%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL682+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n027.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 03:00:38 PM UTC 2026
% Result : Theorem 2.97s 3.29s
% Output : Proof 3.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL682+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E %s %d THM
% 0.15/0.40 % Computer : n027.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 5 13:49:45 UTC 2026
% 0.15/0.41 % CPUTime :
% 2.97/3.29 % SZS status Theorem
% 2.97/3.29 % SZS output start Proof
% 2.97/3.29 tff(r1_type, type, (
% 2.97/3.29 r1: ( $i * $i ) > $o)).
% 2.97/3.29 tff(tptp_fun_Y_2_type, type, (
% 2.97/3.29 tptp_fun_Y_2: $i > $i)).
% 2.97/3.29 tff(tptp_fun_X_26_type, type, (
% 2.97/3.29 tptp_fun_X_26: $i > $i)).
% 2.97/3.29 tff(tptp_fun_Y_18_type, type, (
% 2.97/3.29 tptp_fun_Y_18: $i > $i)).
% 2.97/3.29 tff(tptp_fun_X_15_type, type, (
% 2.97/3.29 tptp_fun_X_15: $i > $i)).
% 2.97/3.29 tff(tptp_fun_X_10_type, type, (
% 2.97/3.29 tptp_fun_X_10: $i)).
% 2.97/3.29 tff(p54_type, type, (
% 2.97/3.29 p54: $i > $o)).
% 2.97/3.29 tff(p41_type, type, (
% 2.97/3.29 p41: $i > $o)).
% 2.97/3.29 tff(p34_type, type, (
% 2.97/3.29 p34: $i > $o)).
% 2.97/3.29 tff(tptp_fun_Y_9_type, type, (
% 2.97/3.29 tptp_fun_Y_9: $i)).
% 2.97/3.29 tff(p21_type, type, (
% 2.97/3.29 p21: $i > $o)).
% 2.97/3.29 tff(tptp_fun_X_0_type, type, (
% 2.97/3.29 tptp_fun_X_0: $i)).
% 2.97/3.29 tff(p12_type, type, (
% 2.97/3.29 p12: $i > $o)).
% 2.97/3.29 tff(p55_type, type, (
% 2.97/3.29 p55: $i > $o)).
% 2.97/3.29 tff(tptp_fun_Y_30_type, type, (
% 2.97/3.29 tptp_fun_Y_30: $i > $i)).
% 2.97/3.29 tff(p45_type, type, (
% 2.97/3.29 p45: $i > $o)).
% 2.97/3.29 tff(p53_type, type, (
% 2.97/3.29 p53: $i > $o)).
% 2.97/3.29 tff(tptp_fun_Y_29_type, type, (
% 2.97/3.29 tptp_fun_Y_29: $i > $i)).
% 2.97/3.29 tff(p51_type, type, (
% 2.97/3.29 p51: $i > $o)).
% 2.97/3.29 tff(tptp_fun_Y_28_type, type, (
% 2.97/3.29 tptp_fun_Y_28: $i > $i)).
% 2.97/3.29 tff(p44_type, type, (
% 2.97/3.29 p44: $i > $o)).
% 2.97/3.29 tff(tptp_fun_X_32_type, type, (
% 2.97/3.29 tptp_fun_X_32: $i > $i)).
% 2.97/3.29 tff(p36_type, type, (
% 2.97/3.29 p36: $i > $o)).
% 2.97/3.29 tff(p32_type, type, (
% 2.97/3.29 p32: $i > $o)).
% 2.97/3.29 tff(p43_type, type, (
% 2.97/3.29 p43: $i > $o)).
% 2.97/3.29 tff(p42_type, type, (
% 2.97/3.29 p42: $i > $o)).
% 2.97/3.29 tff(tptp_fun_X_31_type, type, (
% 2.97/3.29 tptp_fun_X_31: $i > $i)).
% 2.97/3.29 tff(tptp_fun_Y_27_type, type, (
% 2.97/3.29 tptp_fun_Y_27: $i > $i)).
% 2.97/3.29 tff(p26_type, type, (
% 2.97/3.29 p26: $i > $o)).
% 2.97/3.29 tff(p24_type, type, (
% 2.97/3.29 p24: $i > $o)).
% 2.97/3.29 tff(p22_type, type, (
% 2.97/3.29 p22: $i > $o)).
% 2.97/3.29 tff(tptp_fun_X_24_type, type, (
% 2.97/3.29 tptp_fun_X_24: $i > $i)).
% 2.97/3.29 tff(p35_type, type, (
% 2.97/3.29 p35: $i > $o)).
% 2.97/3.29 tff(tptp_fun_X_23_type, type, (
% 2.97/3.29 tptp_fun_X_23: $i > $i)).
% 2.97/3.29 tff(p33_type, type, (
% 2.97/3.29 p33: $i > $o)).
% 2.97/3.29 tff(tptp_fun_Y_25_type, type, (
% 2.97/3.29 tptp_fun_Y_25: $i > $i)).
% 2.97/3.29 tff(p31_type, type, (
% 2.97/3.29 p31: $i > $o)).
% 2.97/3.29 tff(tptp_fun_X_22_type, type, (
% 2.97/3.29 tptp_fun_X_22: $i > $i)).
% 2.97/3.29 tff(p16_type, type, (
% 2.97/3.29 p16: $i > $o)).
% 2.97/3.29 tff(p14_type, type, (
% 2.97/3.29 p14: $i > $o)).
% 2.97/3.29 tff(tptp_fun_Y_19_type, type, (
% 2.97/3.29 tptp_fun_Y_19: $i > $i)).
% 2.97/3.29 tff(p25_type, type, (
% 2.97/3.29 p25: $i > $o)).
% 2.97/3.29 tff(tptp_fun_Y_17_type, type, (
% 2.97/3.29 tptp_fun_Y_17: $i > $i)).
% 2.97/3.29 tff(tptp_fun_Y_16_type, type, (
% 2.97/3.29 tptp_fun_Y_16: $i > $i)).
% 2.97/3.29 tff(tptp_fun_X_21_type, type, (
% 2.97/3.29 tptp_fun_X_21: $i > $i)).
% 2.97/3.29 tff(p23_type, type, (
% 2.97/3.29 p23: $i > $o)).
% 2.97/3.29 tff(tptp_fun_X_20_type, type, (
% 2.97/3.29 tptp_fun_X_20: $i > $i)).
% 2.97/3.29 tff(tptp_fun_X_14_type, type, (
% 2.97/3.29 tptp_fun_X_14: $i > $i)).
% 2.97/3.29 tff(p15_type, type, (
% 2.97/3.29 p15: $i > $o)).
% 2.97/3.29 tff(tptp_fun_X_13_type, type, (
% 2.97/3.29 tptp_fun_X_13: $i > $i)).
% 2.97/3.29 tff(p13_type, type, (
% 2.97/3.29 p13: $i > $o)).
% 2.97/3.29 tff(p11_type, type, (
% 2.97/3.29 p11: $i > $o)).
% 2.97/3.29 tff(tptp_fun_X_12_type, type, (
% 2.97/3.29 tptp_fun_X_12: $i)).
% 2.97/3.29 tff(tptp_fun_Y_11_type, type, (
% 2.97/3.29 tptp_fun_Y_11: $i)).
% 2.97/3.29 tff(tptp_fun_X_8_type, type, (
% 2.97/3.29 tptp_fun_X_8: $i)).
% 2.97/3.29 tff(tptp_fun_Y_7_type, type, (
% 2.97/3.29 tptp_fun_Y_7: $i)).
% 2.97/3.29 tff(tptp_fun_X_6_type, type, (
% 2.97/3.29 tptp_fun_X_6: $i)).
% 2.97/3.29 tff(tptp_fun_Y_5_type, type, (
% 2.97/3.29 tptp_fun_Y_5: $i)).
% 2.97/3.29 tff(tptp_fun_X_4_type, type, (
% 2.97/3.29 tptp_fun_X_4: $i > $i)).
% 2.97/3.29 tff(p46_type, type, (
% 2.97/3.29 p46: $i > $o)).
% 2.97/3.29 tff(tptp_fun_Y_3_type, type, (
% 2.97/3.29 tptp_fun_Y_3: $i > $i)).
% 2.97/3.29 tff(p52_type, type, (
% 2.97/3.29 p52: $i > $o)).
% 2.97/3.29 tff(tptp_fun_Y_1_type, type, (
% 2.97/3.29 tptp_fun_Y_1: $i > $i)).
% 2.97/3.29 tff(p56_type, type, (
% 2.97/3.29 p56: $i > $o)).
% 2.97/3.29 tff(1,plain,
% 2.97/3.29 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p54(X) | (~r1(Y, X))) & ![X: $i] : (p56(X) | (~r1(Y, X))) & ![X: $i] : (p52(X) | (~r1(Y, X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & (r1(X!0, Y!5) & (~((~r1(Y!5, X!6)) | p13(X!6)))) & (r1(X!0, Y!7) & (~((~r1(Y!7, X!8)) | p11(X!8)))) & (r1(X!0, Y!9) & (~((~r1(Y!9, X!10)) | p12(X!10)))) & (r1(X!0, Y!11) & (~((~r1(Y!11, X!12)) | p15(X!12)))) & ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y))))) & ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p54(X) | (~r1(Y, X))) & ![X: $i] : (p56(X) | (~r1(Y, X))) & ![X: $i] : (p52(X) | (~r1(Y, X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & r1(X!0, Y!5) & (~((~r1(Y!5, X!6)) | p13(X!6))) & r1(X!0, Y!7) & (~((~r1(Y!7, X!8)) | p11(X!8))) & r1(X!0, Y!9) & (~((~r1(Y!9, X!10)) | p12(X!10))) & r1(X!0, Y!11) & (~((~r1(Y!11, X!12)) | p15(X!12))) & ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y))))) & ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))),
% 3.07/3.31 inference(rewrite,[status(thm)],[])).
% 3.07/3.31 tff(2,plain,
% 3.07/3.31 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p41(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))),
% 3.07/3.31 inference(bind,[status(th)],[])).
% 3.07/3.31 tff(3,plain,
% 3.07/3.31 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p41(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.07/3.31 inference(quant_intro,[status(thm)],[2])).
