%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL646+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n003.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 03:00:22 PM UTC 2026
% Result : Theorem 1.35s 1.66s
% Output : Proof 1.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL646+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E %s %d THM
% 0.14/0.40 % Computer : n003.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 4 19:45:51 UTC 2026
% 0.14/0.41 % CPUTime :
% 1.35/1.66 % SZS status Theorem
% 1.35/1.66 % SZS output start Proof
% 1.35/1.66 tff(r1_type, type, (
% 1.35/1.66 r1: ( $i * $i ) > $o)).
% 1.35/1.66 tff(tptp_fun_X_9_type, type, (
% 1.35/1.66 tptp_fun_X_9: $i > $i)).
% 1.35/1.66 tff(tptp_fun_Y_12_type, type, (
% 1.35/1.66 tptp_fun_Y_12: $i > $i)).
% 1.35/1.66 tff(tptp_fun_Y_2_type, type, (
% 1.35/1.66 tptp_fun_Y_2: $i)).
% 1.35/1.66 tff(p4_type, type, (
% 1.35/1.66 p4: $i > $o)).
% 1.35/1.66 tff(p1_type, type, (
% 1.35/1.66 p1: $i > $o)).
% 1.35/1.66 tff(tptp_fun_X_0_type, type, (
% 1.35/1.66 tptp_fun_X_0: $i)).
% 1.35/1.66 tff(p2_type, type, (
% 1.35/1.66 p2: $i > $o)).
% 1.35/1.66 tff(tptp_fun_X_7_type, type, (
% 1.35/1.66 tptp_fun_X_7: $i > $i)).
% 1.35/1.66 tff(p6_type, type, (
% 1.35/1.66 p6: $i > $o)).
% 1.35/1.66 tff(tptp_fun_Y_5_type, type, (
% 1.35/1.66 tptp_fun_Y_5: $i > $i)).
% 1.35/1.66 tff(tptp_fun_Y_16_type, type, (
% 1.35/1.66 tptp_fun_Y_16: $i > $i)).
% 1.35/1.66 tff(p5_type, type, (
% 1.35/1.66 p5: $i > $o)).
% 1.35/1.66 tff(tptp_fun_Y_13_type, type, (
% 1.35/1.66 tptp_fun_Y_13: $i > $i)).
% 1.35/1.66 tff(p3_type, type, (
% 1.35/1.66 p3: $i > $o)).
% 1.35/1.66 tff(tptp_fun_Y_11_type, type, (
% 1.35/1.66 tptp_fun_Y_11: $i > $i)).
% 1.35/1.66 tff(tptp_fun_Y_10_type, type, (
% 1.35/1.66 tptp_fun_Y_10: $i > $i)).
% 1.35/1.66 tff(tptp_fun_X_15_type, type, (
% 1.35/1.66 tptp_fun_X_15: $i > $i)).
% 1.35/1.66 tff(tptp_fun_X_14_type, type, (
% 1.35/1.66 tptp_fun_X_14: $i > $i)).
% 1.35/1.66 tff(tptp_fun_X_8_type, type, (
% 1.35/1.66 tptp_fun_X_8: $i > $i)).
% 1.35/1.66 tff(tptp_fun_X_1_type, type, (
% 1.35/1.66 tptp_fun_X_1: $i > $i)).
% 1.35/1.66 tff(tptp_fun_Y_6_type, type, (
% 1.35/1.66 tptp_fun_Y_6: $i)).
% 1.35/1.66 tff(tptp_fun_Y_4_type, type, (
% 1.35/1.66 tptp_fun_Y_4: $i)).
% 1.35/1.66 tff(tptp_fun_Y_3_type, type, (
% 1.35/1.66 tptp_fun_Y_3: $i)).
% 1.35/1.66 tff(1,plain,
% 1.35/1.66 (^[Y: $i] : refl((p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y))) <=> (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y))))),
% 1.35/1.66 inference(bind,[status(th)],[])).
% 1.35/1.66 tff(2,plain,
% 1.35/1.66 (![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y))) <=> ![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))),
% 1.35/1.66 inference(quant_intro,[status(thm)],[1])).
