%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL672+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n013.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 03:00:34 PM UTC 2026
% Result : Theorem 2.66s 3.03s
% Output : Proof 2.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL672+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 : n013.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 14:34:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 2.66/3.03 % SZS status Theorem
% 2.66/3.03 % SZS output start Proof
% 2.66/3.03 tff(p1_type, type, (
% 2.66/3.03 p1: $i > $o)).
% 2.66/3.03 tff(tptp_fun_Y_6_type, type, (
% 2.66/3.03 tptp_fun_Y_6: $i > $i)).
% 2.66/3.03 tff(tptp_fun_X_7_type, type, (
% 2.66/3.03 tptp_fun_X_7: $i > $i)).
% 2.66/3.03 tff(tptp_fun_X_10_type, type, (
% 2.66/3.03 tptp_fun_X_10: $i)).
% 2.66/3.03 tff(r1_type, type, (
% 2.66/3.03 r1: ( $i * $i ) > $o)).
% 2.66/3.03 tff(tptp_fun_X_4_type, type, (
% 2.66/3.03 tptp_fun_X_4: $i > $i)).
% 2.66/3.03 tff(tptp_fun_Y_3_type, type, (
% 2.66/3.03 tptp_fun_Y_3: $i > $i)).
% 2.66/3.03 tff(tptp_fun_Y_8_type, type, (
% 2.66/3.03 tptp_fun_Y_8: $i)).
% 2.66/3.03 tff(tptp_fun_X_9_type, type, (
% 2.66/3.03 tptp_fun_X_9: $i)).
% 2.66/3.03 tff(tptp_fun_X_0_type, type, (
% 2.66/3.03 tptp_fun_X_0: $i)).
% 2.66/3.03 tff(p2_type, type, (
% 2.66/3.03 p2: $i > $o)).
% 2.66/3.03 tff(tptp_fun_Y_5_type, type, (
% 2.66/3.03 tptp_fun_Y_5: $i > $i)).
% 2.66/3.03 tff(tptp_fun_Y_2_type, type, (
% 2.66/3.03 tptp_fun_Y_2: $i)).
% 2.66/3.03 tff(tptp_fun_Y_1_type, type, (
% 2.66/3.03 tptp_fun_Y_1: $i)).
% 2.66/3.03 tff(1,assumption,(~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))), introduced(assumption)).
% 2.66/3.03 tff(2,plain,
% 2.66/3.03 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.66/3.03 inference(tautology,[status(thm)],[])).
% 2.66/3.03 tff(3,plain,
% 2.66/3.03 (~p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.66/3.03 inference(unit_resolution,[status(thm)],[2, 1])).
% 2.66/3.03 tff(4,plain,
% 2.66/3.03 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.66/3.03 inference(tautology,[status(thm)],[])).
% 2.66/3.03 tff(5,plain,
% 2.66/3.03 (r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.66/3.03 inference(unit_resolution,[status(thm)],[4, 1])).
% 2.66/3.03 tff(6,assumption,(~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))), introduced(assumption)).
% 2.66/3.03 tff(7,plain,
% 2.66/3.03 (((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | (~p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.66/3.03 inference(tautology,[status(thm)],[])).
% 2.66/3.03 tff(8,plain,
% 2.66/3.03 (~p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.66/3.03 inference(unit_resolution,[status(thm)],[7, 6])).
% 2.66/3.03 tff(9,plain,
% 2.66/3.03 (^[Y: $i] : refl((p1(Y) | (~r1(X!10, Y))) <=> (p1(Y) | (~r1(X!10, Y))))),
% 2.66/3.03 inference(bind,[status(th)],[])).
% 2.66/3.03 tff(10,plain,
% 2.66/3.03 (![Y: $i] : (p1(Y) | (~r1(X!10, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!10, Y)))),
% 2.66/3.03 inference(quant_intro,[status(thm)],[9])).
% 2.66/3.03 tff(11,plain,
% 2.66/3.03 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))),
% 2.79/3.03 inference(rewrite,[status(thm)],[])).
% 2.79/3.03 tff(12,plain,
% 2.79/3.03 ((r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))),
% 2.79/3.03 inference(rewrite,[status(thm)],[])).
% 2.79/3.03 tff(13,plain,
% 2.79/3.03 ((r1(Y!8, X!10) & ![Y: $i] : ((~r1(X!10, Y)) | p1(Y))) <=> (r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))),
% 2.79/3.03 inference(rewrite,[status(thm)],[])).
% 2.79/3.03 tff(14,plain,
% 2.79/3.03 ((~((~r1(Y!8, X!9)) | p1(X!9))) <=> (~((~r1(Y!8, X!9)) | p1(X!9)))),
% 2.79/3.03 inference(rewrite,[status(thm)],[])).
% 2.79/3.03 tff(15,plain,
% 2.79/3.03 ((r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (r1(Y!8, X!10) & ![Y: $i] : ((~r1(X!10, Y)) | p1(Y)))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y)))))),
% 2.79/3.03 inference(monotonicity,[status(thm)],[14, 13])).
% 2.79/3.03 tff(16,plain,
% 2.79/3.03 ((r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (r1(Y!8, X!10) & ![Y: $i] : ((~r1(X!10, Y)) | p1(Y)))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))),
% 2.79/3.03 inference(transitivity,[status(thm)],[15, 12])).
% 2.79/3.03 tff(17,plain,
% 2.79/3.03 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.03 inference(rewrite,[status(thm)],[])).
% 2.79/3.03 tff(18,plain,
% 2.79/3.03 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | p1(Y)) <=> (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.03 inference(bind,[status(th)],[])).
% 2.79/3.03 tff(19,plain,
% 2.79/3.03 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 2.79/3.03 inference(quant_intro,[status(thm)],[18])).
% 2.79/3.03 tff(20,plain,
% 2.79/3.03 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.03 inference(monotonicity,[status(thm)],[19])).
% 2.79/3.03 tff(21,plain,
% 2.79/3.03 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.03 inference(transitivity,[status(thm)],[20, 17])).
% 2.79/3.03 tff(22,plain,
% 2.79/3.03 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 2.79/3.03 inference(rewrite,[status(thm)],[])).
% 2.79/3.03 tff(23,plain,
% 2.79/3.03 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) <=> ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))), rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 2.79/3.03 inference(bind,[status(th)],[])).
% 2.79/3.03 tff(24,plain,
% 2.79/3.03 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))),
% 2.79/3.03 inference(quant_intro,[status(thm)],[23])).
% 2.79/3.03 tff(25,plain,
% 2.79/3.03 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.03 inference(monotonicity,[status(thm)],[24, 19])).
% 2.79/3.03 tff(26,plain,
% 2.79/3.03 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 2.79/3.03 inference(transitivity,[status(thm)],[25, 22])).
% 2.79/3.03 tff(27,plain,
% 2.79/3.03 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 2.79/3.03 inference(rewrite,[status(thm)],[])).
% 2.79/3.03 tff(28,plain,
% 2.79/3.03 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 2.79/3.03 inference(bind,[status(th)],[])).
% 2.79/3.03 tff(29,plain,
% 2.79/3.03 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 2.79/3.03 inference(quant_intro,[status(thm)],[28])).
% 2.79/3.03 tff(30,plain,
% 2.79/3.03 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.03 inference(monotonicity,[status(thm)],[29, 19])).
% 2.79/3.03 tff(31,plain,
% 2.79/3.03 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 2.79/3.03 inference(transitivity,[status(thm)],[30, 27])).
% 2.79/3.03 tff(32,plain,
% 2.79/3.03 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.03 inference(rewrite,[status(thm)],[])).
% 2.79/3.03 tff(33,plain,
% 2.79/3.03 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), rewrite(((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))),
% 2.79/3.04 inference(bind,[status(th)],[])).
% 2.79/3.04 tff(34,plain,
% 2.79/3.04 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))),
% 2.79/3.04 inference(quant_intro,[status(thm)],[33])).
% 2.79/3.04 tff(35,plain,
% 2.79/3.04 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.04 inference(monotonicity,[status(thm)],[34, 19])).
% 2.79/3.04 tff(36,plain,
% 2.79/3.04 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.04 inference(transitivity,[status(thm)],[35, 32])).
% 2.79/3.04 tff(37,plain,
% 2.79/3.04 ((~((~r1(X!0, Y!1)) | p1(Y!1))) <=> (~((~r1(X!0, Y!1)) | p1(Y!1)))),
% 2.79/3.04 inference(rewrite,[status(thm)],[])).
% 2.79/3.04 tff(38,plain,
% 2.79/3.04 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (r1(Y!8, X!10) & ![Y: $i] : ((~r1(X!10, Y)) | p1(Y))))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y)))))),
% 2.79/3.04 inference(monotonicity,[status(thm)],[37, 36, 31, 26, 21, 16])).
% 2.79/3.04 tff(39,plain,
% 2.79/3.04 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (r1(Y!8, X!10) & ![Y: $i] : ((~r1(X!10, Y)) | p1(Y))))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y))))),
% 2.79/3.04 inference(transitivity,[status(thm)],[38, 11])).