% 3.07/3.31 tff(4,plain,
% 3.07/3.31 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))) | p45(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))))),
% 3.07/3.31 inference(bind,[status(th)],[])).
% 3.07/3.31 tff(5,plain,
% 3.07/3.31 (![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_30(X))) | p55(tptp_fun_Y_30(X)))) | p45(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X))))))))),
% 3.07/3.31 inference(quant_intro,[status(thm)],[4])).
% 3.07/3.31 tff(6,plain,
% 3.07/3.31 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))) | p45(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))))),
% 3.07/3.31 inference(bind,[status(th)],[])).
% 3.07/3.31 tff(7,plain,
% 3.07/3.31 (![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_29(X))) | p53(tptp_fun_Y_29(X)))) | p45(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X))))))))),
% 3.07/3.31 inference(quant_intro,[status(thm)],[6])).
% 3.07/3.31 tff(8,plain,
% 3.07/3.31 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))) | p45(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(9,plain,
% 3.07/3.32 (![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_28(X))) | p51(tptp_fun_Y_28(X)))) | p45(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X))))))))),
% 3.07/3.32 inference(quant_intro,[status(thm)],[8])).
% 3.07/3.32 tff(10,plain,
% 3.07/3.32 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y)))) | p36(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(11,plain,
% 3.07/3.32 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y)))) | p36(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y)))))))),
% 3.07/3.32 inference(quant_intro,[status(thm)],[10])).
% 3.07/3.32 tff(12,plain,
% 3.07/3.32 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y)))) | p32(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(13,plain,
% 3.07/3.32 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y)))) | p32(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y)))))))),
% 3.07/3.32 inference(quant_intro,[status(thm)],[12])).
% 3.07/3.32 tff(14,plain,
% 3.07/3.32 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))) | p43(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(15,plain,
% 3.07/3.32 (![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_30(X))) | p55(tptp_fun_Y_30(X)))) | p43(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X))))))))),
% 3.07/3.32 inference(quant_intro,[status(thm)],[14])).
% 3.07/3.32 tff(16,plain,
% 3.07/3.32 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))) | p43(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(17,plain,
% 3.07/3.32 (![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_29(X))) | p53(tptp_fun_Y_29(X)))) | p43(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X))))))))),
% 3.07/3.32 inference(quant_intro,[status(thm)],[16])).
% 3.07/3.32 tff(18,plain,
% 3.07/3.32 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))) | p43(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(19,plain,
% 3.07/3.32 (![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_28(X))) | p51(tptp_fun_Y_28(X)))) | p43(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X))))))))),
% 3.07/3.32 inference(quant_intro,[status(thm)],[18])).
% 3.07/3.32 tff(20,plain,
% 3.07/3.32 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y)))) | p36(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(21,plain,
% 3.07/3.32 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y)))) | p36(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y)))))))),
% 3.07/3.32 inference(quant_intro,[status(thm)],[20])).
% 3.07/3.32 tff(22,plain,
% 3.07/3.32 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y)))) | p32(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(23,plain,
% 3.07/3.32 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y)))) | p32(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y)))))))),
% 3.07/3.32 inference(quant_intro,[status(thm)],[22])).
% 3.07/3.32 tff(24,plain,
% 3.07/3.32 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))) | p41(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(25,plain,
% 3.07/3.32 (![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_30(X))) | p55(tptp_fun_Y_30(X)))) | p41(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X))))))))),
% 3.07/3.32 inference(quant_intro,[status(thm)],[24])).
% 3.07/3.32 tff(26,plain,
% 3.07/3.32 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))) | p41(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(27,plain,
% 3.07/3.32 (![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_29(X))) | p53(tptp_fun_Y_29(X)))) | p41(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X))))))))),
% 3.07/3.32 inference(quant_intro,[status(thm)],[26])).
% 3.07/3.32 tff(28,plain,
% 3.07/3.32 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))) | p41(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))))),
% 3.07/3.32 inference(bind,[status(th)],[])).
% 3.07/3.32 tff(29,plain,
% 3.07/3.32 (![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_28(X))) | p51(tptp_fun_Y_28(X)))) | p41(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X))))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[28])).
% 3.07/3.33 tff(30,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p26(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(31,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p26(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[30])).
% 3.07/3.33 tff(32,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p24(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(33,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p24(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[32])).
% 3.07/3.33 tff(34,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p22(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(35,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p22(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[34])).
% 3.07/3.33 tff(36,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p35(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(37,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p35(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[36])).
% 3.07/3.33 tff(38,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p35(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(39,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p35(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[38])).
% 3.07/3.33 tff(40,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p26(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(41,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p26(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[40])).
% 3.07/3.33 tff(42,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p24(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(43,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p24(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[42])).
% 3.07/3.33 tff(44,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p22(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(45,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p22(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[44])).
% 3.07/3.33 tff(46,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | p34(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(47,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | p34(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[46])).
% 3.07/3.33 tff(48,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p33(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(49,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p33(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[48])).
% 3.07/3.33 tff(50,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p33(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(51,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p33(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[50])).
% 3.07/3.33 tff(52,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p26(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(53,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p26(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[52])).
% 3.07/3.33 tff(54,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p24(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(55,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p24(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[54])).
% 3.07/3.33 tff(56,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p22(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(57,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p22(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[56])).
% 3.07/3.33 tff(58,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p31(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(59,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p31(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[58])).
% 3.07/3.33 tff(60,plain,
% 3.07/3.33 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p31(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))))),
% 3.07/3.33 inference(bind,[status(th)],[])).
% 3.07/3.33 tff(61,plain,
% 3.07/3.33 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p31(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))))))),
% 3.07/3.33 inference(quant_intro,[status(thm)],[60])).
% 3.07/3.33 tff(62,plain,
% 3.07/3.33 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) <=> (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))), (((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p16(Y)) <=> ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p16(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p16(Y)) <=> (p16(Y) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))), (((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p16(Y)) <=> (p16(Y) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p16(Y))) <=> ((~r1(X!0, Y)) | (p16(Y) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))))), rewrite(((~r1(X!0, Y)) | (p16(Y) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))) <=> (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p16(Y))) <=> (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(63,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p16(Y))) <=> ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[62])).
% 3.07/3.34 tff(64,plain,
% 3.07/3.34 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) <=> (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))), (((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p14(Y)) <=> ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p14(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p14(Y)) <=> (p14(Y) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))), (((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p14(Y)) <=> (p14(Y) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p14(Y))) <=> ((~r1(X!0, Y)) | (p14(Y) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))))), rewrite(((~r1(X!0, Y)) | (p14(Y) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p14(Y))) <=> (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(65,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p14(Y))) <=> ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[64])).
% 3.07/3.34 tff(66,plain,
% 3.07/3.34 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p25(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(67,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p25(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X))))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[66])).
% 3.07/3.34 tff(68,plain,
% 3.07/3.34 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p25(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(69,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p25(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X))))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[68])).
% 3.07/3.34 tff(70,plain,
% 3.07/3.34 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p25(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(71,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p25(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X))))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[70])).
% 3.07/3.34 tff(72,plain,
% 3.07/3.34 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) <=> (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))), (((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p16(Y)) <=> ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p16(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p16(Y)) <=> (p16(Y) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))), (((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p16(Y)) <=> (p16(Y) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p16(Y))) <=> ((~r1(X!0, Y)) | (p16(Y) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))))), rewrite(((~r1(X!0, Y)) | (p16(Y) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))) <=> (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p16(Y))) <=> (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(73,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p16(Y))) <=> ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[72])).
% 3.07/3.34 tff(74,plain,
% 3.07/3.34 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) <=> (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))), (((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p14(Y)) <=> ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p14(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p14(Y)) <=> (p14(Y) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))), (((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p14(Y)) <=> (p14(Y) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p14(Y))) <=> ((~r1(X!0, Y)) | (p14(Y) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))))), rewrite(((~r1(X!0, Y)) | (p14(Y) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p14(Y))) <=> (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(75,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p14(Y))) <=> ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[74])).
% 3.07/3.34 tff(76,plain,
% 3.07/3.34 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p23(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(77,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p23(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X))))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[76])).
% 3.07/3.34 tff(78,plain,
% 3.07/3.34 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p23(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(79,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p23(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X))))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[78])).
% 3.07/3.34 tff(80,plain,
% 3.07/3.34 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p23(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(81,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p23(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X))))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[80])).
% 3.07/3.34 tff(82,plain,
% 3.07/3.34 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) <=> (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))), (((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p16(Y)) <=> ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p16(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p16(Y)) <=> (p16(Y) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))), (((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p16(Y)) <=> (p16(Y) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p16(Y))) <=> ((~r1(X!0, Y)) | (p16(Y) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))))), rewrite(((~r1(X!0, Y)) | (p16(Y) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))) <=> (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p16(Y))) <=> (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(83,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p16(Y))) <=> ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[82])).
% 3.07/3.34 tff(84,plain,
% 3.07/3.34 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) <=> (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))), (((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p14(Y)) <=> ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p14(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p14(Y)) <=> (p14(Y) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))), (((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p14(Y)) <=> (p14(Y) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p14(Y))) <=> ((~r1(X!0, Y)) | (p14(Y) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))))), rewrite(((~r1(X!0, Y)) | (p14(Y) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p14(Y))) <=> (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(85,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p14(Y))) <=> ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[84])).
% 3.07/3.34 tff(86,plain,
% 3.07/3.34 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p21(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(87,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p21(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X))))))),
% 3.07/3.34 inference(quant_intro,[status(thm)],[86])).
% 3.07/3.34 tff(88,plain,
% 3.07/3.34 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p21(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))))),
% 3.07/3.34 inference(bind,[status(th)],[])).
% 3.07/3.34 tff(89,plain,
% 3.07/3.34 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p21(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.07/3.35 inference(quant_intro,[status(thm)],[88])).
% 3.07/3.35 tff(90,plain,
% 3.07/3.35 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p21(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))))),
% 3.07/3.35 inference(bind,[status(th)],[])).
% 3.07/3.35 tff(91,plain,
% 3.07/3.35 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p21(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X))))))),
% 3.07/3.35 inference(quant_intro,[status(thm)],[90])).
% 3.07/3.35 tff(92,plain,
% 3.07/3.35 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p21(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))))),
% 3.07/3.35 inference(bind,[status(th)],[])).