% 1.35/1.66 tff(3,plain,
% 1.35/1.66 ((![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_1(Y))) | p3(tptp_fun_X_1(Y)))) | p1(Y))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p6(Y) | (~r1(X, Y))))))) & (~((~r1(X!0, Y!3)) | p5(Y!3))) & (~((~r1(X!0, Y!4)) | p3(Y!4))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))) | p6(X)))))) & (~((~r1(X!0, Y!6)) | p1(Y!6))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))) | p4(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))) | p2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))) | p6(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))) | p2(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p5(tptp_fun_X_8(Y)))) | p1(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | p2(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_1(Y))) | p3(tptp_fun_X_1(Y)))) | p3(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p5(tptp_fun_X_8(Y)))) | p3(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_1(Y))) | p3(tptp_fun_X_1(Y)))) | p5(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p5(tptp_fun_X_8(Y)))) | p5(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))) | p1(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) | p1(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | p1(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))) | p1(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y)))) | p4(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y)))) | p6(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))) | p3(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) | p3(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))) | p3(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y)))) | p4(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y)))) | p6(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))) | p5(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) | p5(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))) | p5(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_1(Y))) | p3(tptp_fun_X_1(Y)))) | p1(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p5(tptp_fun_X_8(Y)))) | p1(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))) | p2(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))) | p4(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))) | p6(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_1(Y))) | p3(tptp_fun_X_1(Y)))) | p3(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p5(tptp_fun_X_8(Y)))) | p3(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | p4(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | p2(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | p4(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | p6(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_1(Y))) | p3(tptp_fun_X_1(Y)))) | p5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p5(tptp_fun_X_8(Y)))) | p5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))) | p1(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) | p1(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | p1(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))) | p1(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y)))) | p2(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y)))) | p6(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))) | p3(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) | p3(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))) | p3(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y)))) | p2(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y)))) | p6(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))) | p5(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) | p5(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))) | p5(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))) | p2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))) | p4(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))) | p6(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | p2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | p4(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | p6(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))) | p6(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))) | p4(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))) | p2(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))) | p6(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))) | p4(Y)))) <=> (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p6(Y) | (~r1(X, Y))))))) & (~((~r1(X!0, Y!3)) | p5(Y!3))) & (~((~r1(X!0, Y!4)) | p3(Y!4))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))))) & (~((~r1(X!0, Y!6)) | p1(Y!6))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p6(Y) | (~r1(X, Y)) | (~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))) & ![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))) & ![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & ![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y))))) & ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y))))) & ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p6(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p6(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))) & ![Y: $i] : (p6(Y) | (~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : (p4(Y) | (~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))) | (~r1(X!0, Y))))),
% 1.35/1.68 inference(rewrite,[status(thm)],[])).
% 1.35/1.68 tff(4,plain,
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% 1.46/1.71 inference(rewrite,[status(thm)],[])).
% 1.46/1.71 tff(5,plain,
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p1(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p4(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p6(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p4(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p6(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p6(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p4(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p6(X) | (~r1(Y, X))) & (~p6(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p6(X) | (~r1(Y, X))) & (~p4(Y))))))))),
% 1.46/1.73 inference(rewrite,[status(thm)],[])).
% 1.46/1.73 tff(6,plain,
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% 1.46/1.75 inference(rewrite,[status(thm)],[])).
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p4(X)) & (~p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p6(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p4(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p6(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p4(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p6(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p6(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p4(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p6(X) | (~r1(Y, X))) & (~p6(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p6(X) | (~r1(Y, X))) & (~p4(Y))))))))))),
% 1.46/1.77 inference(monotonicity,[status(thm)],[6])).
% 1.46/1.77 tff(8,plain,
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$i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p4(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p6(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) & (~p5(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p5(X)) & (~p5(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p2(X)) & (~p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p2(X)) & (~p6(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p3(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p3(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p3(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p6(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p4(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p6(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p4(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p6(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p6(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p4(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p6(X) | (~r1(Y, X))) & (~p6(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p6(X) | (~r1(Y, X))) & (~p4(Y))))))))),
% 1.56/1.80 inference(transitivity,[status(thm)],[7, 5])).
% 1.56/1.80 tff(9,axiom,(~(~?[X: $i] : (~((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p6(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y)) & (~p6(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y)) & (~p4(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y)) & (~p2(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p6(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p4(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p2(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p6(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p4(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p2(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) & (~p6(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) & (~p2(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p5(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p5(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p5(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p6(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p2(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p3(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p2(X)) & (~p6(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p2(X)) & (~p2(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y)) & (~p6(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y)) & (~p4(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y)) & (~p2(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p5(X)) & (~p5(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) & (~p5(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p6(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p4(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p2(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) & (~p4(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p5(X)) & (~p3(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) & (~p3(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p6(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p4(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p2(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p5(X)) & (~p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) & (~p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) & (~p6(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) & (~p4(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p5(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p5(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p5(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p6(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p4(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p2(X)) & (~p6(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p2(X)) & (~p4(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : 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% 1.56/1.82 tff(11,plain,
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((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p2(X)) & (~p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p2(X)) & (~p6(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p3(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p3(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p3(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p6(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p5(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p5(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p5(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p5(X)) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p4(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p6(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) & (~p3(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p5(X)) & (~p3(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) & (~p4(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p4(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p6(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) & (~p5(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p5(X)) & (~p5(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p2(X)) & (~p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p2(X)) & (~p6(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p3(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p3(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p3(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p2(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) & (~p6(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) & (~p5(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p4(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) & (~p6(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p4(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) & (~p6(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p6(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p4(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p6(Y) | (~r1(X, Y))) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p6(X) | (~r1(Y, X))) & (~p6(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p6(X) | (~r1(Y, X))) & (~p4(Y))))))))),
% 1.56/1.83 inference(modus_ponens,[status(thm)],[10, 4])).