% 2.79/3.04 tff(40,plain,
% 2.79/3.04 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 2.79/3.04 inference(rewrite,[status(thm)],[])).
% 2.79/3.04 tff(41,plain,
% 2.79/3.04 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 2.79/3.04 inference(rewrite,[status(thm)],[])).
% 2.79/3.04 tff(42,plain,
% 2.79/3.04 ((~?[X: $i] : (~(((((((((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 2.79/3.05 inference(rewrite,[status(thm)],[])).
% 2.79/3.05 tff(43,plain,
% 2.79/3.05 ((~(~?[X: $i] : (~(((((((((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))),
% 2.79/3.05 inference(monotonicity,[status(thm)],[42])).
% 2.79/3.05 tff(44,plain,
% 2.79/3.05 ((~(~?[X: $i] : (~(((((((((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 2.79/3.05 inference(transitivity,[status(thm)],[43, 41])).
% 2.79/3.05 tff(45,axiom,(~(~?[X: $i] : (~(((((((((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 2.79/3.05 tff(46,plain,
% 2.79/3.05 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 2.79/3.05 inference(modus_ponens,[status(thm)],[45, 44])).
% 2.79/3.05 tff(47,plain,
% 2.79/3.05 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 2.79/3.05 inference(modus_ponens,[status(thm)],[46, 40])).
% 2.79/3.05 tff(48,plain,
% 2.79/3.05 ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & r1(Y!8, X!10) & ![Y: $i] : (p1(Y) | (~r1(X!10, Y)))),
% 2.79/3.05 inference(modus_ponens,[status(thm)],[47, 39])).
% 2.79/3.05 tff(49,plain,
% 2.79/3.05 (![Y: $i] : (p1(Y) | (~r1(X!10, Y)))),
% 2.79/3.05 inference(and_elim,[status(thm)],[48])).
% 2.79/3.05 tff(50,plain,
% 2.79/3.05 (![Y: $i] : (p1(Y) | (~r1(X!10, Y)))),
% 2.79/3.05 inference(modus_ponens,[status(thm)],[49, 10])).
% 2.79/3.05 tff(51,plain,
% 2.79/3.05 (((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | (p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 2.79/3.05 inference(rewrite,[status(thm)],[])).
% 2.79/3.05 tff(52,plain,
% 2.79/3.05 ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | (p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 2.79/3.05 inference(quant_inst,[status(thm)],[])).
% 2.79/3.05 tff(53,plain,
% 2.79/3.05 ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.05 inference(modus_ponens,[status(thm)],[52, 51])).
% 2.79/3.05 tff(54,plain,
% 2.79/3.05 (~r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.05 inference(unit_resolution,[status(thm)],[53, 50, 8])).
% 2.79/3.05 tff(55,plain,
% 2.79/3.05 (((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.05 inference(tautology,[status(thm)],[])).
% 2.79/3.05 tff(56,plain,
% 2.79/3.05 (r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.05 inference(unit_resolution,[status(thm)],[55, 6])).
% 2.79/3.05 tff(57,plain,
% 2.79/3.05 (r1(Y!8, X!10)),
% 2.79/3.05 inference(and_elim,[status(thm)],[48])).
% 2.79/3.05 tff(58,plain,
% 2.79/3.05 (r1(X!0, Y!8)),
% 2.79/3.05 inference(and_elim,[status(thm)],[48])).
% 2.79/3.05 tff(59,plain,
% 2.79/3.05 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 2.79/3.05 inference(rewrite,[status(thm)],[])).
% 2.79/3.05 tff(60,plain,
% 2.79/3.05 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(X, Y) & r1(Y, Z)) <=> (~((~r1(Y, Z)) | (~r1(X, Y))))), ((~(r1(X, Y) & r1(Y, Z))) <=> (~(~((~r1(Y, Z)) | (~r1(X, Y))))))), rewrite((~(~((~r1(Y, Z)) | (~r1(X, Y))))) <=> ((~r1(Y, Z)) | (~r1(X, Y)))), ((~(r1(X, Y) & r1(Y, Z))) <=> ((~r1(Y, Z)) | (~r1(X, Y))))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)))), rewrite((((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))))),
% 2.79/3.05 inference(bind,[status(th)],[])).
% 2.79/3.05 tff(61,plain,
% 2.79/3.05 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 2.79/3.05 inference(quant_intro,[status(thm)],[60])).
% 2.79/3.05 tff(62,plain,
% 2.79/3.05 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 2.79/3.05 inference(rewrite,[status(thm)],[])).
% 2.79/3.05 tff(63,plain,
% 2.79/3.05 (^[X: $i, Y: $i, Z: $i] : rewrite(((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)))),
% 2.79/3.05 inference(bind,[status(th)],[])).
% 2.79/3.05 tff(64,plain,
% 2.79/3.05 (![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 2.79/3.05 inference(quant_intro,[status(thm)],[63])).
% 2.79/3.05 tff(65,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity')).
% 2.79/3.05 tff(66,plain,
% 2.79/3.05 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 2.79/3.05 inference(modus_ponens,[status(thm)],[65, 64])).
% 2.79/3.05 tff(67,plain,
% 2.79/3.05 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 2.79/3.05 inference(modus_ponens,[status(thm)],[66, 62])).
% 2.79/3.05 tff(68,plain,(
% 2.79/3.05 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 2.79/3.05 inference(skolemize,[status(sab)],[67])).
% 2.79/3.05 tff(69,plain,
% 2.79/3.05 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 2.79/3.05 inference(modus_ponens,[status(thm)],[68, 61])).
% 2.79/3.05 tff(70,plain,
% 2.79/3.05 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 2.79/3.05 inference(modus_ponens,[status(thm)],[69, 59])).
% 2.79/3.05 tff(71,plain,
% 2.79/3.05 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10))),
% 2.79/3.05 inference(rewrite,[status(thm)],[])).
% 2.79/3.05 tff(72,plain,
% 2.79/3.05 ((r1(X!0, X!10) | (~r1(Y!8, X!10)) | (~r1(X!0, Y!8))) <=> ((~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10))),
% 2.79/3.05 inference(rewrite,[status(thm)],[])).
% 2.79/3.05 tff(73,plain,
% 2.79/3.05 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!10) | (~r1(Y!8, X!10)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10)))),
% 2.79/3.05 inference(monotonicity,[status(thm)],[72])).
% 2.79/3.05 tff(74,plain,
% 2.79/3.05 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!10) | (~r1(Y!8, X!10)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10))),
% 2.79/3.05 inference(transitivity,[status(thm)],[73, 71])).
% 2.79/3.05 tff(75,plain,
% 2.79/3.05 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!10) | (~r1(Y!8, X!10)) | (~r1(X!0, Y!8)))),
% 2.79/3.05 inference(quant_inst,[status(thm)],[])).
% 2.79/3.05 tff(76,plain,
% 2.79/3.05 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!10)) | r1(X!0, X!10)),
% 2.79/3.05 inference(modus_ponens,[status(thm)],[75, 74])).
% 2.79/3.05 tff(77,plain,
% 2.79/3.05 (r1(X!0, X!10)),
% 2.79/3.05 inference(unit_resolution,[status(thm)],[76, 70, 58, 57])).
% 2.79/3.05 tff(78,assumption,(![Y: $i] : (p2(Y) | (~r1(X!0, Y)))), introduced(assumption)).
% 2.79/3.05 tff(79,plain,
% 2.79/3.05 (~(p2(Y!2) | (~r1(X!0, Y!2)))),
% 2.79/3.05 inference(and_elim,[status(thm)],[48])).
% 2.79/3.05 tff(80,plain,
% 2.79/3.05 (r1(X!0, Y!2)),
% 2.79/3.05 inference(or_elim,[status(thm)],[79])).
% 2.79/3.05 tff(81,plain,
% 2.79/3.05 (~p2(Y!2)),
% 2.79/3.06 inference(or_elim,[status(thm)],[79])).
% 2.79/3.06 tff(82,plain,
% 2.79/3.06 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(Y!2) | (~r1(X!0, Y!2)))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(Y!2) | (~r1(X!0, Y!2)))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(83,plain,
% 2.79/3.06 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(Y!2) | (~r1(X!0, Y!2)))),
% 2.79/3.06 inference(quant_inst,[status(thm)],[])).
% 2.79/3.06 tff(84,plain,
% 2.79/3.06 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(Y!2) | (~r1(X!0, Y!2))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.79/3.06 tff(85,plain,
% 2.79/3.06 ($false),
% 2.79/3.06 inference(unit_resolution,[status(thm)],[84, 81, 80, 78])).
% 2.79/3.06 tff(86,plain,(~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.06 tff(87,assumption,(![Y: $i] : (p1(Y) | (~r1(X!0, Y)))), introduced(assumption)).
% 2.79/3.06 tff(88,plain,
% 2.79/3.06 (~((~r1(X!0, Y!1)) | p1(Y!1))),
% 2.79/3.06 inference(and_elim,[status(thm)],[48])).
% 2.79/3.06 tff(89,plain,
% 2.79/3.06 (~p1(Y!1)),
% 2.79/3.06 inference(or_elim,[status(thm)],[88])).