% 3.07/3.35 tff(93,plain,
% 3.07/3.35 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p21(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X))))))),
% 3.07/3.35 inference(quant_intro,[status(thm)],[92])).
% 3.07/3.35 tff(94,plain,
% 3.07/3.35 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) <=> (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))), (((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p15(Y)) <=> ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p15(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p15(Y)) <=> (p15(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))), (((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p15(Y)) <=> (p15(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p15(Y))) <=> ((~r1(X!0, Y)) | (p15(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))))), rewrite(((~r1(X!0, Y)) | (p15(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p15(Y))) <=> (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))))),
% 3.07/3.35 inference(bind,[status(th)],[])).
% 3.07/3.35 tff(95,plain,
% 3.07/3.35 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p15(Y))) <=> ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))),
% 3.07/3.35 inference(quant_intro,[status(thm)],[94])).
% 3.07/3.35 tff(96,plain,
% 3.07/3.35 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) <=> (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))), (((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p15(Y)) <=> ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p15(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p15(Y)) <=> (p15(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))), (((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p15(Y)) <=> (p15(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p15(Y))) <=> ((~r1(X!0, Y)) | (p15(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))))), rewrite(((~r1(X!0, Y)) | (p15(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p15(Y))) <=> (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))))),
% 3.07/3.35 inference(bind,[status(th)],[])).
% 3.07/3.35 tff(97,plain,
% 3.07/3.35 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p15(Y))) <=> ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))),
% 3.07/3.35 inference(quant_intro,[status(thm)],[96])).
% 3.07/3.35 tff(98,plain,
% 3.07/3.35 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) <=> (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))), (((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p13(Y)) <=> ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p13(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p13(Y)) <=> (p13(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))), (((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p13(Y)) <=> (p13(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p13(Y))) <=> ((~r1(X!0, Y)) | (p13(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))))), rewrite(((~r1(X!0, Y)) | (p13(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))) <=> (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p13(Y))) <=> (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))))),
% 3.07/3.35 inference(bind,[status(th)],[])).
% 3.07/3.35 tff(99,plain,
% 3.07/3.35 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p13(Y))) <=> ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))),
% 3.07/3.35 inference(quant_intro,[status(thm)],[98])).
% 3.07/3.35 tff(100,plain,
% 3.07/3.35 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) <=> (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))), (((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p13(Y)) <=> ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p13(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p13(Y)) <=> (p13(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))), (((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p13(Y)) <=> (p13(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p13(Y))) <=> ((~r1(X!0, Y)) | (p13(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))))), rewrite(((~r1(X!0, Y)) | (p13(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))) <=> (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p13(Y))) <=> (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))))),
% 3.07/3.35 inference(bind,[status(th)],[])).
% 3.07/3.35 tff(101,plain,
% 3.07/3.35 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p13(Y))) <=> ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))),
% 3.07/3.35 inference(quant_intro,[status(thm)],[100])).
% 3.07/3.35 tff(102,plain,
% 3.07/3.35 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))) <=> (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y))))), (((~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))) | p12(Y)) <=> ((~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))) | p12(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))) | p12(Y)) <=> (p12(Y) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))), (((~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))) | p12(Y)) <=> (p12(Y) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))) | p12(Y))) <=> ((~r1(X!0, Y)) | (p12(Y) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))))), rewrite(((~r1(X!0, Y)) | (p12(Y) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))) <=> (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))) | p12(Y))) <=> (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))))),
% 3.07/3.35 inference(bind,[status(th)],[])).
% 3.07/3.35 tff(103,plain,
% 3.07/3.35 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))) | p12(Y))) <=> ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))),
% 3.07/3.35 inference(quant_intro,[status(thm)],[102])).
% 3.07/3.35 tff(104,plain,
% 3.07/3.35 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) <=> (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))), (((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p11(Y)) <=> ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p11(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p11(Y)) <=> (p11(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))), (((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p11(Y)) <=> (p11(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p11(Y))) <=> ((~r1(X!0, Y)) | (p11(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))))), rewrite(((~r1(X!0, Y)) | (p11(Y) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p11(Y))) <=> (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))))),
% 3.07/3.35 inference(bind,[status(th)],[])).
% 3.07/3.35 tff(105,plain,
% 3.07/3.35 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p11(Y))) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))))),
% 3.07/3.35 inference(quant_intro,[status(thm)],[104])).
% 3.07/3.35 tff(106,plain,
% 3.07/3.35 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) <=> (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))), (((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p11(Y)) <=> ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p11(Y)))), rewrite(((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p11(Y)) <=> (p11(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))), (((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p11(Y)) <=> (p11(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p11(Y))) <=> ((~r1(X!0, Y)) | (p11(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))))), rewrite(((~r1(X!0, Y)) | (p11(Y) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))), (((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p11(Y))) <=> (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))))),
% 3.07/3.35 inference(bind,[status(th)],[])).
% 3.07/3.35 tff(107,plain,
% 3.07/3.35 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p11(Y))) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))))),
% 3.07/3.35 inference(quant_intro,[status(thm)],[106])).
% 3.07/3.35 tff(108,plain,
% 3.07/3.35 ((~((~r1(Y!11, X!12)) | p15(X!12))) <=> (~((~r1(Y!11, X!12)) | p15(X!12)))),
% 3.07/3.35 inference(rewrite,[status(thm)],[])).
% 3.07/3.35 tff(109,plain,
% 3.07/3.35 ((r1(X!0, Y!11) & (~((~r1(Y!11, X!12)) | p15(X!12)))) <=> (r1(X!0, Y!11) & (~((~r1(Y!11, X!12)) | p15(X!12))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[108])).
% 3.07/3.35 tff(110,plain,
% 3.07/3.35 ((~((~r1(Y!9, X!10)) | p12(X!10))) <=> (~((~r1(Y!9, X!10)) | p12(X!10)))),
% 3.07/3.35 inference(rewrite,[status(thm)],[])).
% 3.07/3.35 tff(111,plain,
% 3.07/3.35 ((r1(X!0, Y!9) & (~((~r1(Y!9, X!10)) | p12(X!10)))) <=> (r1(X!0, Y!9) & (~((~r1(Y!9, X!10)) | p12(X!10))))),
% 3.07/3.35 inference(monotonicity,[status(thm)],[110])).
% 3.07/3.36 tff(112,plain,
% 3.07/3.36 ((~((~r1(Y!7, X!8)) | p11(X!8))) <=> (~((~r1(Y!7, X!8)) | p11(X!8)))),
% 3.07/3.36 inference(rewrite,[status(thm)],[])).
% 3.07/3.36 tff(113,plain,
% 3.07/3.36 ((r1(X!0, Y!7) & (~((~r1(Y!7, X!8)) | p11(X!8)))) <=> (r1(X!0, Y!7) & (~((~r1(Y!7, X!8)) | p11(X!8))))),
% 3.07/3.36 inference(monotonicity,[status(thm)],[112])).
% 3.07/3.36 tff(114,plain,
% 3.07/3.36 ((~((~r1(Y!5, X!6)) | p13(X!6))) <=> (~((~r1(Y!5, X!6)) | p13(X!6)))),
% 3.07/3.36 inference(rewrite,[status(thm)],[])).
% 3.07/3.36 tff(115,plain,
% 3.07/3.36 ((r1(X!0, Y!5) & (~((~r1(Y!5, X!6)) | p13(X!6)))) <=> (r1(X!0, Y!5) & (~((~r1(Y!5, X!6)) | p13(X!6))))),
% 3.07/3.36 inference(monotonicity,[status(thm)],[114])).
% 3.07/3.36 tff(116,plain,
% 3.07/3.36 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))) | p32(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))))),
% 3.07/3.36 inference(bind,[status(th)],[])).
% 3.07/3.36 tff(117,plain,
% 3.07/3.36 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))) | p32(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 3.07/3.36 inference(quant_intro,[status(thm)],[116])).
% 3.07/3.36 tff(118,plain,
% 3.07/3.36 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))) | p36(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))))),
% 3.07/3.36 inference(bind,[status(th)],[])).
% 3.07/3.36 tff(119,plain,
% 3.07/3.36 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))) | p36(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))))))),
% 3.07/3.36 inference(quant_intro,[status(thm)],[118])).
% 3.07/3.36 tff(120,plain,
% 3.07/3.36 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p42(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))))),
% 3.07/3.36 inference(bind,[status(th)],[])).
% 3.07/3.36 tff(121,plain,
% 3.07/3.36 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p42(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))))),
% 3.07/3.36 inference(quant_intro,[status(thm)],[120])).
% 3.07/3.36 tff(122,plain,
% 3.07/3.36 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p44(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))))),
% 3.07/3.36 inference(bind,[status(th)],[])).
% 3.07/3.36 tff(123,plain,
% 3.07/3.36 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p44(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))))),
% 3.07/3.36 inference(quant_intro,[status(thm)],[122])).
% 3.07/3.36 tff(124,plain,
% 3.07/3.36 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p46(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))))),
% 3.07/3.36 inference(bind,[status(th)],[])).
% 3.07/3.36 tff(125,plain,
% 3.07/3.36 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p46(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X)))))))))),
% 3.07/3.36 inference(quant_intro,[status(thm)],[124])).
% 3.07/3.36 tff(126,plain,
% 3.07/3.36 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p42(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))),
% 3.07/3.36 inference(bind,[status(th)],[])).
% 3.07/3.36 tff(127,plain,
% 3.07/3.36 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p42(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.07/3.36 inference(quant_intro,[status(thm)],[126])).
% 3.07/3.36 tff(128,plain,
% 3.07/3.36 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p44(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))),
% 3.07/3.36 inference(bind,[status(th)],[])).
% 3.07/3.36 tff(129,plain,
% 3.07/3.36 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p44(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.07/3.36 inference(quant_intro,[status(thm)],[128])).
% 3.07/3.36 tff(130,plain,
% 3.07/3.36 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p46(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))),
% 3.07/3.36 inference(bind,[status(th)],[])).
% 3.07/3.36 tff(131,plain,
% 3.07/3.36 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p46(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.07/3.36 inference(quant_intro,[status(thm)],[130])).
% 3.07/3.36 tff(132,plain,
% 3.07/3.36 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p42(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 3.07/3.36 inference(bind,[status(th)],[])).
