun_X_2(Y))))))) | (~(p101(Y) | (~p102(Y)))) | (~(p100(Y) | (~p101(Y)))) | (~((~p101(Y)) | (~((~(p2(Y) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(Y, X))))) | (~((~p2(Y)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(Y, X))))))))) | (~((~p100(Y)) | (~((~(p1(Y) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(Y, X))))) | (~((~p1(Y)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(Y, X))))))))))))) | (~r1(X!0, X!0)) | (~((~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p100(X!0) | (~p101(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0)))))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.43 tff(44,plain,
% 0.13/0.43 ((~r1(X!0, X!0)) | (~((~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p100(X!0) | (~p101(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0)))))))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.13/0.43 tff(45,plain,
% 0.13/0.43 (~((~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p100(X!0) | (~p101(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[44, 11])).
% 0.13/0.43 tff(46,plain,
% 0.13/0.43 (((~((~p100(X!0)) | (~((~(p1(X!0) | ![X: $i] : ((~p100(X)) | (~p1(X)) | (~r1(X!0, X))))) | (~((~p1(X!0)) | ![X: $i] : ((~p100(X)) | p1(X) | (~r1(X!0, X))))))))) | (~((~p101(X!0)) | (~((~(p2(X!0) | ![X: $i] : ((~p2(X)) | (~p101(X)) | (~r1(X!0, X))))) | (~((~p2(X!0)) | ![X: $i] : (p2(X) | (~p101(X)) | (~r1(X!0, X))))))))) | (~(p100(X!0) | (~p101(X!0)))) | (~(p101(X!0) | (~p102(X!0)))) | (~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0)))))))) | (p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(47,plain,
% 0.13/0.43 (p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0)))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.13/0.43 tff(48,plain,
% 0.13/0.43 (p100(X!0)),
% 0.13/0.43 inference(and_elim,[status(thm)],[33])).
% 0.13/0.43 tff(49,plain,
% 0.13/0.43 (~p101(X!0)),
% 0.13/0.43 inference(and_elim,[status(thm)],[33])).
% 0.13/0.43 tff(50,plain,
% 0.13/0.43 ((~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))))) | p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0)))))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(51,plain,
% 0.13/0.43 ((~(p101(X!0) | (~p100(X!0)) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))))) | (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0)))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[50, 49, 48])).
% 0.13/0.43 tff(52,plain,
% 0.13/0.43 (~((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[51, 47])).
% 0.13/0.43 tff(53,plain,
% 0.13/0.43 (((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0)))) | r1(X!0, tptp_fun_X_1(X!0))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(54,plain,
% 0.13/0.43 (r1(X!0, tptp_fun_X_1(X!0))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.13/0.43 tff(55,plain,
% 0.13/0.43 (((~p101(tptp_fun_X_2(X!0))) | (~p2(tptp_fun_X_2(X!0))) | (~p101(tptp_fun_X_1(X!0))) | p102(tptp_fun_X_2(X!0)) | (~r1(X!0, tptp_fun_X_2(X!0))) | p102(tptp_fun_X_1(X!0)) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0)))) | (~p2(tptp_fun_X_1(X!0)))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(56,plain,
% 0.13/0.43 (~p2(tptp_fun_X_1(X!0))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.13/0.43 tff(57,plain,
% 0.13/0.43 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y))) <=> (p2(Y) | (~r1(X!0, Y))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(58,plain,
% 0.13/0.43 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[57])).
% 0.13/0.43 tff(59,plain,
% 0.13/0.43 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)))),
% 0.13/0.43 inference(and_elim,[status(thm)],[33])).
% 0.13/0.43 tff(60,plain,
% 0.13/0.43 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.13/0.43 tff(61,plain,
% 0.13/0.43 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(62,plain,
% 0.13/0.43 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(63,plain,
% 0.13/0.43 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(tptp_fun_X_1(X!0)) | (~r1(X!0, tptp_fun_X_1(X!0)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.13/0.43 tff(64,plain,
% 0.13/0.43 ($false),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[63, 60, 56, 54])).
% 0.13/0.43 % SZS output end Proof
% 0.13/0.43 % E exiting
%------------------------------------------------------------------------------