% 2.79/3.06 tff(90,plain,
% 2.79/3.06 (r1(X!0, Y!1)),
% 2.79/3.06 inference(or_elim,[status(thm)],[88])).
% 2.79/3.06 tff(91,plain,
% 2.79/3.06 (((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | (p1(Y!1) | (~r1(X!0, Y!1)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | p1(Y!1) | (~r1(X!0, Y!1)))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(92,plain,
% 2.79/3.06 ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | (p1(Y!1) | (~r1(X!0, Y!1)))),
% 2.79/3.06 inference(quant_inst,[status(thm)],[])).
% 2.79/3.06 tff(93,plain,
% 2.79/3.06 ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | p1(Y!1) | (~r1(X!0, Y!1))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[92, 91])).
% 2.79/3.06 tff(94,plain,
% 2.79/3.06 ($false),
% 2.79/3.06 inference(unit_resolution,[status(thm)],[93, 90, 89, 87])).
% 2.79/3.06 tff(95,plain,(~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.06 tff(96,plain,
% 2.79/3.06 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(97,plain,
% 2.79/3.06 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(98,plain,
% 2.79/3.06 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 2.79/3.06 inference(and_elim,[status(thm)],[48])).
% 2.79/3.06 tff(99,plain,
% 2.79/3.06 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[98, 97])).
% 2.79/3.06 tff(100,plain,
% 2.79/3.06 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[99, 96])).
% 2.79/3.06 tff(101,plain,
% 2.79/3.06 (![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 2.79/3.06 inference(unit_resolution,[status(thm)],[100, 95, 86])).
% 2.79/3.06 tff(102,plain,
% 2.79/3.06 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!10)) | r1(X!10, tptp_fun_X_7(X!10)))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!10)) | r1(X!10, tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(103,plain,
% 2.79/3.06 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!10)) | r1(X!10, tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(quant_inst,[status(thm)],[])).
% 2.79/3.06 tff(104,plain,
% 2.79/3.06 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!10)) | r1(X!10, tptp_fun_X_7(X!10))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[103, 102])).
% 2.79/3.06 tff(105,plain,
% 2.79/3.06 (r1(X!10, tptp_fun_X_7(X!10))),
% 2.79/3.06 inference(unit_resolution,[status(thm)],[104, 101, 77])).
% 2.79/3.06 tff(106,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(107,plain,
% 2.79/3.06 ((r1(X!0, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(X!0, X!10))) <=> ((~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(108,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(X!0, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(monotonicity,[status(thm)],[107])).
% 2.79/3.06 tff(109,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(X!0, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(transitivity,[status(thm)],[108, 106])).
% 2.79/3.06 tff(110,plain,
% 2.79/3.06 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(X!0, X!10)))),
% 2.79/3.06 inference(quant_inst,[status(thm)],[])).
% 2.79/3.06 tff(111,plain,
% 2.79/3.06 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(X!0, tptp_fun_X_7(X!10))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[110, 109])).
% 2.79/3.06 tff(112,plain,
% 2.79/3.06 (r1(X!0, tptp_fun_X_7(X!10))),
% 2.79/3.06 inference(unit_resolution,[status(thm)],[111, 70, 77, 105])).
% 2.79/3.06 tff(113,plain,
% 2.79/3.06 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(X!10))) | r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(X!10))) | r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(114,plain,
% 2.79/3.06 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(X!10))) | r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(quant_inst,[status(thm)],[])).
% 2.79/3.06 tff(115,plain,
% 2.79/3.06 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(X!10))) | r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[114, 113])).
% 2.79/3.06 tff(116,plain,
% 2.79/3.06 (r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(unit_resolution,[status(thm)],[115, 101, 112])).
% 2.79/3.06 tff(117,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(118,plain,
% 2.79/3.06 ((r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(X!10)))) <=> ((~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(119,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.06 inference(monotonicity,[status(thm)],[118])).
% 2.79/3.06 tff(120,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(transitivity,[status(thm)],[119, 117])).
% 2.79/3.06 tff(121,plain,
% 2.79/3.06 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(quant_inst,[status(thm)],[])).
% 2.79/3.06 tff(122,plain,
% 2.79/3.06 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[121, 120])).
% 2.79/3.06 tff(123,plain,
% 2.79/3.06 (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(unit_resolution,[status(thm)],[122, 70, 112, 116])).
% 2.79/3.06 tff(124,plain,
% 2.79/3.06 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(125,plain,
% 2.79/3.06 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.06 inference(quant_inst,[status(thm)],[])).
% 2.79/3.06 tff(126,plain,
% 2.79/3.06 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[125, 124])).
% 2.79/3.06 tff(127,plain,
% 2.79/3.06 (r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(unit_resolution,[status(thm)],[126, 101, 123])).
% 2.79/3.06 tff(128,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(129,plain,
% 2.79/3.06 ((r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!10, tptp_fun_X_7(X!10)))) <=> ((~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(130,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!10, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.06 inference(monotonicity,[status(thm)],[129])).
% 2.79/3.06 tff(131,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!10, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(transitivity,[status(thm)],[130, 128])).
% 2.79/3.06 tff(132,plain,
% 2.79/3.06 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!10, tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(quant_inst,[status(thm)],[])).
% 2.79/3.06 tff(133,plain,
% 2.79/3.06 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[132, 131])).
% 2.79/3.06 tff(134,plain,
% 2.79/3.06 (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 2.79/3.06 inference(unit_resolution,[status(thm)],[133, 70, 105, 116])).
% 2.79/3.06 tff(135,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(136,plain,
% 2.79/3.06 ((r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(137,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.06 inference(monotonicity,[status(thm)],[136])).
% 2.79/3.06 tff(138,plain,
% 2.79/3.06 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.06 inference(transitivity,[status(thm)],[137, 135])).
% 2.79/3.06 tff(139,plain,
% 2.79/3.06 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.06 inference(quant_inst,[status(thm)],[])).
% 2.79/3.06 tff(140,plain,
% 2.79/3.06 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(modus_ponens,[status(thm)],[139, 138])).
% 2.79/3.06 tff(141,plain,
% 2.79/3.06 (r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.06 inference(unit_resolution,[status(thm)],[140, 70, 134, 127])).
% 2.79/3.06 tff(142,plain,
% 2.79/3.06 (((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | (p1(tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | p1(tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.06 inference(rewrite,[status(thm)],[])).
% 2.79/3.06 tff(143,plain,
% 2.79/3.06 ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | (p1(tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.07 inference(quant_inst,[status(thm)],[])).
% 2.79/3.07 tff(144,plain,
% 2.79/3.07 ((~![Y: $i] : (p1(Y) | (~r1(X!10, Y)))) | p1(tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.07 inference(modus_ponens,[status(thm)],[143, 142])).
% 2.79/3.07 tff(145,plain,
% 2.79/3.07 (p1(tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 2.79/3.07 inference(unit_resolution,[status(thm)],[144, 50, 134])).
% 2.79/3.07 tff(146,plain,
% 2.79/3.07 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(147,plain,
% 2.79/3.07 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(148,plain,
% 2.79/3.07 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 2.79/3.07 inference(and_elim,[status(thm)],[48])).
% 2.79/3.07 tff(149,plain,
% 2.79/3.07 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 2.79/3.07 inference(modus_ponens,[status(thm)],[148, 147])).
% 2.79/3.07 tff(150,plain,
% 2.79/3.07 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))),
% 2.79/3.07 inference(modus_ponens,[status(thm)],[149, 146])).
% 2.79/3.07 tff(151,plain,
% 2.79/3.07 (![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))),
% 2.79/3.07 inference(unit_resolution,[status(thm)],[150, 95, 86])).
% 2.79/3.07 tff(152,plain,
% 2.79/3.07 (((~![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | ((~p1(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) <=> ((~![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | (~p1(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(153,plain,
% 2.79/3.07 ((~![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | ((~p1(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))),
% 2.79/3.07 inference(quant_inst,[status(thm)],[])).
% 2.79/3.07 tff(154,plain,
% 2.79/3.07 ((~![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | (~p1(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))),
% 2.79/3.07 inference(modus_ponens,[status(thm)],[153, 152])).
% 2.79/3.07 tff(155,plain,
% 2.79/3.07 (![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))),
% 2.79/3.07 inference(unit_resolution,[status(thm)],[154, 151, 123, 145])).
% 2.79/3.07 tff(156,plain,
% 2.79/3.07 (((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(157,plain,
% 2.79/3.07 (((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(158,plain,
% 2.79/3.07 (((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))))),
% 2.79/3.07 inference(monotonicity,[status(thm)],[157])).
% 2.79/3.07 tff(159,plain,
% 2.79/3.07 (((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 2.79/3.07 inference(transitivity,[status(thm)],[158, 156])).
% 2.79/3.07 tff(160,plain,
% 2.79/3.07 ((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 2.79/3.07 inference(quant_inst,[status(thm)],[])).
% 2.79/3.07 tff(161,plain,
% 2.79/3.07 ((~![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 2.79/3.07 inference(modus_ponens,[status(thm)],[160, 159])).
% 2.79/3.07 tff(162,plain,
% 2.79/3.07 (~((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.07 inference(unit_resolution,[status(thm)],[161, 127, 155])).