% 1.56/1.83 tff(12,plain,
% 1.56/1.83 (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p6(Y) | (~r1(X, Y))))))) & (~((~r1(X!0, Y!3)) | p5(Y!3))) & (~((~r1(X!0, Y!4)) | p3(Y!4))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))))) & (~((~r1(X!0, Y!6)) | p1(Y!6))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p6(Y) | (~r1(X, Y)) | (~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))) & ![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))) & ![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & ![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y))))) & ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y))))) & ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p3(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p6(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p2(tptp_fun_X_14(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p6(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p4(tptp_fun_X_15(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p1(tptp_fun_Y_10(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~((~r1(X, tptp_fun_Y_13(X))) | p5(tptp_fun_Y_13(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_16(X))) | p2(tptp_fun_Y_16(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p6(X) | (~r1(Y, X)) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p6(tptp_fun_Y_5(X)) | (~r1(X, tptp_fun_Y_5(X))))))) & ![Y: $i] : (p6(Y) | (~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : (p4(Y) | (~(p6(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))) | (~r1(X!0, Y)))),
% 1.56/1.84 inference(modus_ponens,[status(thm)],[11, 3])).
% 1.56/1.84 tff(13,plain,
% 1.56/1.84 (![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))),
% 1.56/1.84 inference(and_elim,[status(thm)],[12])).
% 1.56/1.84 tff(14,plain,
% 1.56/1.84 (![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))),
% 1.56/1.84 inference(modus_ponens,[status(thm)],[13, 2])).
% 1.56/1.84 tff(15,plain,
% 1.56/1.84 (~((~r1(X!0, Y!2)) | p2(Y!2))),
% 1.56/1.84 inference(and_elim,[status(thm)],[12])).
% 1.56/1.84 tff(16,plain,
% 1.56/1.84 (~p2(Y!2)),
% 1.56/1.84 inference(or_elim,[status(thm)],[15])).
% 1.56/1.84 tff(17,plain,
% 1.56/1.84 (r1(X!0, Y!2)),
% 1.56/1.84 inference(or_elim,[status(thm)],[15])).
% 1.56/1.84 tff(18,plain,
% 1.56/1.84 (((~![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))) | ((~r1(X!0, Y!2)) | p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))))) <=> ((~![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))) | (~r1(X!0, Y!2)) | p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))))),
% 1.56/1.85 inference(rewrite,[status(thm)],[])).
% 1.56/1.85 tff(19,plain,
% 1.56/1.85 ((p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))) | (~r1(X!0, Y!2))) <=> ((~r1(X!0, Y!2)) | p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))))),
% 1.56/1.85 inference(rewrite,[status(thm)],[])).
% 1.56/1.85 tff(20,plain,
% 1.56/1.85 ((~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))) <=> (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2))))),
% 1.56/1.85 inference(rewrite,[status(thm)],[])).
% 1.56/1.85 tff(21,plain,
% 1.56/1.85 ((p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))) | (~r1(X!0, Y!2))) <=> (p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))) | (~r1(X!0, Y!2)))),
% 1.56/1.85 inference(monotonicity,[status(thm)],[20])).
% 1.56/1.85 tff(22,plain,
% 1.56/1.85 ((p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))) | (~r1(X!0, Y!2))) <=> ((~r1(X!0, Y!2)) | p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))))),
% 1.56/1.85 inference(transitivity,[status(thm)],[21, 19])).
% 1.56/1.85 tff(23,plain,
% 1.56/1.85 (((~![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))) | (p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))) | (~r1(X!0, Y!2)))) <=> ((~![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))) | ((~r1(X!0, Y!2)) | p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2))))))),
% 1.56/1.85 inference(monotonicity,[status(thm)],[22])).
% 1.56/1.85 tff(24,plain,
% 1.56/1.85 (((~![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))) | (p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))) | (~r1(X!0, Y!2)))) <=> ((~![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))) | (~r1(X!0, Y!2)) | p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))))),
% 1.56/1.85 inference(transitivity,[status(thm)],[23, 18])).