% 3.07/3.36 tff(133,plain,
% 3.07/3.36 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p42(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 3.07/3.36 inference(quant_intro,[status(thm)],[132])).
% 3.07/3.36 tff(134,plain,
% 3.07/3.36 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p44(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 3.07/3.37 inference(bind,[status(th)],[])).
% 3.07/3.37 tff(135,plain,
% 3.07/3.37 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p44(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 3.07/3.37 inference(quant_intro,[status(thm)],[134])).
% 3.07/3.37 tff(136,plain,
% 3.07/3.37 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p46(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 3.07/3.37 inference(bind,[status(th)],[])).
% 3.07/3.37 tff(137,plain,
% 3.07/3.37 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p46(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 3.07/3.37 inference(quant_intro,[status(thm)],[136])).
% 3.07/3.37 tff(138,plain,
% 3.07/3.37 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p54(X) | (~r1(Y, X))) & ![X: $i] : (p56(X) | (~r1(Y, X))) & ![X: $i] : (p52(X) | (~r1(Y, X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p46(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p44(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p42(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p46(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p44(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p42(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p46(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p44(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p42(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))) | p36(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))) | p32(Y))))) & (r1(X!0, Y!5) & (~((~r1(Y!5, X!6)) | p13(X!6)))) & (r1(X!0, Y!7) & (~((~r1(Y!7, X!8)) | p11(X!8)))) & (r1(X!0, Y!9) & (~((~r1(Y!9, X!10)) | p12(X!10)))) & (r1(X!0, Y!11) & (~((~r1(Y!11, X!12)) | p15(X!12)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p11(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p11(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))) | p12(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p13(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p13(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p15(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p15(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p21(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p21(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p21(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p21(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p14(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p16(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p23(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p23(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p23(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p14(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p16(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p25(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p25(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p25(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p14(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p16(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p31(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p31(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p22(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p24(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p26(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p33(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p33(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | p34(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p22(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p24(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p26(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p35(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p35(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p22(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p24(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p26(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_28(X))) | p51(tptp_fun_Y_28(X)))) | p41(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_29(X))) | p53(tptp_fun_Y_29(X)))) | p41(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_30(X))) | p55(tptp_fun_Y_30(X)))) | p41(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y)))) | p32(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y)))) | p36(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_28(X))) | p51(tptp_fun_Y_28(X)))) | p43(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_29(X))) | p53(tptp_fun_Y_29(X)))) | p43(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_30(X))) | p55(tptp_fun_Y_30(X)))) | p43(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y)))) | p32(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y)))) | p36(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_28(X))) | p51(tptp_fun_Y_28(X)))) | p45(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_29(X))) | p53(tptp_fun_Y_29(X)))) | p45(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_30(X))) | p55(tptp_fun_Y_30(X)))) | p45(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p41(X))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p54(X) | (~r1(Y, X))) & ![X: $i] : (p56(X) | (~r1(Y, X))) & ![X: $i] : (p52(X) | (~r1(Y, X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & (r1(X!0, Y!5) & (~((~r1(Y!5, X!6)) | p13(X!6)))) & (r1(X!0, Y!7) & (~((~r1(Y!7, X!8)) | p11(X!8)))) & (r1(X!0, Y!9) & (~((~r1(Y!9, X!10)) | p12(X!10)))) & (r1(X!0, Y!11) & (~((~r1(Y!11, X!12)) | p15(X!12)))) & ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y))))) & ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))),
% 3.07/3.39 inference(monotonicity,[status(thm)],[137, 135, 133, 131, 129, 127, 125, 123, 121, 119, 117, 115, 113, 111, 109, 107, 105, 103, 101, 99, 97, 95, 93, 91, 89, 87, 85, 83, 81, 79, 77, 75, 73, 71, 69, 67, 65, 63, 61, 59, 57, 55, 53, 51, 49, 47, 45, 43, 41, 39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3])).
% 3.07/3.39 tff(139,plain,
% 3.07/3.39 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p54(X) | (~r1(Y, X))) & ![X: $i] : (p56(X) | (~r1(Y, X))) & ![X: $i] : (p52(X) | (~r1(Y, X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p46(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p44(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | p42(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p46(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p44(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p42(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p46(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p44(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))) | p42(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))) | p36(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y))))) | p32(Y))))) & (r1(X!0, Y!5) & (~((~r1(Y!5, X!6)) | p13(X!6)))) & (r1(X!0, Y!7) & (~((~r1(Y!7, X!8)) | p11(X!8)))) & (r1(X!0, Y!9) & (~((~r1(Y!9, X!10)) | p12(X!10)))) & (r1(X!0, Y!11) & (~((~r1(Y!11, X!12)) | p15(X!12)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p11(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p11(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))) | p12(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p13(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p13(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y)))) | p15(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y)))) | p15(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p21(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p21(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p21(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p21(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p14(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y)))) | p16(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p23(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p23(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p23(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p14(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y)))) | p16(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))) | p25(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))) | p25(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))) | p25(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p14(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y)))) | p16(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p31(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p31(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p22(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p24(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))) | p26(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p33(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p33(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | p34(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p22(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p24(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))) | p26(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y)))) | p35(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y)))) | p35(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p22(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p24(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))) | p26(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_28(X))) | p51(tptp_fun_Y_28(X)))) | p41(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_29(X))) | p53(tptp_fun_Y_29(X)))) | p41(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_30(X))) | p55(tptp_fun_Y_30(X)))) | p41(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y)))) | p32(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y)))) | p36(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_28(X))) | p51(tptp_fun_Y_28(X)))) | p43(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_29(X))) | p53(tptp_fun_Y_29(X)))) | p43(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_30(X))) | p55(tptp_fun_Y_30(X)))) | p43(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y)))) | p32(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y)))) | p36(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_28(X))) | p51(tptp_fun_Y_28(X)))) | p45(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_29(X))) | p53(tptp_fun_Y_29(X)))) | p45(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_30(X))) | p55(tptp_fun_Y_30(X)))) | p45(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | p41(X))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p54(X) | (~r1(Y, X))) & ![X: $i] : (p56(X) | (~r1(Y, X))) & ![X: $i] : (p52(X) | (~r1(Y, X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & r1(X!0, Y!5) & (~((~r1(Y!5, X!6)) | p13(X!6))) & r1(X!0, Y!7) & (~((~r1(Y!7, X!8)) | p11(X!8))) & r1(X!0, Y!9) & (~((~r1(Y!9, X!10)) | p12(X!10))) & r1(X!0, Y!11) & (~((~r1(Y!11, X!12)) | p15(X!12))) & ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y))))) & ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))),
% 3.17/3.42 inference(transitivity,[status(thm)],[138, 1])).
% 3.17/3.42 tff(140,plain,
% 3.17/3.42 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p56(Y) | (~r1(X, Y))) & (~p46(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p56(Y) | (~r1(X, Y))) & (~p44(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p56(Y) | (~r1(X, Y))) & (~p42(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p54(Y) | (~r1(X, Y))) & (~p46(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p54(Y) | (~r1(X, Y))) & (~p44(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p54(Y) | (~r1(X, Y))) & (~p42(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p52(Y) | (~r1(X, Y))) & (~p46(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p52(Y) | (~r1(X, Y))) & (~p44(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p52(Y) | (~r1(X, Y))) & (~p42(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p46(X) | (~r1(Y, X))) & (~p36(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p46(X) | (~r1(Y, X))) & (~p32(Y)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p13(X))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p11(X))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p12(X))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p15(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p23(X)) & (~p11(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p25(X)) & (~p11(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p21(X)) & (~p12(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p23(X)) & (~p13(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p25(X)) & (~p13(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p23(X)) & (~p15(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p25(X)) & (~p15(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p31(Y)) & (~p21(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p33(Y)) & (~p21(X))))))) | (~![Y: $i] : 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(p54(Y) | (~r1(X, Y))) & (~p41(X)))))))))))),
% 3.17/3.44 inference(rewrite,[status(thm)],[])).
% 3.17/3.44 tff(142,plain,
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% 3.17/3.46 inference(rewrite,[status(thm)],[])).
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((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p41(X)) & (~p34(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p22(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p24(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p26(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p43(X)) & (~p35(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p45(X)) & (~p35(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p22(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p24(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p26(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)) | p51(Y)) & (~p41(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)) | p53(Y)) & (~p41(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)) | p55(Y)) & (~p41(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p42(X)) & (~p32(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p42(X)) & (~p36(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)) | p51(Y)) & (~p43(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)) | p53(Y)) & (~p43(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)) | p55(Y)) & (~p43(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p44(X)) & (~p32(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p44(X)) & (~p36(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)) | p51(Y)) & (~p45(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)) | p53(Y)) & (~p45(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : 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% 3.17/3.47 inference(monotonicity,[status(thm)],[142])).
% 3.17/3.47 tff(144,plain,
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(~(![X: $i] : ((~r1(Y, X)) | p26(X)) & (~p16(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p43(X)) & (~p31(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p45(X)) & (~p31(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p32(Y)) & (~p22(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p32(Y)) & (~p24(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p32(Y)) & (~p26(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p43(X)) & (~p33(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p45(X)) & (~p33(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p41(X)) & (~p34(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p22(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p24(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p26(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p43(X)) & (~p35(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p45(X)) & (~p35(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p22(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p24(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p26(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)) | p51(Y)) & (~p41(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)) | p53(Y)) & (~p41(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)) | p55(Y)) & (~p41(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p42(X)) & (~p32(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p42(X)) & (~p36(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)) | p51(Y)) & (~p43(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)) | p53(Y)) & (~p43(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)) | p55(Y)) & (~p43(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p44(X)) & (~p32(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p44(X)) & (~p36(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)) | p51(Y)) & (~p45(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)) | p53(Y)) & (~p45(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)) | p55(Y)) & (~p45(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p54(Y) | (~r1(X, Y))) & (~p41(X)))))))))))),
% 3.17/3.48 inference(transitivity,[status(thm)],[143, 141])).