% 2.79/3.07 tff(163,plain,
% 2.79/3.07 (((~p1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.07 inference(tautology,[status(thm)],[])).
% 2.79/3.07 tff(164,plain,
% 2.79/3.07 (r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.07 inference(unit_resolution,[status(thm)],[163, 162])).
% 2.79/3.07 tff(165,plain,
% 2.79/3.07 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(166,plain,
% 2.79/3.07 ((r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(167,plain,
% 2.79/3.07 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.07 inference(monotonicity,[status(thm)],[166])).
% 2.79/3.07 tff(168,plain,
% 2.79/3.07 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.07 inference(transitivity,[status(thm)],[167, 165])).
% 2.79/3.07 tff(169,plain,
% 2.79/3.07 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.07 inference(quant_inst,[status(thm)],[])).
% 2.79/3.07 tff(170,plain,
% 2.79/3.07 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(X!10, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.07 inference(modus_ponens,[status(thm)],[169, 168])).
% 2.79/3.07 tff(171,plain,
% 2.79/3.07 (r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.07 inference(unit_resolution,[status(thm)],[170, 70, 164, 141])).
% 2.79/3.07 tff(172,plain,
% 2.79/3.07 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(173,plain,
% 2.79/3.07 ((r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(174,plain,
% 2.79/3.07 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 2.79/3.07 inference(monotonicity,[status(thm)],[173])).
% 2.79/3.07 tff(175,plain,
% 2.79/3.07 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.07 inference(transitivity,[status(thm)],[174, 172])).
% 2.79/3.07 tff(176,plain,
% 2.79/3.07 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.07 inference(quant_inst,[status(thm)],[])).
% 2.79/3.07 tff(177,plain,
% 2.79/3.07 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | r1(X!10, tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.07 inference(modus_ponens,[status(thm)],[176, 175])).
% 2.79/3.07 tff(178,plain,
% 2.79/3.07 ($false),
% 2.79/3.07 inference(unit_resolution,[status(thm)],[177, 70, 171, 56, 54])).
% 2.79/3.07 tff(179,plain,((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.07 tff(180,assumption,(![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))), introduced(assumption)).
% 2.79/3.07 tff(181,plain,
% 2.79/3.07 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(182,plain,
% 2.79/3.07 (((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(183,plain,
% 2.79/3.07 ((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 2.79/3.07 inference(rewrite,[status(thm)],[])).
% 2.79/3.07 tff(184,plain,
% 2.79/3.07 (((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.07 inference(monotonicity,[status(thm)],[183])).
% 2.79/3.07 tff(185,plain,
% 2.79/3.07 (((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 2.79/3.07 inference(transitivity,[status(thm)],[184, 182])).
% 2.79/3.07 tff(186,plain,
% 2.79/3.07 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | ((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))))),
% 2.79/3.07 inference(monotonicity,[status(thm)],[185])).
% 2.79/3.07 tff(187,plain,
% 2.79/3.07 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | ((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))))),
% 2.79/3.07 inference(transitivity,[status(thm)],[186, 181])).
% 2.79/3.07 tff(188,plain,
% 2.79/3.07 ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | ((~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.07 inference(quant_inst,[status(thm)],[])).
% 2.79/3.07 tff(189,plain,
% 2.79/3.07 ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | (~((~r1(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))), tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) | p1(tptp_fun_X_4(tptp_fun_Y_3(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 2.79/3.08 inference(modus_ponens,[status(thm)],[188, 187])).
% 2.79/3.08 tff(190,plain,
% 2.79/3.08 ($false),
% 2.79/3.08 inference(unit_resolution,[status(thm)],[189, 164, 180, 179])).
% 2.79/3.08 tff(191,plain,(~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.08 tff(192,plain,
% 2.79/3.08 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 2.79/3.08 inference(rewrite,[status(thm)],[])).
% 2.79/3.08 tff(193,plain,
% 2.79/3.08 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 2.79/3.08 inference(bind,[status(th)],[])).
% 2.79/3.08 tff(194,plain,
% 2.79/3.08 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 2.79/3.08 inference(quant_intro,[status(thm)],[193])).
% 2.79/3.08 tff(195,plain,
% 2.79/3.08 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 2.79/3.08 inference(monotonicity,[status(thm)],[194])).
% 2.79/3.08 tff(196,plain,
% 2.79/3.08 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 2.79/3.08 inference(transitivity,[status(thm)],[195, 192])).
% 2.79/3.08 tff(197,plain,
% 2.79/3.08 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 2.79/3.08 inference(rewrite,[status(thm)],[])).
% 2.79/3.08 tff(198,plain,
% 2.79/3.08 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 2.79/3.08 inference(and_elim,[status(thm)],[48])).
% 2.79/3.08 tff(199,plain,
% 2.79/3.08 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 2.79/3.08 inference(modus_ponens,[status(thm)],[198, 197])).
% 2.79/3.08 tff(200,plain,
% 2.79/3.08 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 2.79/3.08 inference(modus_ponens,[status(thm)],[199, 196])).
% 2.79/3.08 tff(201,plain,
% 2.79/3.08 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 2.79/3.08 inference(unit_resolution,[status(thm)],[200, 95, 86])).
% 2.79/3.08 tff(202,plain,
% 2.79/3.08 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X))))),
% 2.79/3.08 inference(rewrite,[status(thm)],[])).
% 2.79/3.08 tff(203,plain,
% 2.79/3.08 (((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X))))),
% 2.79/3.08 inference(rewrite,[status(thm)],[])).
% 2.79/3.08 tff(204,plain,
% 2.79/3.08 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))))),
% 2.79/3.08 inference(monotonicity,[status(thm)],[203])).
% 2.79/3.08 tff(205,plain,
% 2.79/3.08 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X))))),
% 2.79/3.08 inference(transitivity,[status(thm)],[204, 202])).
% 2.79/3.08 tff(206,plain,
% 2.79/3.08 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 2.79/3.08 inference(quant_inst,[status(thm)],[])).
% 2.79/3.08 tff(207,plain,
% 2.79/3.08 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))),
% 2.79/3.08 inference(modus_ponens,[status(thm)],[206, 205])).
% 2.79/3.08 tff(208,plain,
% 2.79/3.08 (![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))),
% 2.79/3.08 inference(unit_resolution,[status(thm)],[207, 201, 123])).
% 2.79/3.08 tff(209,plain,
% 2.79/3.08 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))),
% 2.79/3.08 inference(rewrite,[status(thm)],[])).
% 2.79/3.08 tff(210,plain,
% 2.79/3.08 ((![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))),
% 2.79/3.08 inference(rewrite,[status(thm)],[])).
% 2.79/3.08 tff(211,plain,
% 2.79/3.08 (^[Y: $i] : trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) <=> (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))), (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))), rewrite(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))), (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))))),
% 2.79/3.08 inference(bind,[status(th)],[])).
% 2.79/3.08 tff(212,plain,
% 2.79/3.08 (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))),
% 2.79/3.08 inference(quant_intro,[status(thm)],[211])).
% 2.79/3.08 tff(213,plain,
% 2.79/3.08 (^[Y: $i] : rewrite(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) <=> (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))),
% 2.79/3.08 inference(bind,[status(th)],[])).
% 2.79/3.08 tff(214,plain,
% 2.79/3.08 (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))),
% 2.79/3.08 inference(quant_intro,[status(thm)],[213])).
% 2.79/3.08 tff(215,plain,
% 2.79/3.08 ((![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.08 inference(monotonicity,[status(thm)],[214, 212])).
% 2.79/3.08 tff(216,plain,
% 2.79/3.08 ((![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))),
% 2.79/3.08 inference(transitivity,[status(thm)],[215, 210])).
% 2.79/3.08 tff(217,plain,
% 2.79/3.08 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))))),
% 2.79/3.08 inference(monotonicity,[status(thm)],[216])).
% 2.79/3.08 tff(218,plain,
% 2.79/3.08 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))))),
% 2.79/3.08 inference(transitivity,[status(thm)],[217, 209])).
% 2.79/3.08 tff(219,plain,
% 2.79/3.08 ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.08 inference(quant_inst,[status(thm)],[])).
% 2.79/3.08 tff(220,plain,
% 2.79/3.08 ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))),
% 2.79/3.08 inference(modus_ponens,[status(thm)],[219, 218])).
% 2.79/3.08 tff(221,plain,
% 2.79/3.08 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))),
% 2.79/3.08 inference(unit_resolution,[status(thm)],[220, 127, 208])).
% 2.79/3.08 tff(222,plain,
% 2.79/3.08 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))),
% 2.79/3.08 inference(unit_resolution,[status(thm)],[221, 191])).
% 2.79/3.08 tff(223,plain,
% 2.79/3.08 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | (p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.08 inference(rewrite,[status(thm)],[])).
% 2.79/3.08 tff(224,plain,
% 2.79/3.08 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | (p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.79/3.08 inference(quant_inst,[status(thm)],[])).
% 2.79/3.08 tff(225,plain,
% 2.79/3.08 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), Y)))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.08 inference(modus_ponens,[status(thm)],[224, 223])).