% 1.56/1.85 tff(25,plain,
% 1.56/1.85 ((~![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))) | (p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))) | (~r1(X!0, Y!2)))),
% 1.56/1.85 inference(quant_inst,[status(thm)],[])).
% 1.56/1.85 tff(26,plain,
% 1.56/1.85 ((~![Y: $i] : (p2(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(X!0, Y)))) | (~r1(X!0, Y!2)) | p2(Y!2) | (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2))))),
% 1.56/1.85 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.56/1.85 tff(27,plain,
% 1.56/1.85 (~((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)))),
% 1.56/1.85 inference(unit_resolution,[status(thm)],[26, 17, 16, 14])).
% 1.56/1.85 tff(28,plain,
% 1.56/1.85 (((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2))) | r1(Y!2, tptp_fun_X_9(Y!2))),
% 1.56/1.85 inference(tautology,[status(thm)],[])).
% 1.56/1.85 tff(29,plain,
% 1.56/1.85 (r1(Y!2, tptp_fun_X_9(Y!2))),
% 1.56/1.85 inference(unit_resolution,[status(thm)],[28, 27])).
% 1.56/1.85 tff(30,plain,
% 1.56/1.85 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))))),
% 1.56/1.85 inference(bind,[status(th)],[])).
% 1.56/1.85 tff(31,plain,
% 1.56/1.85 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))),
% 1.56/1.85 inference(quant_intro,[status(thm)],[30])).
% 1.56/1.85 tff(32,plain,
% 1.56/1.85 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))))),
% 1.56/1.85 inference(bind,[status(th)],[])).
% 1.56/1.85 tff(33,plain,
% 1.56/1.85 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))),
% 1.56/1.85 inference(quant_intro,[status(thm)],[32])).
% 1.56/1.85 tff(34,plain,
% 1.56/1.85 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))),
% 1.56/1.85 inference(transitivity,[status(thm)],[33, 31])).
% 1.56/1.85 tff(35,plain,
% 1.56/1.85 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))),
% 1.56/1.85 inference(and_elim,[status(thm)],[12])).
% 1.56/1.85 tff(36,plain,
% 1.56/1.85 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))),
% 1.56/1.85 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.56/1.85 tff(37,plain,
% 1.56/1.85 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))),
% 1.56/1.85 inference(rewrite,[status(thm)],[])).
% 1.56/1.85 tff(38,plain,
% 1.56/1.85 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))),
% 1.56/1.85 inference(quant_inst,[status(thm)],[])).
% 1.56/1.85 tff(39,plain,
% 1.56/1.85 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))),
% 1.56/1.85 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.56/1.85 tff(40,plain,
% 1.56/1.85 (![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))),
% 1.56/1.85 inference(unit_resolution,[status(thm)],[39, 17, 36])).
% 1.56/1.85 tff(41,plain,
% 1.56/1.85 (((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y))))),
% 1.56/1.85 inference(rewrite,[status(thm)],[])).
% 1.56/1.85 tff(42,plain,
% 1.56/1.85 (((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))))) <=> ((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y))))),
% 1.56/1.85 inference(rewrite,[status(thm)],[])).
% 1.56/1.85 tff(43,plain,
% 1.56/1.85 (((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))))),
% 1.56/1.85 inference(monotonicity,[status(thm)],[42])).
% 1.56/1.85 tff(44,plain,
% 1.56/1.85 (((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y))))),
% 1.56/1.85 inference(transitivity,[status(thm)],[43, 41])).
% 1.56/1.85 tff(45,plain,
% 1.56/1.85 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))),
% 1.56/1.85 inference(quant_inst,[status(thm)],[])).
% 1.56/1.85 tff(46,plain,
% 1.56/1.85 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y))))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))),
% 1.56/1.85 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.56/1.85 tff(47,plain,
% 1.56/1.85 (![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))),
% 1.56/1.85 inference(unit_resolution,[status(thm)],[46, 40, 29])).
% 1.56/1.85 tff(48,plain,
% 1.56/1.85 (((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2))) | (~p1(tptp_fun_X_9(Y!2)))),
% 1.56/1.85 inference(tautology,[status(thm)],[])).
% 1.56/1.85 tff(49,plain,
% 1.56/1.85 (~p1(tptp_fun_X_9(Y!2))),
% 1.56/1.85 inference(unit_resolution,[status(thm)],[48, 27])).
% 1.56/1.85 tff(50,plain,
% 1.56/1.85 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))),
% 1.56/1.85 inference(bind,[status(th)],[])).
% 1.56/1.85 tff(51,plain,
% 1.56/1.85 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))),
% 1.56/1.85 inference(quant_intro,[status(thm)],[50])).
% 1.56/1.85 tff(52,plain,
% 1.56/1.85 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))),
% 1.56/1.85 inference(bind,[status(th)],[])).