% 3.17/3.48 tff(145,axiom,(~(~?[X: $i] : (~(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | (~((((~![X: $i] : ((~r1(Y, X)) | p56(X))) | (~![X: $i] : ((~r1(Y, X)) | p54(X)))) | (~![X: $i] : ((~r1(Y, X)) | p54(X)))) | (~![X: $i] : ((~r1(Y, X)) | p52(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)) | p56(Y)) & (~p46(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)) | p56(Y)) & (~p44(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)) | p56(Y)) & (~p42(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)) | p54(Y)) & (~p46(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)) | p54(Y)) & (~p44(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)) | p54(Y)) & (~p42(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)) | p52(Y)) & (~p46(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)) | p52(Y)) & (~p44(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)) | p52(Y)) & (~p42(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p46(X)) & (~p36(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p46(X)) & (~p32(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)) | p55(Y)) & (~p45(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)) | p53(Y)) & (~p45(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)) | p51(Y)) & (~p45(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p44(X)) & (~p36(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p44(X)) & (~p32(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)) | p55(Y)) & (~p43(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)) | p53(Y)) & (~p43(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)) | p51(Y)) & (~p43(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p42(X)) & (~p36(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p42(X)) & (~p32(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)) | p55(Y)) & (~p41(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)) | p54(Y)) & (~p41(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)) | p53(Y)) & (~p41(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)) | p51(Y)) & (~p41(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p26(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p24(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p22(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p45(X)) & (~p35(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p43(X)) & (~p35(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p26(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p24(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p22(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p41(X)) & (~p34(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p45(X)) & (~p33(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p43(X)) & (~p33(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p32(Y)) & (~p26(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p32(Y)) & (~p24(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p32(Y)) & (~p22(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p45(X)) & (~p31(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p43(X)) & (~p31(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p26(X)) & (~p16(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p26(X)) & (~p14(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p35(Y)) & (~p25(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p33(Y)) & (~p25(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p31(Y)) & (~p25(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p24(X)) & (~p16(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p24(X)) & (~p14(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : 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% 3.17/3.49 tff(146,plain,
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% 3.17/3.49 tff(147,plain,
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(~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p54(Y) | (~r1(X, Y))) & (~p42(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p52(Y) | (~r1(X, Y))) & (~p46(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p52(Y) | (~r1(X, Y))) & (~p44(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p52(Y) | (~r1(X, Y))) & (~p42(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p46(X) | (~r1(Y, X))) & (~p36(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : (p46(X) | (~r1(Y, X))) & (~p32(Y)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p13(X))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p11(X))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p12(X))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p15(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p23(X)) & (~p11(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p25(X)) & (~p11(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p21(X)) & (~p12(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p23(X)) & (~p13(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p25(X)) & (~p13(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p23(X)) & (~p15(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p25(X)) & (~p15(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p31(Y)) & (~p21(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p33(Y)) & (~p21(X))))))) | (~![Y: $i] : 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Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p33(Y)) & (~p25(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p35(Y)) & (~p25(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p26(X)) & (~p14(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p26(X)) & (~p16(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p43(X)) & (~p31(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p45(X)) & (~p31(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p32(Y)) & (~p22(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p32(Y)) & (~p24(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p32(Y)) & (~p26(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p43(X)) & (~p33(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p45(X)) & (~p33(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p41(X)) & (~p34(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p22(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p24(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p26(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p43(X)) & (~p35(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p45(X)) & (~p35(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p22(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p24(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p36(Y)) & (~p26(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)) | p51(Y)) & (~p41(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)) | p53(Y)) & (~p41(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)) | p55(Y)) & (~p41(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p42(X)) & (~p32(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p42(X)) & (~p36(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)) | p51(Y)) & (~p43(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)) | p53(Y)) & (~p43(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)) | p55(Y)) & (~p43(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p44(X)) & (~p32(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p44(X)) & (~p36(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)) | p51(Y)) & (~p45(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)) | p53(Y)) & (~p45(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)) | p55(Y)) & (~p45(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : (p54(Y) | (~r1(X, Y))) & (~p41(X)))))))))))),
% 3.27/3.50 inference(modus_ponens,[status(thm)],[146, 140])).
% 3.27/3.50 tff(148,plain,
% 3.27/3.50 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p54(X) | (~r1(Y, X))) & ![X: $i] : (p56(X) | (~r1(Y, X))) & ![X: $i] : (p52(X) | (~r1(Y, X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p56(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p46(X) | (~r1(Y, X)) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~(p52(tptp_fun_Y_3(X)) | (~r1(X, tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~(p46(tptp_fun_X_4(Y)) | (~r1(Y, tptp_fun_X_4(Y)))))))) & r1(X!0, Y!5) & (~((~r1(Y!5, X!6)) | p13(X!6))) & r1(X!0, Y!7) & (~((~r1(Y!7, X!8)) | p11(X!8))) & r1(X!0, Y!9) & (~((~r1(Y!9, X!10)) | p12(X!10))) & r1(X!0, Y!11) & (~((~r1(Y!11, X!12)) | p15(X!12))) & ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y))))) & ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p23(tptp_fun_X_13(Y))))) & ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p25(tptp_fun_X_14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p22(tptp_fun_X_20(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_21(Y))) | p24(tptp_fun_X_21(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_16(X))) | p31(tptp_fun_Y_16(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_17(X))) | p33(tptp_fun_Y_17(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_19(X))) | p35(tptp_fun_Y_19(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_22(Y))) | p26(tptp_fun_X_22(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_25(X))) | p32(tptp_fun_Y_25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_23(Y))) | p43(tptp_fun_X_23(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_24(Y))) | p45(tptp_fun_X_24(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_27(X))) | p36(tptp_fun_Y_27(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_31(Y))) | p42(tptp_fun_X_31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p43(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_32(Y))) | p44(tptp_fun_X_32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p51(tptp_fun_Y_28(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_29(X))) | p53(tptp_fun_Y_29(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p45(X) | (~((~r1(X, tptp_fun_Y_30(X))) | p55(tptp_fun_Y_30(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.27/3.52 inference(modus_ponens,[status(thm)],[147, 139])).
% 3.27/3.52 tff(149,plain,
% 3.27/3.52 (~((~r1(Y!9, X!10)) | p12(X!10))),
% 3.27/3.52 inference(and_elim,[status(thm)],[148])).
% 3.27/3.52 tff(150,plain,
% 3.27/3.52 (r1(Y!9, X!10)),
% 3.27/3.52 inference(or_elim,[status(thm)],[149])).
% 3.27/3.52 tff(151,plain,
% 3.27/3.52 (r1(X!0, Y!9)),
% 3.27/3.52 inference(and_elim,[status(thm)],[148])).
% 3.27/3.52 tff(152,plain,
% 3.27/3.52 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 3.27/3.52 inference(rewrite,[status(thm)],[])).
% 3.27/3.52 tff(153,plain,
% 3.27/3.52 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(X, Y) & r1(Y, Z)) <=> (~((~r1(Y, Z)) | (~r1(X, Y))))), ((~(r1(X, Y) & r1(Y, Z))) <=> (~(~((~r1(Y, Z)) | (~r1(X, Y))))))), rewrite((~(~((~r1(Y, Z)) | (~r1(X, Y))))) <=> ((~r1(Y, Z)) | (~r1(X, Y)))), ((~(r1(X, Y) & r1(Y, Z))) <=> ((~r1(Y, Z)) | (~r1(X, Y))))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)))), rewrite((((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))))),
% 3.27/3.52 inference(bind,[status(th)],[])).
% 3.27/3.52 tff(154,plain,
% 3.27/3.52 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 3.27/3.52 inference(quant_intro,[status(thm)],[153])).
% 3.27/3.52 tff(155,plain,
% 3.27/3.52 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 3.27/3.52 inference(rewrite,[status(thm)],[])).
% 3.27/3.52 tff(156,plain,
% 3.27/3.52 (^[X: $i, Y: $i, Z: $i] : rewrite(((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)))),
% 3.27/3.52 inference(bind,[status(th)],[])).
% 3.27/3.52 tff(157,plain,
% 3.27/3.52 (![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 3.27/3.52 inference(quant_intro,[status(thm)],[156])).
% 3.27/3.52 tff(158,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity')).
% 3.27/3.52 tff(159,plain,
% 3.27/3.52 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 3.27/3.52 inference(modus_ponens,[status(thm)],[158, 157])).
% 3.27/3.52 tff(160,plain,
% 3.27/3.52 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 3.27/3.52 inference(modus_ponens,[status(thm)],[159, 155])).
% 3.27/3.52 tff(161,plain,(
% 3.27/3.52 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 3.27/3.52 inference(skolemize,[status(sab)],[160])).
% 3.27/3.52 tff(162,plain,
% 3.27/3.52 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 3.27/3.52 inference(modus_ponens,[status(thm)],[161, 154])).
% 3.27/3.52 tff(163,plain,
% 3.27/3.52 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 3.27/3.52 inference(modus_ponens,[status(thm)],[162, 152])).
% 3.27/3.52 tff(164,plain,
% 3.27/3.52 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!9)) | (~r1(Y!9, X!10)) | r1(X!0, X!10))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!9)) | (~r1(Y!9, X!10)) | r1(X!0, X!10))),
% 3.27/3.52 inference(rewrite,[status(thm)],[])).
% 3.27/3.52 tff(165,plain,
% 3.27/3.52 ((r1(X!0, X!10) | (~r1(Y!9, X!10)) | (~r1(X!0, Y!9))) <=> ((~r1(X!0, Y!9)) | (~r1(Y!9, X!10)) | r1(X!0, X!10))),
% 3.27/3.52 inference(rewrite,[status(thm)],[])).
% 3.27/3.52 tff(166,plain,
% 3.27/3.52 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!10) | (~r1(Y!9, X!10)) | (~r1(X!0, Y!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!9)) | (~r1(Y!9, X!10)) | r1(X!0, X!10)))),
% 3.27/3.52 inference(monotonicity,[status(thm)],[165])).
% 3.27/3.52 tff(167,plain,
% 3.27/3.52 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!10) | (~r1(Y!9, X!10)) | (~r1(X!0, Y!9)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!9)) | (~r1(Y!9, X!10)) | r1(X!0, X!10))),
% 3.27/3.52 inference(transitivity,[status(thm)],[166, 164])).
% 3.27/3.52 tff(168,plain,
% 3.27/3.52 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!10) | (~r1(Y!9, X!10)) | (~r1(X!0, Y!9)))),
% 3.27/3.52 inference(quant_inst,[status(thm)],[])).