% 2.79/3.08 tff(226,plain,
% 2.79/3.08 ($false),
% 2.79/3.08 inference(unit_resolution,[status(thm)],[225, 222, 5, 3])).
% 2.79/3.08 tff(227,plain,((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.08 tff(228,plain,
% 2.79/3.08 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10)))),
% 2.79/3.08 inference(rewrite,[status(thm)],[])).
% 2.79/3.08 tff(229,plain,
% 2.79/3.08 ((r1(Y!8, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(Y!8, X!10))) <=> ((~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10)))),
% 2.79/3.08 inference(rewrite,[status(thm)],[])).
% 2.79/3.08 tff(230,plain,
% 2.79/3.08 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(Y!8, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10))))),
% 2.79/3.08 inference(monotonicity,[status(thm)],[229])).
% 2.79/3.08 tff(231,plain,
% 2.79/3.08 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(Y!8, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10)))),
% 2.79/3.08 inference(transitivity,[status(thm)],[230, 228])).
% 2.79/3.08 tff(232,plain,
% 2.79/3.08 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | (~r1(Y!8, X!10)))),
% 2.79/3.09 inference(quant_inst,[status(thm)],[])).
% 2.79/3.09 tff(233,plain,
% 2.79/3.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!10)) | (~r1(X!10, tptp_fun_X_7(X!10))) | r1(Y!8, tptp_fun_X_7(X!10))),
% 2.79/3.09 inference(modus_ponens,[status(thm)],[232, 231])).
% 2.79/3.09 tff(234,plain,
% 2.79/3.09 (r1(Y!8, tptp_fun_X_7(X!10))),
% 2.79/3.09 inference(unit_resolution,[status(thm)],[233, 70, 57, 105])).
% 2.79/3.09 tff(235,plain,
% 2.79/3.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(236,plain,
% 2.79/3.09 ((r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(Y!8, tptp_fun_X_7(X!10)))) <=> ((~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(237,plain,
% 2.79/3.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(Y!8, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.09 inference(monotonicity,[status(thm)],[236])).
% 2.79/3.09 tff(238,plain,
% 2.79/3.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(Y!8, tptp_fun_X_7(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.09 inference(transitivity,[status(thm)],[237, 235])).
% 2.79/3.09 tff(239,plain,
% 2.79/3.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(Y!8, tptp_fun_X_7(X!10))))),
% 2.79/3.09 inference(quant_inst,[status(thm)],[])).
% 2.79/3.09 tff(240,plain,
% 2.79/3.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!10))) | (~r1(tptp_fun_X_7(X!10), tptp_fun_X_7(tptp_fun_X_7(X!10)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 2.79/3.09 inference(modus_ponens,[status(thm)],[239, 238])).
% 2.79/3.09 tff(241,plain,
% 2.79/3.09 (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))),
% 2.79/3.09 inference(unit_resolution,[status(thm)],[240, 70, 234, 116])).
% 2.79/3.09 tff(242,plain,
% 2.79/3.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(243,plain,
% 2.79/3.09 ((r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10))))) <=> ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(244,plain,
% 2.79/3.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))),
% 2.79/3.09 inference(monotonicity,[status(thm)],[243])).
% 2.79/3.09 tff(245,plain,
% 2.79/3.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.09 inference(transitivity,[status(thm)],[244, 242])).
% 2.79/3.09 tff(246,plain,
% 2.79/3.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))))),
% 2.79/3.09 inference(quant_inst,[status(thm)],[])).
% 2.79/3.09 tff(247,plain,
% 2.79/3.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!10)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!10)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.09 inference(modus_ponens,[status(thm)],[246, 245])).
% 2.79/3.09 tff(248,plain,
% 2.79/3.09 (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))),
% 2.79/3.09 inference(unit_resolution,[status(thm)],[247, 70, 241, 127])).
% 2.79/3.09 tff(249,assumption,(~r1(X!9, X!9)), introduced(assumption)).
% 2.79/3.09 tff(250,plain,
% 2.79/3.09 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 2.79/3.09 inference(bind,[status(th)],[])).
% 2.79/3.09 tff(251,plain,
% 2.79/3.09 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 2.79/3.09 inference(quant_intro,[status(thm)],[250])).
% 2.79/3.09 tff(252,plain,
% 2.79/3.09 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(253,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity')).
% 2.79/3.09 tff(254,plain,
% 2.79/3.09 (![X: $i] : r1(X, X)),
% 2.79/3.09 inference(modus_ponens,[status(thm)],[253, 252])).
% 2.79/3.09 tff(255,plain,(
% 2.79/3.09 ![X: $i] : r1(X, X)),
% 2.79/3.09 inference(skolemize,[status(sab)],[254])).
% 2.79/3.09 tff(256,plain,
% 2.79/3.09 (![X: $i] : r1(X, X)),
% 2.79/3.09 inference(modus_ponens,[status(thm)],[255, 251])).
% 2.79/3.09 tff(257,plain,
% 2.79/3.09 ((~![X: $i] : r1(X, X)) | r1(X!9, X!9)),
% 2.79/3.09 inference(quant_inst,[status(thm)],[])).
% 2.79/3.09 tff(258,plain,
% 2.79/3.09 ($false),
% 2.79/3.09 inference(unit_resolution,[status(thm)],[257, 256, 249])).
% 2.79/3.09 tff(259,plain,(r1(X!9, X!9)), inference(lemma,lemma(discharge,[]))).
% 2.79/3.09 tff(260,assumption,(![Y: $i] : (p1(Y) | (~r1(X!9, Y)))), introduced(assumption)).
% 2.79/3.09 tff(261,plain,
% 2.79/3.09 (~((~r1(Y!8, X!9)) | p1(X!9))),
% 2.79/3.09 inference(and_elim,[status(thm)],[48])).
% 2.79/3.09 tff(262,plain,
% 2.79/3.09 (~p1(X!9)),
% 2.79/3.09 inference(or_elim,[status(thm)],[261])).
% 2.79/3.09 tff(263,plain,
% 2.79/3.09 (((~![Y: $i] : (p1(Y) | (~r1(X!9, Y)))) | (p1(X!9) | (~r1(X!9, X!9)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!9, Y)))) | p1(X!9) | (~r1(X!9, X!9)))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(264,plain,
% 2.79/3.09 ((~![Y: $i] : (p1(Y) | (~r1(X!9, Y)))) | (p1(X!9) | (~r1(X!9, X!9)))),
% 2.79/3.09 inference(quant_inst,[status(thm)],[])).
% 2.79/3.09 tff(265,plain,
% 2.79/3.09 ((~![Y: $i] : (p1(Y) | (~r1(X!9, Y)))) | p1(X!9) | (~r1(X!9, X!9))),
% 2.79/3.09 inference(modus_ponens,[status(thm)],[264, 263])).
% 2.79/3.09 tff(266,plain,
% 2.79/3.09 ($false),
% 2.79/3.09 inference(unit_resolution,[status(thm)],[265, 262, 260, 259])).
% 2.79/3.09 tff(267,plain,(~![Y: $i] : (p1(Y) | (~r1(X!9, Y)))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.09 tff(268,plain,
% 2.79/3.09 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(269,plain,
% 2.79/3.09 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 2.79/3.09 inference(quant_inst,[status(thm)],[])).
% 2.79/3.09 tff(270,plain,
% 2.79/3.09 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 2.79/3.09 inference(modus_ponens,[status(thm)],[269, 268])).
% 2.79/3.09 tff(271,plain,
% 2.79/3.09 (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 2.79/3.09 inference(unit_resolution,[status(thm)],[270, 201, 58])).
% 2.79/3.09 tff(272,plain,
% 2.79/3.09 (r1(Y!8, X!9)),
% 2.79/3.09 inference(or_elim,[status(thm)],[261])).
% 2.79/3.09 tff(273,plain,
% 2.79/3.09 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(274,plain,
% 2.79/3.09 (((~r1(Y!8, X!9)) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(275,plain,
% 2.79/3.09 (^[Y: $i] : rewrite(((~r1(X!9, Y)) | p1(Y)) <=> (p1(Y) | (~r1(X!9, Y))))),
% 2.79/3.09 inference(bind,[status(th)],[])).
% 2.79/3.09 tff(276,plain,
% 2.79/3.09 (![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(X!9, Y)))),
% 2.79/3.09 inference(quant_intro,[status(thm)],[275])).
% 2.79/3.09 tff(277,plain,
% 2.79/3.09 (((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> ((~r1(Y!8, X!9)) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 2.79/3.09 inference(monotonicity,[status(thm)],[276])).
% 2.79/3.09 tff(278,plain,
% 2.79/3.09 (((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))))),
% 2.79/3.09 inference(transitivity,[status(thm)],[277, 274])).
% 2.79/3.09 tff(279,plain,
% 2.79/3.09 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y)))))),
% 2.79/3.09 inference(monotonicity,[status(thm)],[278])).
% 2.79/3.09 tff(280,plain,
% 2.79/3.09 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y))))),
% 2.79/3.09 inference(transitivity,[status(thm)],[279, 273])).