% 1.56/1.85 tff(53,plain,
% 1.56/1.85 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))),
% 1.56/1.85 inference(quant_intro,[status(thm)],[52])).
% 1.56/1.85 tff(54,plain,
% 1.56/1.85 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))),
% 1.56/1.85 inference(transitivity,[status(thm)],[53, 51])).
% 1.56/1.85 tff(55,plain,
% 1.56/1.85 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))),
% 1.56/1.85 inference(and_elim,[status(thm)],[12])).
% 1.56/1.85 tff(56,plain,
% 1.56/1.85 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))),
% 1.56/1.85 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.56/1.85 tff(57,plain,
% 1.56/1.85 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | (~r1(X!0, Y!2)) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X))))),
% 1.56/1.86 inference(rewrite,[status(thm)],[])).
% 1.56/1.86 tff(58,plain,
% 1.56/1.86 (((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) <=> ((~r1(X!0, Y!2)) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X))))),
% 1.56/1.86 inference(rewrite,[status(thm)],[])).
% 1.56/1.86 tff(59,plain,
% 1.56/1.86 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))))),
% 1.56/1.86 inference(monotonicity,[status(thm)],[58])).
% 1.56/1.86 tff(60,plain,
% 1.56/1.86 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | (~r1(X!0, Y!2)) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X))))),
% 1.56/1.86 inference(transitivity,[status(thm)],[59, 57])).
% 1.56/1.86 tff(61,plain,
% 1.56/1.86 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))),
% 1.56/1.86 inference(quant_inst,[status(thm)],[])).
% 1.56/1.86 tff(62,plain,
% 1.56/1.86 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | (~r1(X!0, Y!2)) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))),
% 1.56/1.86 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.56/1.86 tff(63,plain,
% 1.56/1.86 (![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))),
% 1.56/1.86 inference(unit_resolution,[status(thm)],[62, 17, 56])).
% 1.56/1.86 tff(64,plain,
% 1.56/1.86 (((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) <=> ((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))) | (~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.56/1.86 inference(rewrite,[status(thm)],[])).
% 1.56/1.86 tff(65,plain,
% 1.56/1.86 ((p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(Y!2, tptp_fun_X_9(Y!2)))) <=> ((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.56/1.86 inference(rewrite,[status(thm)],[])).
% 1.56/1.86 tff(66,plain,
% 1.56/1.86 ((~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) <=> (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))),
% 1.56/1.86 inference(rewrite,[status(thm)],[])).
% 1.56/1.86 tff(67,plain,
% 1.56/1.86 ((p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(Y!2, tptp_fun_X_9(Y!2)))) <=> (p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))))),
% 1.56/1.86 inference(monotonicity,[status(thm)],[66])).
% 1.56/1.86 tff(68,plain,
% 1.56/1.86 ((p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(Y!2, tptp_fun_X_9(Y!2)))) <=> ((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.56/1.86 inference(transitivity,[status(thm)],[67, 65])).
% 1.56/1.86 tff(69,plain,
% 1.56/1.86 (((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))) | (p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))))) <=> ((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))),
% 1.56/1.86 inference(monotonicity,[status(thm)],[68])).
% 1.56/1.86 tff(70,plain,
% 1.56/1.86 (((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))) | (p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))))) <=> ((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))) | (~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.56/1.86 inference(transitivity,[status(thm)],[69, 64])).
% 1.56/1.86 tff(71,plain,
% 1.56/1.86 ((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))) | (p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))))),
% 1.56/1.86 inference(quant_inst,[status(thm)],[])).
% 1.56/1.86 tff(72,plain,
% 1.56/1.86 ((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(Y!2, X)))) | (~r1(Y!2, tptp_fun_X_9(Y!2))) | p1(tptp_fun_X_9(Y!2)) | (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))),
% 1.56/1.86 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.56/1.86 tff(73,plain,
% 1.56/1.86 (~((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))),
% 1.56/1.86 inference(unit_resolution,[status(thm)],[72, 63, 29, 49])).
% 1.56/1.86 tff(74,plain,
% 1.56/1.86 (((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))),
% 1.56/1.86 inference(tautology,[status(thm)],[])).
% 1.56/1.86 tff(75,plain,
% 1.56/1.86 (~p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))),
% 1.56/1.86 inference(unit_resolution,[status(thm)],[74, 73])).
% 1.56/1.86 tff(76,plain,
% 1.56/1.86 (((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))),
% 1.56/1.86 inference(tautology,[status(thm)],[])).
% 1.56/1.86 tff(77,plain,
% 1.56/1.86 (r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))),
% 1.56/1.86 inference(unit_resolution,[status(thm)],[76, 73])).