% 3.27/3.52 tff(169,plain,
% 3.27/3.52 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!9)) | (~r1(Y!9, X!10)) | r1(X!0, X!10)),
% 3.27/3.52 inference(modus_ponens,[status(thm)],[168, 167])).
% 3.27/3.52 tff(170,plain,
% 3.27/3.52 (r1(X!0, X!10)),
% 3.27/3.52 inference(unit_resolution,[status(thm)],[169, 163, 151, 150])).
% 3.27/3.52 tff(171,plain,
% 3.27/3.52 (^[Y: $i] : refl((p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y))))) <=> (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y))))))),
% 3.27/3.52 inference(bind,[status(th)],[])).
% 3.27/3.52 tff(172,plain,
% 3.27/3.52 (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y))))) <=> ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))),
% 3.27/3.52 inference(quant_intro,[status(thm)],[171])).
% 3.27/3.52 tff(173,plain,
% 3.27/3.52 (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))),
% 3.27/3.52 inference(and_elim,[status(thm)],[148])).
% 3.27/3.52 tff(174,plain,
% 3.27/3.52 (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))),
% 3.27/3.52 inference(modus_ponens,[status(thm)],[173, 172])).
% 3.27/3.52 tff(175,plain,
% 3.27/3.52 (~p12(X!10)),
% 3.27/3.52 inference(or_elim,[status(thm)],[149])).
% 3.27/3.52 tff(176,plain,
% 3.27/3.52 (((~![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))) | (p12(X!10) | (~r1(X!0, X!10)) | (~((~r1(X!10, tptp_fun_X_15(X!10))) | p21(tptp_fun_X_15(X!10)))))) <=> ((~![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))) | p12(X!10) | (~r1(X!0, X!10)) | (~((~r1(X!10, tptp_fun_X_15(X!10))) | p21(tptp_fun_X_15(X!10)))))),
% 3.27/3.52 inference(rewrite,[status(thm)],[])).
% 3.27/3.52 tff(177,plain,
% 3.27/3.52 ((~![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))) | (p12(X!10) | (~r1(X!0, X!10)) | (~((~r1(X!10, tptp_fun_X_15(X!10))) | p21(tptp_fun_X_15(X!10)))))),
% 3.27/3.52 inference(quant_inst,[status(thm)],[])).
% 3.27/3.52 tff(178,plain,
% 3.27/3.52 ((~![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p21(tptp_fun_X_15(Y)))))) | p12(X!10) | (~r1(X!0, X!10)) | (~((~r1(X!10, tptp_fun_X_15(X!10))) | p21(tptp_fun_X_15(X!10))))),
% 3.27/3.52 inference(modus_ponens,[status(thm)],[177, 176])).
% 3.27/3.52 tff(179,plain,
% 3.27/3.52 (~((~r1(X!10, tptp_fun_X_15(X!10))) | p21(tptp_fun_X_15(X!10)))),
% 3.27/3.52 inference(unit_resolution,[status(thm)],[178, 175, 174, 170])).
% 3.27/3.52 tff(180,plain,
% 3.27/3.52 (((~r1(X!10, tptp_fun_X_15(X!10))) | p21(tptp_fun_X_15(X!10))) | r1(X!10, tptp_fun_X_15(X!10))),
% 3.27/3.52 inference(tautology,[status(thm)],[])).
% 3.27/3.52 tff(181,plain,
% 3.27/3.52 (r1(X!10, tptp_fun_X_15(X!10))),
% 3.27/3.52 inference(unit_resolution,[status(thm)],[180, 179])).
% 3.27/3.52 tff(182,plain,
% 3.27/3.52 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!9, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(Y!9, tptp_fun_X_15(X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!9, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(Y!9, tptp_fun_X_15(X!10)))),
% 3.27/3.52 inference(rewrite,[status(thm)],[])).
% 3.27/3.52 tff(183,plain,
% 3.27/3.52 ((r1(Y!9, tptp_fun_X_15(X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(Y!9, X!10))) <=> ((~r1(Y!9, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(Y!9, tptp_fun_X_15(X!10)))),
% 3.27/3.52 inference(rewrite,[status(thm)],[])).
% 3.27/3.52 tff(184,plain,
% 3.27/3.52 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!9, tptp_fun_X_15(X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(Y!9, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!9, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(Y!9, tptp_fun_X_15(X!10))))),
% 3.27/3.52 inference(monotonicity,[status(thm)],[183])).
% 3.27/3.52 tff(185,plain,
% 3.27/3.52 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!9, tptp_fun_X_15(X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(Y!9, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!9, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(Y!9, tptp_fun_X_15(X!10)))),
% 3.27/3.53 inference(transitivity,[status(thm)],[184, 182])).
% 3.27/3.53 tff(186,plain,
% 3.27/3.53 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!9, tptp_fun_X_15(X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(Y!9, X!10)))),
% 3.27/3.53 inference(quant_inst,[status(thm)],[])).
% 3.27/3.53 tff(187,plain,
% 3.27/3.53 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!9, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(Y!9, tptp_fun_X_15(X!10))),
% 3.27/3.53 inference(modus_ponens,[status(thm)],[186, 185])).
% 3.27/3.53 tff(188,plain,
% 3.27/3.53 (r1(Y!9, tptp_fun_X_15(X!10))),
% 3.27/3.53 inference(unit_resolution,[status(thm)],[187, 163, 150, 181])).
% 3.27/3.53 tff(189,plain,
% 3.27/3.53 (((~r1(X!10, tptp_fun_X_15(X!10))) | p21(tptp_fun_X_15(X!10))) | (~p21(tptp_fun_X_15(X!10)))),
% 3.27/3.53 inference(tautology,[status(thm)],[])).
% 3.27/3.53 tff(190,plain,
% 3.27/3.53 (~p21(tptp_fun_X_15(X!10))),
% 3.27/3.53 inference(unit_resolution,[status(thm)],[189, 179])).
% 3.27/3.53 tff(191,plain,
% 3.27/3.53 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))))),
% 3.27/3.53 inference(bind,[status(th)],[])).
% 3.27/3.53 tff(192,plain,
% 3.27/3.53 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.27/3.53 inference(quant_intro,[status(thm)],[191])).
% 3.27/3.53 tff(193,plain,
% 3.27/3.53 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))))),
% 3.27/3.53 inference(bind,[status(th)],[])).
% 3.27/3.53 tff(194,plain,
% 3.27/3.53 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.27/3.53 inference(quant_intro,[status(thm)],[193])).
% 3.27/3.53 tff(195,plain,
% 3.27/3.53 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.27/3.53 inference(transitivity,[status(thm)],[194, 192])).
% 3.27/3.53 tff(196,plain,
% 3.27/3.53 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.27/3.53 inference(and_elim,[status(thm)],[148])).
% 3.27/3.53 tff(197,plain,
% 3.27/3.53 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.27/3.53 inference(modus_ponens,[status(thm)],[196, 195])).
% 3.27/3.53 tff(198,plain,
% 3.27/3.53 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) | ((~r1(X!0, Y!9)) | ![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) | (~r1(X!0, Y!9)) | ![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.27/3.53 inference(rewrite,[status(thm)],[])).
% 3.27/3.53 tff(199,plain,
% 3.27/3.53 (((~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) <=> ((~r1(X!0, Y!9)) | ![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.27/3.53 inference(rewrite,[status(thm)],[])).
% 3.27/3.53 tff(200,plain,
% 3.27/3.53 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) | ((~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) | ((~r1(X!0, Y!9)) | ![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))))),
% 3.27/3.53 inference(monotonicity,[status(thm)],[199])).
% 3.27/3.53 tff(201,plain,
% 3.27/3.53 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) | ((~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) | (~r1(X!0, Y!9)) | ![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.27/3.53 inference(transitivity,[status(thm)],[200, 198])).
% 3.27/3.53 tff(202,plain,
% 3.27/3.53 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) | ((~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))),
% 3.27/3.53 inference(quant_inst,[status(thm)],[])).
% 3.27/3.53 tff(203,plain,
% 3.27/3.53 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X))))))) | (~r1(X!0, Y!9)) | ![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))),
% 3.27/3.53 inference(modus_ponens,[status(thm)],[202, 201])).
% 3.27/3.53 tff(204,plain,
% 3.27/3.53 (![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))),
% 3.27/3.53 inference(unit_resolution,[status(thm)],[203, 151, 197])).
% 3.27/3.53 tff(205,plain,
% 3.27/3.53 (((~![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) | (p21(tptp_fun_X_15(X!10)) | (~r1(Y!9, tptp_fun_X_15(X!10))) | (~((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | p34(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))) <=> ((~![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) | p21(tptp_fun_X_15(X!10)) | (~r1(Y!9, tptp_fun_X_15(X!10))) | (~((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | p34(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.53 inference(rewrite,[status(thm)],[])).
% 3.27/3.53 tff(206,plain,
% 3.27/3.53 ((~![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) | (p21(tptp_fun_X_15(X!10)) | (~r1(Y!9, tptp_fun_X_15(X!10))) | (~((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | p34(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.53 inference(quant_inst,[status(thm)],[])).
% 3.27/3.53 tff(207,plain,
% 3.27/3.53 ((~![X: $i] : (p21(X) | (~r1(Y!9, X)) | (~((~r1(X, tptp_fun_Y_18(X))) | p34(tptp_fun_Y_18(X)))))) | p21(tptp_fun_X_15(X!10)) | (~r1(Y!9, tptp_fun_X_15(X!10))) | (~((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | p34(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.53 inference(modus_ponens,[status(thm)],[206, 205])).
% 3.27/3.53 tff(208,plain,
% 3.27/3.53 (~((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | p34(tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.53 inference(unit_resolution,[status(thm)],[207, 204, 190, 188])).
% 3.27/3.53 tff(209,plain,
% 3.27/3.53 (((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | p34(tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))),
% 3.27/3.53 inference(tautology,[status(thm)],[])).
% 3.27/3.53 tff(210,plain,
% 3.27/3.53 (r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))),
% 3.27/3.53 inference(unit_resolution,[status(thm)],[209, 208])).
% 3.27/3.53 tff(211,plain,
% 3.27/3.53 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.53 inference(rewrite,[status(thm)],[])).
% 3.27/3.53 tff(212,plain,
% 3.27/3.53 ((r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!10, tptp_fun_X_15(X!10)))) <=> ((~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.53 inference(rewrite,[status(thm)],[])).