% 2.79/3.09 tff(281,plain,
% 2.79/3.09 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 2.79/3.09 inference(quant_inst,[status(thm)],[])).
% 2.79/3.09 tff(282,plain,
% 2.79/3.09 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y)))),
% 2.79/3.09 inference(modus_ponens,[status(thm)],[281, 280])).
% 2.79/3.09 tff(283,plain,
% 2.79/3.09 (![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!9, Y)))),
% 2.79/3.09 inference(unit_resolution,[status(thm)],[282, 272, 271])).
% 2.79/3.09 tff(284,plain,
% 2.79/3.09 (![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))),
% 2.79/3.09 inference(unit_resolution,[status(thm)],[283, 267])).
% 2.79/3.09 tff(285,assumption,((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))), introduced(assumption)).
% 2.79/3.09 tff(286,plain,
% 2.79/3.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(287,plain,
% 2.79/3.09 ((r1(X!0, X!9) | (~r1(Y!8, X!9)) | (~r1(X!0, Y!8))) <=> ((~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(288,plain,
% 2.79/3.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!9) | (~r1(Y!8, X!9)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9)))),
% 2.79/3.09 inference(monotonicity,[status(thm)],[287])).
% 2.79/3.09 tff(289,plain,
% 2.79/3.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!9) | (~r1(Y!8, X!9)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9))),
% 2.79/3.09 inference(transitivity,[status(thm)],[288, 286])).
% 2.79/3.09 tff(290,plain,
% 2.79/3.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!9) | (~r1(Y!8, X!9)) | (~r1(X!0, Y!8)))),
% 2.79/3.09 inference(quant_inst,[status(thm)],[])).
% 2.79/3.09 tff(291,plain,
% 2.79/3.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!9)) | r1(X!0, X!9)),
% 2.79/3.09 inference(modus_ponens,[status(thm)],[290, 289])).
% 2.79/3.09 tff(292,plain,
% 2.79/3.09 (r1(X!0, X!9)),
% 2.79/3.09 inference(unit_resolution,[status(thm)],[291, 70, 58, 272])).
% 2.79/3.09 tff(293,plain,
% 2.79/3.09 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!9)) | r1(X!9, tptp_fun_X_7(X!9)))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!9)) | r1(X!9, tptp_fun_X_7(X!9)))),
% 2.79/3.09 inference(rewrite,[status(thm)],[])).
% 2.79/3.09 tff(294,plain,
% 2.79/3.10 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!9)) | r1(X!9, tptp_fun_X_7(X!9)))),
% 2.79/3.10 inference(quant_inst,[status(thm)],[])).
% 2.79/3.10 tff(295,plain,
% 2.79/3.10 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!9)) | r1(X!9, tptp_fun_X_7(X!9))),
% 2.79/3.10 inference(modus_ponens,[status(thm)],[294, 293])).
% 2.79/3.10 tff(296,plain,
% 2.79/3.10 (r1(X!9, tptp_fun_X_7(X!9))),
% 2.79/3.10 inference(unit_resolution,[status(thm)],[295, 101, 292])).
% 2.79/3.10 tff(297,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9)))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(298,plain,
% 2.79/3.10 ((r1(X!0, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(X!0, X!9))) <=> ((~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9)))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(299,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(X!0, X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(monotonicity,[status(thm)],[298])).
% 2.79/3.10 tff(300,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(X!0, X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9)))),
% 2.79/3.10 inference(transitivity,[status(thm)],[299, 297])).
% 2.79/3.10 tff(301,plain,
% 2.79/3.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(X!0, X!9)))),
% 2.79/3.10 inference(quant_inst,[status(thm)],[])).
% 2.79/3.10 tff(302,plain,
% 2.79/3.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(X!0, tptp_fun_X_7(X!9))),
% 2.79/3.10 inference(modus_ponens,[status(thm)],[301, 300])).
% 2.79/3.10 tff(303,plain,
% 2.79/3.10 (r1(X!0, tptp_fun_X_7(X!9))),
% 2.79/3.10 inference(unit_resolution,[status(thm)],[302, 70, 292, 296])).
% 2.79/3.10 tff(304,plain,
% 2.79/3.10 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(X!9))) | r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(X!9))) | r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(305,plain,
% 2.79/3.10 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(X!9))) | r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(quant_inst,[status(thm)],[])).
% 2.79/3.10 tff(306,plain,
% 2.79/3.10 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(X!9))) | r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 2.79/3.10 inference(modus_ponens,[status(thm)],[305, 304])).
% 2.79/3.10 tff(307,plain,
% 2.79/3.10 (r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 2.79/3.10 inference(unit_resolution,[status(thm)],[306, 101, 303])).
% 2.79/3.10 tff(308,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(309,plain,
% 2.79/3.10 ((r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!0, tptp_fun_X_7(X!9)))) <=> ((~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(310,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!0, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(monotonicity,[status(thm)],[309])).
% 2.79/3.10 tff(311,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!0, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(transitivity,[status(thm)],[310, 308])).
% 2.79/3.10 tff(312,plain,
% 2.79/3.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!0, tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(quant_inst,[status(thm)],[])).
% 2.79/3.10 tff(313,plain,
% 2.79/3.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 2.79/3.10 inference(modus_ponens,[status(thm)],[312, 311])).
% 2.79/3.10 tff(314,plain,
% 2.79/3.10 (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 2.79/3.10 inference(unit_resolution,[status(thm)],[313, 70, 303, 307])).
% 2.79/3.10 tff(315,plain,
% 2.79/3.10 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(316,plain,
% 2.79/3.10 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(quant_inst,[status(thm)],[])).
% 2.79/3.10 tff(317,plain,
% 2.79/3.10 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(modus_ponens,[status(thm)],[316, 315])).
% 2.79/3.10 tff(318,plain,
% 2.79/3.10 (r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(unit_resolution,[status(thm)],[317, 101, 314])).
% 2.79/3.10 tff(319,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(320,plain,
% 2.79/3.10 ((r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(321,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.10 inference(monotonicity,[status(thm)],[320])).
% 2.79/3.10 tff(322,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(transitivity,[status(thm)],[321, 319])).
% 2.79/3.10 tff(323,plain,
% 2.79/3.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(quant_inst,[status(thm)],[])).
% 2.79/3.10 tff(324,plain,
% 2.79/3.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(modus_ponens,[status(thm)],[323, 322])).
% 2.79/3.10 tff(325,plain,
% 2.79/3.10 (r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(unit_resolution,[status(thm)],[324, 70, 314, 318])).
% 2.79/3.10 tff(326,plain,
% 2.79/3.10 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(327,plain,
% 2.79/3.10 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.10 inference(quant_inst,[status(thm)],[])).
% 2.79/3.10 tff(328,plain,
% 2.79/3.10 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(modus_ponens,[status(thm)],[327, 326])).
% 2.79/3.10 tff(329,plain,
% 2.79/3.10 (r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(unit_resolution,[status(thm)],[328, 101, 325])).
% 2.79/3.10 tff(330,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(331,plain,
% 2.79/3.10 ((r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!9, tptp_fun_X_7(X!9)))) <=> ((~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(332,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!9, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(monotonicity,[status(thm)],[331])).
% 2.79/3.10 tff(333,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!9, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(transitivity,[status(thm)],[332, 330])).
% 2.79/3.10 tff(334,plain,
% 2.79/3.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(X!9, tptp_fun_X_7(X!9))))),
% 2.79/3.10 inference(quant_inst,[status(thm)],[])).
% 2.79/3.10 tff(335,plain,
% 2.79/3.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 2.79/3.10 inference(modus_ponens,[status(thm)],[334, 333])).
% 2.79/3.10 tff(336,plain,
% 2.79/3.10 (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 2.79/3.10 inference(unit_resolution,[status(thm)],[335, 70, 296, 307])).
% 2.79/3.10 tff(337,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(338,plain,
% 2.79/3.10 ((r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(rewrite,[status(thm)],[])).
% 2.79/3.10 tff(339,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.10 inference(monotonicity,[status(thm)],[338])).
% 2.79/3.10 tff(340,plain,
% 2.79/3.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(transitivity,[status(thm)],[339, 337])).
% 2.79/3.10 tff(341,plain,
% 2.79/3.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.10 inference(quant_inst,[status(thm)],[])).
% 2.79/3.10 tff(342,plain,
% 2.79/3.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.11 inference(modus_ponens,[status(thm)],[341, 340])).
% 2.79/3.11 tff(343,plain,
% 2.79/3.11 (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.11 inference(unit_resolution,[status(thm)],[342, 70, 336, 318])).
% 2.79/3.11 tff(344,plain,
% 2.79/3.11 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.11 inference(rewrite,[status(thm)],[])).
% 2.79/3.11 tff(345,plain,
% 2.79/3.11 ((r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.11 inference(rewrite,[status(thm)],[])).
% 2.79/3.11 tff(346,plain,
% 2.79/3.11 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 2.79/3.11 inference(monotonicity,[status(thm)],[345])).
% 2.79/3.11 tff(347,plain,
% 2.79/3.11 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.11 inference(transitivity,[status(thm)],[346, 344])).