% 1.56/1.86 tff(78,plain,
% 1.56/1.86 (((~![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))) | ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))) <=> ((~![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))),
% 1.56/1.86 inference(rewrite,[status(thm)],[])).
% 1.56/1.86 tff(79,plain,
% 1.56/1.86 ((p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) <=> ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))),
% 1.56/1.87 inference(rewrite,[status(thm)],[])).
% 1.56/1.87 tff(80,plain,
% 1.56/1.87 ((~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) <=> (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.56/1.87 inference(rewrite,[status(thm)],[])).
% 1.56/1.87 tff(81,plain,
% 1.56/1.87 ((p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) <=> (p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))),
% 1.56/1.87 inference(monotonicity,[status(thm)],[80])).
% 1.56/1.87 tff(82,plain,
% 1.56/1.87 ((p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) <=> ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))),
% 1.56/1.87 inference(transitivity,[status(thm)],[81, 79])).
% 1.56/1.87 tff(83,plain,
% 1.56/1.87 (((~![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))) | (p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) <=> ((~![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))) | ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))))),
% 1.56/1.87 inference(monotonicity,[status(thm)],[82])).
% 1.56/1.87 tff(84,plain,
% 1.56/1.87 (((~![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))) | (p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) <=> ((~![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))),
% 1.56/1.87 inference(transitivity,[status(thm)],[83, 78])).
% 1.56/1.87 tff(85,plain,
% 1.56/1.87 ((~![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))) | (p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))),
% 1.56/1.87 inference(quant_inst,[status(thm)],[])).
% 1.56/1.87 tff(86,plain,
% 1.56/1.87 ((~![Y: $i] : (p4(Y) | (~((~r1(Y, tptp_fun_X_9(Y))) | p1(tptp_fun_X_9(Y)))) | (~r1(tptp_fun_X_9(Y!2), Y)))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(Y!2))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.56/1.87 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.56/1.87 tff(87,plain,
% 1.56/1.87 (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))),
% 1.56/1.87 inference(unit_resolution,[status(thm)],[86, 77, 75, 47])).
% 1.56/1.87 tff(88,plain,
% 1.56/1.87 (((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))),
% 1.56/1.87 inference(tautology,[status(thm)],[])).
% 1.56/1.87 tff(89,plain,
% 1.56/1.87 (r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))),
% 1.56/1.87 inference(unit_resolution,[status(thm)],[88, 87])).
% 1.56/1.87 tff(90,plain,
% 1.56/1.87 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))))),
% 1.56/1.87 inference(bind,[status(th)],[])).
% 1.56/1.87 tff(91,plain,
% 1.56/1.87 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))),
% 1.56/1.87 inference(quant_intro,[status(thm)],[90])).
% 1.56/1.87 tff(92,plain,
% 1.56/1.87 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))))),
% 1.56/1.87 inference(bind,[status(th)],[])).
% 1.56/1.87 tff(93,plain,
% 1.56/1.87 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))),
% 1.56/1.87 inference(quant_intro,[status(thm)],[92])).
% 1.56/1.87 tff(94,plain,
% 1.56/1.87 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))),
% 1.56/1.87 inference(transitivity,[status(thm)],[93, 91])).
% 1.56/1.87 tff(95,plain,
% 1.56/1.87 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))),
% 1.56/1.87 inference(and_elim,[status(thm)],[12])).
% 1.56/1.87 tff(96,plain,
% 1.56/1.87 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))),
% 1.56/1.87 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.56/1.87 tff(97,plain,
% 1.56/1.87 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))),
% 1.56/1.87 inference(rewrite,[status(thm)],[])).
% 1.56/1.87 tff(98,plain,
% 1.56/1.87 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))),
% 1.56/1.87 inference(quant_inst,[status(thm)],[])).
% 1.56/1.87 tff(99,plain,
% 1.56/1.87 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))),
% 1.56/1.88 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.56/1.88 tff(100,plain,
% 1.56/1.88 (![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))),
% 1.56/1.88 inference(unit_resolution,[status(thm)],[99, 17, 96])).
% 1.56/1.88 tff(101,plain,
% 1.56/1.88 (((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))),
% 1.56/1.88 inference(rewrite,[status(thm)],[])).
% 1.56/1.88 tff(102,plain,
% 1.56/1.88 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))),
% 1.56/1.88 inference(quant_inst,[status(thm)],[])).
% 1.56/1.88 tff(103,plain,
% 1.56/1.88 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))),
% 1.56/1.88 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.56/1.88 tff(104,plain,
% 1.56/1.88 (![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))),
% 1.56/1.88 inference(unit_resolution,[status(thm)],[103, 100, 29])).
% 1.56/1.88 tff(105,plain,
% 1.56/1.88 (((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))),
% 1.56/1.88 inference(rewrite,[status(thm)],[])).