% 3.27/3.53 tff(213,plain,
% 3.27/3.53 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!10, tptp_fun_X_15(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.53 inference(monotonicity,[status(thm)],[212])).
% 3.27/3.53 tff(214,plain,
% 3.27/3.53 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!10, tptp_fun_X_15(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.53 inference(transitivity,[status(thm)],[213, 211])).
% 3.27/3.53 tff(215,plain,
% 3.27/3.53 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!10, tptp_fun_X_15(X!10))))),
% 3.27/3.53 inference(quant_inst,[status(thm)],[])).
% 3.27/3.53 tff(216,plain,
% 3.27/3.53 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10)))),
% 3.27/3.53 inference(modus_ponens,[status(thm)],[215, 214])).
% 3.27/3.53 tff(217,plain,
% 3.27/3.53 (r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10)))),
% 3.27/3.53 inference(unit_resolution,[status(thm)],[216, 163, 181, 210])).
% 3.27/3.53 tff(218,plain,
% 3.27/3.53 (((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | p34(tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~p34(tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.53 inference(tautology,[status(thm)],[])).
% 3.27/3.53 tff(219,plain,
% 3.27/3.53 (~p34(tptp_fun_Y_18(tptp_fun_X_15(X!10)))),
% 3.27/3.53 inference(unit_resolution,[status(thm)],[218, 208])).
% 3.27/3.53 tff(220,plain,
% 3.27/3.53 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))))),
% 3.27/3.53 inference(bind,[status(th)],[])).
% 3.27/3.53 tff(221,plain,
% 3.27/3.53 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))),
% 3.27/3.53 inference(quant_intro,[status(thm)],[220])).
% 3.27/3.53 tff(222,plain,
% 3.27/3.53 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))))),
% 3.27/3.53 inference(bind,[status(th)],[])).
% 3.27/3.53 tff(223,plain,
% 3.27/3.53 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))),
% 3.27/3.53 inference(quant_intro,[status(thm)],[222])).
% 3.27/3.53 tff(224,plain,
% 3.27/3.53 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))),
% 3.27/3.53 inference(transitivity,[status(thm)],[223, 221])).
% 3.27/3.53 tff(225,plain,
% 3.27/3.53 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))),
% 3.27/3.54 inference(and_elim,[status(thm)],[148])).
% 3.27/3.54 tff(226,plain,
% 3.27/3.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))),
% 3.27/3.54 inference(modus_ponens,[status(thm)],[225, 224])).
% 3.27/3.54 tff(227,plain,
% 3.27/3.54 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))) | ((~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))) | (~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))),
% 3.27/3.54 inference(rewrite,[status(thm)],[])).
% 3.27/3.54 tff(228,plain,
% 3.27/3.54 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))) | ((~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))),
% 3.27/3.54 inference(quant_inst,[status(thm)],[])).
% 3.27/3.54 tff(229,plain,
% 3.27/3.54 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))))) | (~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))),
% 3.27/3.54 inference(modus_ponens,[status(thm)],[228, 227])).
% 3.27/3.54 tff(230,plain,
% 3.27/3.54 (![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))),
% 3.27/3.54 inference(unit_resolution,[status(thm)],[229, 151, 226])).
% 3.27/3.54 tff(231,plain,
% 3.27/3.54 (((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) | ((~r1(Y!9, X!10)) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y))))) <=> ((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) | (~r1(Y!9, X!10)) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y))))),
% 3.27/3.54 inference(rewrite,[status(thm)],[])).
% 3.27/3.54 tff(232,plain,
% 3.27/3.54 (((~r1(Y!9, X!10)) | ![Y: $i] : ((~r1(X!10, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))))) <=> ((~r1(Y!9, X!10)) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y))))),
% 3.27/3.54 inference(rewrite,[status(thm)],[])).
% 3.27/3.54 tff(233,plain,
% 3.27/3.54 (((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) | ((~r1(Y!9, X!10)) | ![Y: $i] : ((~r1(X!10, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) <=> ((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) | ((~r1(Y!9, X!10)) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y)))))),
% 3.27/3.54 inference(monotonicity,[status(thm)],[232])).
% 3.27/3.54 tff(234,plain,
% 3.27/3.54 (((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) | ((~r1(Y!9, X!10)) | ![Y: $i] : ((~r1(X!10, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) <=> ((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) | (~r1(Y!9, X!10)) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y))))),
% 3.27/3.54 inference(transitivity,[status(thm)],[233, 231])).
% 3.27/3.54 tff(235,plain,
% 3.27/3.54 ((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) | ((~r1(Y!9, X!10)) | ![Y: $i] : ((~r1(X!10, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))),
% 3.27/3.54 inference(quant_inst,[status(thm)],[])).
% 3.27/3.54 tff(236,plain,
% 3.27/3.54 ((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y))))))) | (~r1(Y!9, X!10)) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y)))),
% 3.27/3.54 inference(modus_ponens,[status(thm)],[235, 234])).
% 3.27/3.54 tff(237,plain,
% 3.27/3.54 (![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y)))),
% 3.27/3.54 inference(unit_resolution,[status(thm)],[236, 150, 230])).
% 3.27/3.54 tff(238,plain,
% 3.27/3.54 (((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y)))) | (p34(tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~((~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | (~r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) <=> ((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y)))) | p34(tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~((~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | (~r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.54 inference(rewrite,[status(thm)],[])).
% 3.27/3.54 tff(239,plain,
% 3.27/3.54 ((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y)))) | (p34(tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~((~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | (~r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.54 inference(quant_inst,[status(thm)],[])).
% 3.27/3.54 tff(240,plain,
% 3.27/3.54 ((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p41(tptp_fun_X_26(Y)))) | (~r1(X!10, Y)))) | p34(tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~((~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | (~r1(X!10, tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.54 inference(modus_ponens,[status(thm)],[239, 238])).
% 3.27/3.54 tff(241,plain,
% 3.27/3.54 (~((~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.54 inference(unit_resolution,[status(thm)],[240, 237, 219, 217])).
% 3.27/3.54 tff(242,plain,
% 3.27/3.54 (((~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.54 inference(tautology,[status(thm)],[])).
% 3.27/3.54 tff(243,plain,
% 3.27/3.54 (r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.54 inference(unit_resolution,[status(thm)],[242, 241])).
% 3.27/3.54 tff(244,plain,
% 3.27/3.54 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.54 inference(rewrite,[status(thm)],[])).
% 3.27/3.54 tff(245,plain,
% 3.27/3.54 ((r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10))))) <=> ((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.55 inference(rewrite,[status(thm)],[])).
% 3.27/3.55 tff(246,plain,
% 3.27/3.55 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.55 inference(monotonicity,[status(thm)],[245])).
% 3.27/3.55 tff(247,plain,
% 3.27/3.55 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.55 inference(transitivity,[status(thm)],[246, 244])).
% 3.27/3.55 tff(248,plain,
% 3.27/3.55 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.55 inference(quant_inst,[status(thm)],[])).
% 3.27/3.55 tff(249,plain,
% 3.27/3.55 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.55 inference(modus_ponens,[status(thm)],[248, 247])).
% 3.27/3.55 tff(250,plain,
% 3.27/3.55 (r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.55 inference(unit_resolution,[status(thm)],[249, 163, 210, 243])).
% 3.27/3.55 tff(251,plain,
% 3.27/3.55 (((~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.55 inference(tautology,[status(thm)],[])).
% 3.27/3.55 tff(252,plain,
% 3.27/3.55 (~p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.55 inference(unit_resolution,[status(thm)],[251, 241])).
% 3.27/3.55 tff(253,plain,
% 3.27/3.55 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))),
% 3.27/3.55 inference(bind,[status(th)],[])).
% 3.27/3.55 tff(254,plain,
% 3.27/3.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.27/3.55 inference(quant_intro,[status(thm)],[253])).
% 3.27/3.55 tff(255,plain,
% 3.27/3.55 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))),
% 3.27/3.55 inference(bind,[status(th)],[])).
% 3.27/3.55 tff(256,plain,
% 3.27/3.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.27/3.55 inference(quant_intro,[status(thm)],[255])).
% 3.27/3.55 tff(257,plain,
% 3.27/3.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.27/3.55 inference(transitivity,[status(thm)],[256, 254])).
% 3.27/3.55 tff(258,plain,
% 3.27/3.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.27/3.55 inference(and_elim,[status(thm)],[148])).
% 3.27/3.55 tff(259,plain,
% 3.27/3.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.27/3.55 inference(modus_ponens,[status(thm)],[258, 257])).
% 3.27/3.55 tff(260,plain,
% 3.27/3.55 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))) | ((~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))) | (~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.27/3.55 inference(rewrite,[status(thm)],[])).
% 3.27/3.55 tff(261,plain,
% 3.27/3.55 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))) | ((~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))),
% 3.27/3.55 inference(quant_inst,[status(thm)],[])).
% 3.27/3.55 tff(262,plain,
% 3.27/3.55 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))))) | (~r1(X!0, Y!9)) | ![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))),
% 3.27/3.55 inference(modus_ponens,[status(thm)],[261, 260])).
% 3.27/3.55 tff(263,plain,
% 3.27/3.55 (![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))),
% 3.27/3.55 inference(unit_resolution,[status(thm)],[262, 151, 259])).
% 3.27/3.55 tff(264,plain,
% 3.27/3.55 (((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ((~r1(Y!9, X!10)) | ![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) <=> ((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | (~r1(Y!9, X!10)) | ![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))),
% 3.27/3.55 inference(rewrite,[status(thm)],[])).
% 3.27/3.55 tff(265,plain,
% 3.27/3.55 ((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ((~r1(Y!9, X!10)) | ![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))),
% 3.27/3.55 inference(quant_inst,[status(thm)],[])).
% 3.27/3.55 tff(266,plain,
% 3.27/3.55 ((~![X: $i] : ((~r1(Y!9, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | (~r1(Y!9, X!10)) | ![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))),
% 3.27/3.55 inference(modus_ponens,[status(thm)],[265, 264])).
% 3.27/3.55 tff(267,plain,
% 3.27/3.55 (![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))),
% 3.27/3.55 inference(unit_resolution,[status(thm)],[266, 150, 263])).