% 2.79/3.11 tff(348,plain,
% 2.79/3.11 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.11 inference(quant_inst,[status(thm)],[])).
% 2.79/3.11 tff(349,plain,
% 2.79/3.11 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.11 inference(modus_ponens,[status(thm)],[348, 347])).
% 2.79/3.11 tff(350,plain,
% 2.79/3.11 (r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.11 inference(unit_resolution,[status(thm)],[349, 70, 343, 329])).
% 2.79/3.11 tff(351,assumption,(![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))), introduced(assumption)).
% 2.79/3.11 tff(352,plain,
% 2.79/3.11 (((~![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 2.79/3.11 inference(rewrite,[status(thm)],[])).
% 2.79/3.11 tff(353,plain,
% 2.79/3.11 ((~![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | ((~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 2.79/3.11 inference(quant_inst,[status(thm)],[])).
% 2.79/3.11 tff(354,plain,
% 2.79/3.11 ((~![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | (~r1(X!9, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 2.79/3.11 inference(modus_ponens,[status(thm)],[353, 352])).
% 2.79/3.11 tff(355,plain,
% 2.79/3.11 ($false),
% 2.79/3.11 inference(unit_resolution,[status(thm)],[354, 351, 350, 285])).
% 2.79/3.11 tff(356,plain,((~![Y: $i] : ((~r1(X!9, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.11 tff(357,plain,
% 2.79/3.11 (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 2.79/3.11 inference(unit_resolution,[status(thm)],[356, 284])).
% 2.79/3.11 tff(358,assumption,(![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))), introduced(assumption)).
% 2.79/3.11 tff(359,assumption,(~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))), introduced(assumption)).
% 2.79/3.11 tff(360,plain,
% 2.79/3.11 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.11 inference(tautology,[status(thm)],[])).
% 2.79/3.11 tff(361,plain,
% 2.79/3.11 (r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.11 inference(unit_resolution,[status(thm)],[360, 359])).
% 2.79/3.11 tff(362,plain,
% 2.79/3.11 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 2.79/3.11 inference(tautology,[status(thm)],[])).
% 2.79/3.11 tff(363,plain,
% 2.79/3.11 (~p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.11 inference(unit_resolution,[status(thm)],[362, 359])).
% 2.79/3.11 tff(364,assumption,(~p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))), introduced(assumption)).
% 2.79/3.11 tff(365,assumption,(r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))), introduced(assumption)).
% 2.79/3.11 tff(366,plain,
% 2.79/3.11 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 2.79/3.11 inference(rewrite,[status(thm)],[])).
% 2.79/3.11 tff(367,plain,
% 2.79/3.11 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 2.79/3.11 inference(quant_inst,[status(thm)],[])).
% 2.79/3.11 tff(368,plain,
% 2.79/3.11 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 2.79/3.11 inference(modus_ponens,[status(thm)],[367, 366])).
% 2.79/3.11 tff(369,plain,
% 2.79/3.11 ($false),
% 2.79/3.11 inference(unit_resolution,[status(thm)],[368, 358, 365, 364])).
% 2.79/3.11 tff(370,plain,((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.11 tff(371,plain,
% 2.79/3.11 ($false),
% 2.79/3.11 inference(unit_resolution,[status(thm)],[370, 363, 361, 358])).
% 2.79/3.11 tff(372,plain,(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | p1(tptp_fun_X_4(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.11 tff(373,plain,
% 2.79/3.11 (~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 2.79/3.11 inference(unit_resolution,[status(thm)],[372, 357])).
% 2.79/3.11 tff(374,plain,
% 2.79/3.11 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X))))),
% 2.79/3.11 inference(rewrite,[status(thm)],[])).
% 2.79/3.11 tff(375,plain,
% 2.79/3.11 (((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X))))),
% 2.79/3.11 inference(rewrite,[status(thm)],[])).
% 2.79/3.11 tff(376,plain,
% 2.79/3.11 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))))),
% 2.79/3.11 inference(monotonicity,[status(thm)],[375])).
% 2.79/3.11 tff(377,plain,
% 2.79/3.11 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X))))),
% 2.79/3.11 inference(transitivity,[status(thm)],[376, 374])).
% 2.79/3.11 tff(378,plain,
% 2.79/3.11 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 2.79/3.11 inference(quant_inst,[status(thm)],[])).
% 2.79/3.11 tff(379,plain,
% 2.79/3.11 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))),
% 2.79/3.11 inference(modus_ponens,[status(thm)],[378, 377])).
% 2.79/3.11 tff(380,plain,
% 2.79/3.11 (![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))),
% 2.79/3.11 inference(unit_resolution,[status(thm)],[379, 201, 325])).
% 2.79/3.11 tff(381,plain,
% 2.79/3.11 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))),
% 2.79/3.11 inference(rewrite,[status(thm)],[])).
% 2.79/3.11 tff(382,plain,
% 2.79/3.11 ((![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))),
% 2.79/3.11 inference(rewrite,[status(thm)],[])).
% 2.79/3.11 tff(383,plain,
% 2.79/3.11 (^[Y: $i] : trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) <=> (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))), (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))), rewrite(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))), (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))))),
% 2.79/3.11 inference(bind,[status(th)],[])).
% 2.79/3.11 tff(384,plain,
% 2.79/3.11 (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) <=> ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 2.79/3.11 inference(quant_intro,[status(thm)],[383])).
% 2.79/3.11 tff(385,plain,
% 2.79/3.11 (^[Y: $i] : rewrite(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) <=> (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))),
% 2.79/3.11 inference(bind,[status(th)],[])).
% 2.79/3.11 tff(386,plain,
% 2.79/3.11 (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 2.79/3.11 inference(quant_intro,[status(thm)],[385])).
% 2.79/3.11 tff(387,plain,
% 2.79/3.11 ((![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 2.79/3.11 inference(monotonicity,[status(thm)],[386, 384])).
% 2.79/3.11 tff(388,plain,
% 2.79/3.11 ((![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))),
% 2.79/3.11 inference(transitivity,[status(thm)],[387, 382])).
% 2.79/3.11 tff(389,plain,
% 2.79/3.11 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))))),
% 2.79/3.11 inference(monotonicity,[status(thm)],[388])).
% 2.79/3.11 tff(390,plain,
% 2.79/3.11 (((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) <=> ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))),
% 2.79/3.11 inference(transitivity,[status(thm)],[389, 381])).
% 2.79/3.11 tff(391,plain,
% 2.79/3.11 ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | p1(Y)) | ![Y: $i] : ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 2.79/3.11 inference(quant_inst,[status(thm)],[])).
% 2.79/3.11 tff(392,plain,
% 2.79/3.11 ((~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), X)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 2.79/3.12 inference(modus_ponens,[status(thm)],[391, 390])).
% 2.79/3.12 tff(393,plain,
% 2.79/3.12 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))) | ![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[392, 329, 380])).
% 2.79/3.12 tff(394,plain,
% 2.79/3.12 (![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[393, 373])).
% 2.79/3.12 tff(395,assumption,(~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))))), introduced(assumption)).
% 2.79/3.12 tff(396,plain,
% 2.79/3.12 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X))))) | r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.12 inference(tautology,[status(thm)],[])).
% 2.79/3.12 tff(397,plain,
% 2.79/3.12 (r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[396, 395])).
% 2.79/3.12 tff(398,assumption,(![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))), introduced(assumption)).
% 2.79/3.12 tff(399,plain,
% 2.79/3.12 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(400,plain,
% 2.79/3.12 (((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(401,plain,
% 2.79/3.12 ((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) <=> (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(402,plain,
% 2.79/3.12 (((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) <=> ((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 2.79/3.12 inference(monotonicity,[status(thm)],[401])).
% 2.79/3.12 tff(403,plain,
% 2.79/3.12 (((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) <=> ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))))),
% 2.79/3.12 inference(transitivity,[status(thm)],[402, 400])).
% 2.79/3.12 tff(404,plain,
% 2.79/3.12 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | ((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))))),
% 2.79/3.12 inference(monotonicity,[status(thm)],[403])).
% 2.79/3.12 tff(405,plain,
% 2.79/3.12 (((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | ((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) <=> ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))))),
% 2.79/3.12 inference(transitivity,[status(thm)],[404, 399])).
% 2.79/3.12 tff(406,plain,
% 2.79/3.12 ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | ((~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 2.79/3.12 inference(quant_inst,[status(thm)],[])).
% 2.79/3.12 tff(407,plain,
% 2.79/3.12 ((~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 2.79/3.12 inference(modus_ponens,[status(thm)],[406, 405])).
% 2.79/3.12 tff(408,plain,
% 2.79/3.12 (~((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[407, 398, 397])).
% 2.79/3.12 tff(409,plain,
% 2.79/3.12 (((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | (~p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 2.79/3.12 inference(tautology,[status(thm)],[])).
% 2.79/3.12 tff(410,plain,
% 2.79/3.12 (~p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[409, 408])).
% 2.79/3.12 tff(411,plain,
% 2.79/3.12 (((~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))) | r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 2.79/3.12 inference(tautology,[status(thm)],[])).
% 2.79/3.12 tff(412,plain,
% 2.79/3.12 (r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[411, 408])).