% 1.56/1.88 tff(106,plain,
% 1.56/1.88 ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))),
% 1.56/1.88 inference(quant_inst,[status(thm)],[])).
% 1.56/1.88 tff(107,plain,
% 1.56/1.88 ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))),
% 1.56/1.88 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.56/1.88 tff(108,plain,
% 1.56/1.88 (![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))),
% 1.56/1.88 inference(unit_resolution,[status(thm)],[107, 77, 104])).
% 1.56/1.88 tff(109,plain,
% 1.56/1.88 (((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | ![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | ![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y))))),
% 1.56/1.88 inference(rewrite,[status(thm)],[])).
% 1.56/1.88 tff(110,plain,
% 1.56/1.88 (((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)) | p4(Y))) <=> ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | ![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y))))),
% 1.56/1.88 inference(rewrite,[status(thm)],[])).
% 1.56/1.88 tff(111,plain,
% 1.56/1.88 (((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)) | p4(Y)))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | ![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)))))),
% 1.56/1.88 inference(monotonicity,[status(thm)],[110])).
% 1.56/1.88 tff(112,plain,
% 1.56/1.88 (((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)) | p4(Y)))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | ![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y))))),
% 1.56/1.88 inference(transitivity,[status(thm)],[111, 109])).
% 1.56/1.88 tff(113,plain,
% 1.56/1.88 ((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)) | p4(Y)))),
% 1.56/1.88 inference(quant_inst,[status(thm)],[])).
% 1.56/1.88 tff(114,plain,
% 1.56/1.88 ((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | ![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)))),
% 1.56/1.88 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.56/1.88 tff(115,plain,
% 1.56/1.88 (![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)))),
% 1.56/1.88 inference(unit_resolution,[status(thm)],[114, 108, 89])).
% 1.56/1.88 tff(116,plain,
% 1.56/1.88 (((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))),
% 1.56/1.88 inference(tautology,[status(thm)],[])).
% 1.56/1.88 tff(117,plain,
% 1.56/1.88 (~p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))),
% 1.56/1.88 inference(unit_resolution,[status(thm)],[116, 87])).
% 1.56/1.88 tff(118,plain,
% 1.56/1.88 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))))),
% 1.56/1.88 inference(bind,[status(th)],[])).
% 1.56/1.88 tff(119,plain,
% 1.56/1.88 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))),
% 1.56/1.88 inference(quant_intro,[status(thm)],[118])).
% 1.56/1.88 tff(120,plain,
% 1.56/1.88 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))))),
% 1.56/1.88 inference(bind,[status(th)],[])).
% 1.56/1.88 tff(121,plain,
% 1.56/1.88 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))),
% 1.56/1.88 inference(quant_intro,[status(thm)],[120])).
% 1.56/1.88 tff(122,plain,
% 1.56/1.88 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))),
% 1.56/1.88 inference(transitivity,[status(thm)],[121, 119])).
% 1.56/1.88 tff(123,plain,
% 1.56/1.88 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))),
% 1.56/1.88 inference(and_elim,[status(thm)],[12])).
% 1.56/1.88 tff(124,plain,
% 1.56/1.88 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))),
% 1.56/1.88 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.56/1.88 tff(125,plain,
% 1.56/1.88 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))),
% 1.56/1.88 inference(rewrite,[status(thm)],[])).
% 1.56/1.88 tff(126,plain,
% 1.56/1.88 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))),
% 1.56/1.88 inference(quant_inst,[status(thm)],[])).
% 1.56/1.88 tff(127,plain,
% 1.56/1.88 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))),
% 1.56/1.88 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.56/1.88 tff(128,plain,
% 1.56/1.88 (![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))),
% 1.56/1.88 inference(unit_resolution,[status(thm)],[127, 17, 124])).
% 1.56/1.88 tff(129,plain,
% 1.56/1.88 (((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))),
% 1.56/1.88 inference(rewrite,[status(thm)],[])).
% 1.56/1.88 tff(130,plain,
% 1.56/1.88 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) | ((~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))),
% 1.56/1.88 inference(quant_inst,[status(thm)],[])).
% 1.56/1.88 tff(131,plain,
% 1.56/1.88 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))))) | (~r1(Y!2, tptp_fun_X_9(Y!2))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))),
% 1.56/1.89 inference(modus_ponens,[status(thm)],[130, 129])).
% 1.56/1.89 tff(132,plain,
% 1.56/1.89 (![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))),
% 1.56/1.89 inference(unit_resolution,[status(thm)],[131, 128, 29])).
% 1.56/1.89 tff(133,plain,
% 1.56/1.89 (((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X))))),
% 1.56/1.89 inference(rewrite,[status(thm)],[])).
% 1.56/1.89 tff(134,plain,
% 1.56/1.89 (((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))))) <=> ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X))))),
% 1.56/1.89 inference(rewrite,[status(thm)],[])).
% 1.56/1.89 tff(135,plain,
% 1.56/1.89 (((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))))),
% 1.56/1.89 inference(monotonicity,[status(thm)],[134])).
% 1.56/1.89 tff(136,plain,
% 1.56/1.89 (((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X))))),
% 1.56/1.89 inference(transitivity,[status(thm)],[135, 133])).
% 1.56/1.89 tff(137,plain,
% 1.56/1.89 ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | ((~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))),
% 1.56/1.89 inference(quant_inst,[status(thm)],[])).
% 1.56/1.89 tff(138,plain,
% 1.56/1.89 ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X))))))) | (~r1(tptp_fun_X_9(Y!2), tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | ![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))),
% 1.56/1.89 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.56/1.89 tff(139,plain,
% 1.56/1.89 (![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))),
% 1.56/1.89 inference(unit_resolution,[status(thm)],[138, 77, 132])).
% 1.56/1.89 tff(140,plain,
% 1.56/1.89 (((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))))) <=> ((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))))),
% 1.56/1.89 inference(rewrite,[status(thm)],[])).
% 1.56/1.89 tff(141,plain,
% 1.56/1.89 ((p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) <=> ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))))),
% 1.56/1.89 inference(rewrite,[status(thm)],[])).
% 1.56/1.89 tff(142,plain,
% 1.56/1.89 ((~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) <=> (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))),
% 1.56/1.89 inference(rewrite,[status(thm)],[])).
% 1.56/1.89 tff(143,plain,
% 1.56/1.89 ((p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) <=> (p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.56/1.89 inference(monotonicity,[status(thm)],[142])).
% 1.56/1.89 tff(144,plain,
% 1.56/1.89 ((p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) <=> ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))))),
% 1.56/1.89 inference(transitivity,[status(thm)],[143, 141])).
% 1.56/1.89 tff(145,plain,
% 1.56/1.89 (((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))) | (p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) <=> ((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))))),
% 1.56/1.89 inference(monotonicity,[status(thm)],[144])).
% 1.56/1.89 tff(146,plain,
% 1.56/1.89 (((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))) | (p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) <=> ((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))))),
% 1.56/1.89 inference(transitivity,[status(thm)],[145, 140])).
% 1.56/1.89 tff(147,plain,
% 1.56/1.89 ((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))) | (p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.56/1.89 inference(quant_inst,[status(thm)],[])).
% 1.56/1.89 tff(148,plain,
% 1.56/1.89 ((~![X: $i] : (p1(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p4(tptp_fun_Y_12(X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), X)))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!2)), tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | p1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))),
% 1.56/1.89 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.56/1.89 tff(149,plain,
% 1.56/1.89 (~((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.56/1.89 inference(unit_resolution,[status(thm)],[148, 139, 89, 117])).
% 1.56/1.89 tff(150,plain,
% 1.56/1.89 (((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | (~p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.56/1.89 inference(tautology,[status(thm)],[])).
% 1.56/1.89 tff(151,plain,
% 1.56/1.89 (~p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))),
% 1.56/1.89 inference(unit_resolution,[status(thm)],[150, 149])).
% 1.56/1.89 tff(152,plain,
% 1.56/1.89 (((~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))) | r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))),
% 1.56/1.89 inference(tautology,[status(thm)],[])).
% 1.56/1.89 tff(153,plain,
% 1.56/1.89 (r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))),
% 1.56/1.89 inference(unit_resolution,[status(thm)],[152, 149])).
% 1.56/1.89 tff(154,plain,
% 1.56/1.89 (((~![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)))) | (p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))) <=> ((~![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))),
% 1.66/1.92 inference(rewrite,[status(thm)],[])).
% 1.66/1.92 tff(155,plain,
% 1.66/1.92 ((~![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)))) | (p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2)))))))),
% 1.66/1.92 inference(quant_inst,[status(thm)],[])).
% 1.66/1.92 tff(156,plain,
% 1.66/1.92 ((~![Y: $i] : (p4(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), Y)))) | p4(tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))), tptp_fun_Y_12(tptp_fun_X_9(tptp_fun_Y_12(tptp_fun_X_9(Y!2))))))),
% 1.66/1.92 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.66/1.92 tff(157,plain,
% 1.66/1.92 ($false),
% 1.66/1.92 inference(unit_resolution,[status(thm)],[156, 153, 151, 115])).
% 1.66/1.92 % SZS output end Proof
% 1.66/1.92 % E exiting
%------------------------------------------------------------------------------