% 2.79/3.12 tff(413,plain,
% 2.79/3.12 (((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X))))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))),
% 2.79/3.12 inference(tautology,[status(thm)],[])).
% 2.79/3.12 tff(414,plain,
% 2.79/3.12 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[413, 395])).
% 2.79/3.12 tff(415,plain,
% 2.79/3.12 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))) | (p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(416,plain,
% 2.79/3.12 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))) | (p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))))),
% 2.79/3.12 inference(quant_inst,[status(thm)],[])).
% 2.79/3.12 tff(417,plain,
% 2.79/3.12 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))) | p1(tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), tptp_fun_X_4(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))))),
% 2.79/3.12 inference(modus_ponens,[status(thm)],[416, 415])).
% 2.79/3.12 tff(418,plain,
% 2.79/3.12 ($false),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[417, 414, 412, 410])).
% 2.79/3.12 tff(419,plain,(((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X))))) | (~![Y: $i] : ((~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), Y))))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.12 tff(420,plain,
% 2.79/3.12 ((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X))))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[419, 394])).
% 2.79/3.12 tff(421,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9)))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(422,plain,
% 2.79/3.12 ((r1(Y!8, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(Y!8, X!9))) <=> ((~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9)))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(423,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(Y!8, X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9))))),
% 2.79/3.12 inference(monotonicity,[status(thm)],[422])).
% 2.79/3.12 tff(424,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(Y!8, X!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9)))),
% 2.79/3.12 inference(transitivity,[status(thm)],[423, 421])).
% 2.79/3.12 tff(425,plain,
% 2.79/3.12 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | (~r1(Y!8, X!9)))),
% 2.79/3.12 inference(quant_inst,[status(thm)],[])).
% 2.79/3.12 tff(426,plain,
% 2.79/3.12 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!9)) | (~r1(X!9, tptp_fun_X_7(X!9))) | r1(Y!8, tptp_fun_X_7(X!9))),
% 2.79/3.12 inference(modus_ponens,[status(thm)],[425, 424])).
% 2.79/3.12 tff(427,plain,
% 2.79/3.12 (r1(Y!8, tptp_fun_X_7(X!9))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[426, 70, 272, 296])).
% 2.79/3.12 tff(428,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(429,plain,
% 2.79/3.12 ((r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(Y!8, tptp_fun_X_7(X!9)))) <=> ((~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(430,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(Y!8, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.12 inference(monotonicity,[status(thm)],[429])).
% 2.79/3.12 tff(431,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(Y!8, tptp_fun_X_7(X!9))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.12 inference(transitivity,[status(thm)],[430, 428])).
% 2.79/3.12 tff(432,plain,
% 2.79/3.12 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(Y!8, tptp_fun_X_7(X!9))))),
% 2.79/3.12 inference(quant_inst,[status(thm)],[])).
% 2.79/3.12 tff(433,plain,
% 2.79/3.12 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(X!9))) | (~r1(tptp_fun_X_7(X!9), tptp_fun_X_7(tptp_fun_X_7(X!9)))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 2.79/3.12 inference(modus_ponens,[status(thm)],[432, 431])).
% 2.79/3.12 tff(434,plain,
% 2.79/3.12 (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[433, 70, 427, 307])).
% 2.79/3.12 tff(435,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(436,plain,
% 2.79/3.12 ((r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9))))) <=> ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(437,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.12 inference(monotonicity,[status(thm)],[436])).
% 2.79/3.12 tff(438,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.12 inference(transitivity,[status(thm)],[437, 435])).
% 2.79/3.12 tff(439,plain,
% 2.79/3.12 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.12 inference(quant_inst,[status(thm)],[])).
% 2.79/3.12 tff(440,plain,
% 2.79/3.12 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(X!9)))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(X!9)), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.12 inference(modus_ponens,[status(thm)],[439, 438])).
% 2.79/3.12 tff(441,plain,
% 2.79/3.12 (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))),
% 2.79/3.12 inference(unit_resolution,[status(thm)],[440, 70, 434, 318])).
% 2.79/3.12 tff(442,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(443,plain,
% 2.79/3.12 ((r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) <=> ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.12 inference(rewrite,[status(thm)],[])).
% 2.79/3.12 tff(444,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))))),
% 2.79/3.12 inference(monotonicity,[status(thm)],[443])).
% 2.79/3.12 tff(445,plain,
% 2.79/3.12 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.13 inference(transitivity,[status(thm)],[444, 442])).
% 2.79/3.13 tff(446,plain,
% 2.79/3.13 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))),
% 2.79/3.13 inference(quant_inst,[status(thm)],[])).
% 2.79/3.13 tff(447,plain,
% 2.79/3.13 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))) | (~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))), tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.13 inference(modus_ponens,[status(thm)],[446, 445])).
% 2.79/3.13 tff(448,plain,
% 2.79/3.13 (r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))),
% 2.79/3.13 inference(unit_resolution,[status(thm)],[447, 70, 441, 329])).
% 2.79/3.13 tff(449,assumption,(![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), introduced(assumption)).
% 2.79/3.13 tff(450,plain,
% 2.79/3.13 (((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))))))),
% 2.79/3.13 inference(rewrite,[status(thm)],[])).
% 2.79/3.13 tff(451,plain,
% 2.79/3.13 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X)))))))),
% 2.79/3.13 inference(quant_inst,[status(thm)],[])).
% 2.79/3.13 tff(452,plain,
% 2.79/3.13 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9)))), tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!9))))), X))))))),
% 2.79/3.13 inference(modus_ponens,[status(thm)],[451, 450])).
% 2.79/3.13 tff(453,plain,
% 2.79/3.13 ($false),
% 2.79/3.13 inference(unit_resolution,[status(thm)],[452, 449, 448, 420])).
% 2.79/3.13 tff(454,plain,(~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), inference(lemma,lemma(discharge,[]))).
% 2.79/3.13 tff(455,plain,
% 2.79/3.13 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 2.90/3.13 inference(rewrite,[status(thm)],[])).
% 2.90/3.13 tff(456,plain,
% 2.90/3.13 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 2.90/3.13 inference(rewrite,[status(thm)],[])).
% 2.90/3.13 tff(457,plain,
% 2.90/3.13 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 2.90/3.13 inference(bind,[status(th)],[])).
% 2.90/3.13 tff(458,plain,
% 2.90/3.13 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 2.90/3.13 inference(quant_intro,[status(thm)],[457])).
% 2.90/3.13 tff(459,plain,
% 2.90/3.13 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 2.90/3.13 inference(monotonicity,[status(thm)],[458])).
% 2.90/3.13 tff(460,plain,
% 2.90/3.13 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 2.90/3.13 inference(transitivity,[status(thm)],[459, 456])).
% 2.90/3.13 tff(461,plain,
% 2.90/3.13 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))),
% 2.90/3.13 inference(and_elim,[status(thm)],[48])).
% 2.90/3.13 tff(462,plain,
% 2.90/3.13 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 2.90/3.13 inference(modus_ponens,[status(thm)],[461, 460])).
% 2.90/3.13 tff(463,plain,
% 2.90/3.13 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 2.90/3.13 inference(modus_ponens,[status(thm)],[462, 455])).
% 2.90/3.13 tff(464,plain,
% 2.90/3.13 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 2.90/3.13 inference(unit_resolution,[status(thm)],[463, 95, 86])).
% 2.90/3.13 tff(465,plain,
% 2.90/3.13 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 2.90/3.13 inference(rewrite,[status(thm)],[])).
% 2.90/3.13 tff(466,plain,
% 2.90/3.13 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 2.90/3.13 inference(quant_inst,[status(thm)],[])).
% 2.90/3.13 tff(467,plain,
% 2.90/3.13 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 2.90/3.13 inference(modus_ponens,[status(thm)],[466, 465])).
% 2.90/3.13 tff(468,plain,
% 2.90/3.13 (![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 2.90/3.13 inference(unit_resolution,[status(thm)],[467, 464, 58])).
% 2.90/3.13 tff(469,plain,
% 2.90/3.13 (![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))),
% 2.90/3.13 inference(unit_resolution,[status(thm)],[468, 454])).
% 2.90/3.13 tff(470,plain,
% 2.90/3.13 (((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 2.90/3.13 inference(rewrite,[status(thm)],[])).
% 2.90/3.13 tff(471,plain,
% 2.90/3.13 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | ((~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))))))),
% 2.90/3.14 inference(quant_inst,[status(thm)],[])).
% 2.90/3.14 tff(472,plain,
% 2.90/3.14 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | (~r1(Y!8, tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))))) | (~((~r1(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10))), tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))) | p1(tptp_fun_Y_6(tptp_fun_X_7(tptp_fun_X_7(tptp_fun_X_7(X!10)))))))),
% 2.90/3.14 inference(modus_ponens,[status(thm)],[471, 470])).
% 2.90/3.14 tff(473,plain,
% 2.90/3.14 ($false),
% 2.90/3.14 inference(unit_resolution,[status(thm)],[472, 469, 248, 227])).
% 2.90/3.14 % SZS output end Proof
% 2.90/3.14 % E exiting
%------------------------------------------------------------------------------