% 3.27/3.55 tff(268,plain,
% 3.27/3.55 (((~![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ((~r1(X!10, tptp_fun_X_15(X!10))) | ![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X))))) <=> ((~![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | (~r1(X!10, tptp_fun_X_15(X!10))) | ![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X))))),
% 3.27/3.55 inference(rewrite,[status(thm)],[])).
% 3.27/3.55 tff(269,plain,
% 3.27/3.55 (((~r1(X!10, tptp_fun_X_15(X!10))) | ![X: $i] : ((~r1(tptp_fun_X_15(X!10), X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) <=> ((~r1(X!10, tptp_fun_X_15(X!10))) | ![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X))))),
% 3.27/3.55 inference(rewrite,[status(thm)],[])).
% 3.27/3.55 tff(270,plain,
% 3.27/3.55 (((~![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ((~r1(X!10, tptp_fun_X_15(X!10))) | ![X: $i] : ((~r1(tptp_fun_X_15(X!10), X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) <=> ((~![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ((~r1(X!10, tptp_fun_X_15(X!10))) | ![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X)))))),
% 3.27/3.55 inference(monotonicity,[status(thm)],[269])).
% 3.27/3.55 tff(271,plain,
% 3.27/3.55 (((~![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ((~r1(X!10, tptp_fun_X_15(X!10))) | ![X: $i] : ((~r1(tptp_fun_X_15(X!10), X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) <=> ((~![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | (~r1(X!10, tptp_fun_X_15(X!10))) | ![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X))))),
% 3.27/3.55 inference(transitivity,[status(thm)],[270, 268])).
% 3.27/3.55 tff(272,plain,
% 3.27/3.55 ((~![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ((~r1(X!10, tptp_fun_X_15(X!10))) | ![X: $i] : ((~r1(tptp_fun_X_15(X!10), X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))),
% 3.27/3.55 inference(quant_inst,[status(thm)],[])).
% 3.27/3.55 tff(273,plain,
% 3.27/3.55 ((~![Y: $i] : ((~r1(X!10, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | (~r1(X!10, tptp_fun_X_15(X!10))) | ![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X)))),
% 3.27/3.55 inference(modus_ponens,[status(thm)],[272, 271])).
% 3.27/3.55 tff(274,plain,
% 3.27/3.55 (![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X)))),
% 3.27/3.55 inference(unit_resolution,[status(thm)],[273, 181, 267])).
% 3.27/3.55 tff(275,plain,
% 3.27/3.55 (((~![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X)))) | (p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~(p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))) <=> ((~![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X)))) | p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~(p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.56 inference(rewrite,[status(thm)],[])).
% 3.27/3.56 tff(276,plain,
% 3.27/3.56 ((~![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X)))) | (p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~(p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.56 inference(quant_inst,[status(thm)],[])).
% 3.27/3.56 tff(277,plain,
% 3.27/3.56 ((~![X: $i] : (p41(X) | (~(p54(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | (~r1(tptp_fun_X_15(X!10), X)))) | p41(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~(p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.56 inference(modus_ponens,[status(thm)],[276, 275])).
% 3.27/3.56 tff(278,plain,
% 3.27/3.56 (~(p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))))),
% 3.27/3.56 inference(unit_resolution,[status(thm)],[277, 274, 252, 250])).
% 3.27/3.56 tff(279,plain,
% 3.27/3.56 ((p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))) | r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.56 inference(tautology,[status(thm)],[])).
% 3.27/3.56 tff(280,plain,
% 3.27/3.56 (r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.56 inference(unit_resolution,[status(thm)],[279, 278])).
% 3.27/3.56 tff(281,plain,
% 3.27/3.56 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.56 inference(rewrite,[status(thm)],[])).
% 3.27/3.56 tff(282,plain,
% 3.27/3.56 ((r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) <=> ((~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.56 inference(rewrite,[status(thm)],[])).
% 3.27/3.56 tff(283,plain,
% 3.27/3.56 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))))),
% 3.27/3.56 inference(monotonicity,[status(thm)],[282])).
% 3.27/3.56 tff(284,plain,
% 3.27/3.56 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.56 inference(transitivity,[status(thm)],[283, 281])).
% 3.27/3.56 tff(285,plain,
% 3.27/3.56 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.56 inference(quant_inst,[status(thm)],[])).
% 3.27/3.56 tff(286,plain,
% 3.27/3.56 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))) | r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.56 inference(modus_ponens,[status(thm)],[285, 284])).
% 3.27/3.56 tff(287,plain,
% 3.27/3.56 (r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.56 inference(unit_resolution,[status(thm)],[286, 163, 243, 280])).
% 3.27/3.56 tff(288,plain,
% 3.27/3.56 ((p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))) | (~p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.56 inference(tautology,[status(thm)],[])).
% 3.27/3.56 tff(289,plain,
% 3.27/3.56 (~p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.56 inference(unit_resolution,[status(thm)],[288, 278])).
% 3.27/3.56 tff(290,plain,
% 3.27/3.56 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_X_15(X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_X_15(X!10)))),
% 3.27/3.56 inference(rewrite,[status(thm)],[])).
% 3.27/3.56 tff(291,plain,
% 3.27/3.56 ((r1(X!0, tptp_fun_X_15(X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(X!0, X!10))) <=> ((~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_X_15(X!10)))),
% 3.27/3.56 inference(rewrite,[status(thm)],[])).
% 3.27/3.56 tff(292,plain,
% 3.27/3.56 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_15(X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(X!0, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_X_15(X!10))))),
% 3.27/3.57 inference(monotonicity,[status(thm)],[291])).
% 3.27/3.57 tff(293,plain,
% 3.27/3.57 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_15(X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(X!0, X!10)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_X_15(X!10)))),
% 3.27/3.57 inference(transitivity,[status(thm)],[292, 290])).
% 3.27/3.57 tff(294,plain,
% 3.27/3.57 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_15(X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | (~r1(X!0, X!10)))),
% 3.27/3.57 inference(quant_inst,[status(thm)],[])).
% 3.27/3.57 tff(295,plain,
% 3.27/3.57 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, X!10)) | (~r1(X!10, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_X_15(X!10))),
% 3.27/3.57 inference(modus_ponens,[status(thm)],[294, 293])).
% 3.27/3.57 tff(296,plain,
% 3.27/3.57 (r1(X!0, tptp_fun_X_15(X!10))),
% 3.27/3.57 inference(unit_resolution,[status(thm)],[295, 163, 170, 181])).
% 3.27/3.57 tff(297,plain,
% 3.27/3.57 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!0, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!0, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.57 inference(rewrite,[status(thm)],[])).
% 3.27/3.57 tff(298,plain,
% 3.27/3.57 ((r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!0, tptp_fun_X_15(X!10)))) <=> ((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!0, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.57 inference(rewrite,[status(thm)],[])).
% 3.27/3.57 tff(299,plain,
% 3.27/3.57 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!0, tptp_fun_X_15(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!0, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))))),
% 3.27/3.57 inference(monotonicity,[status(thm)],[298])).
% 3.27/3.57 tff(300,plain,
% 3.27/3.57 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!0, tptp_fun_X_15(X!10))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!0, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10))))),
% 3.27/3.57 inference(transitivity,[status(thm)],[299, 297])).
% 3.27/3.57 tff(301,plain,
% 3.27/3.57 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!0, tptp_fun_X_15(X!10))))),
% 3.27/3.57 inference(quant_inst,[status(thm)],[])).
% 3.27/3.57 tff(302,plain,
% 3.27/3.57 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(tptp_fun_X_15(X!10), tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~r1(X!0, tptp_fun_X_15(X!10))) | r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))),
% 3.27/3.57 inference(modus_ponens,[status(thm)],[301, 300])).
% 3.27/3.57 tff(303,plain,
% 3.27/3.57 (r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))),
% 3.27/3.57 inference(unit_resolution,[status(thm)],[302, 163, 296, 210])).
% 3.27/3.57 tff(304,plain,
% 3.27/3.57 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X))))))))),
% 3.27/3.57 inference(bind,[status(th)],[])).
% 3.27/3.57 tff(305,plain,
% 3.27/3.57 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))),
% 3.27/3.57 inference(quant_intro,[status(thm)],[304])).
% 3.27/3.57 tff(306,plain,
% 3.27/3.57 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X))))))))),
% 3.27/3.57 inference(bind,[status(th)],[])).
% 3.27/3.57 tff(307,plain,
% 3.27/3.57 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))),
% 3.27/3.57 inference(quant_intro,[status(thm)],[306])).
% 3.27/3.57 tff(308,plain,
% 3.27/3.57 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))),
% 3.27/3.57 inference(transitivity,[status(thm)],[307, 305])).
% 3.27/3.57 tff(309,plain,
% 3.27/3.57 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (![X: $i] : (p54(X) | (~r1(Y, X))) & ![X: $i] : (p56(X) | (~r1(Y, X))) & ![X: $i] : (p52(X) | (~r1(Y, X))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X))))))))),
% 3.27/3.57 inference(bind,[status(th)],[])).
% 3.27/3.57 tff(310,plain,
% 3.27/3.57 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p54(X) | (~r1(Y, X))) & ![X: $i] : (p56(X) | (~r1(Y, X))) & ![X: $i] : (p52(X) | (~r1(Y, X))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))),
% 3.27/3.57 inference(quant_intro,[status(thm)],[309])).
% 3.27/3.57 tff(311,plain,
% 3.27/3.57 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p54(X) | (~r1(Y, X))) & ![X: $i] : (p56(X) | (~r1(Y, X))) & ![X: $i] : (p52(X) | (~r1(Y, X)))))),
% 3.27/3.57 inference(and_elim,[status(thm)],[148])).
% 3.27/3.57 tff(312,plain,
% 3.27/3.57 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))),
% 3.27/3.57 inference(modus_ponens,[status(thm)],[311, 310])).
% 3.27/3.57 tff(313,plain,
% 3.27/3.57 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))),
% 3.27/3.57 inference(modus_ponens,[status(thm)],[312, 308])).
% 3.27/3.57 tff(314,plain,
% 3.27/3.57 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))) | ((~r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~((~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))) | (~r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~((~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))))))),
% 3.27/3.57 inference(rewrite,[status(thm)],[])).
% 3.27/3.57 tff(315,plain,
% 3.27/3.57 (((~r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~((~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X))))))) <=> ((~r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~((~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))))))),
% 3.27/3.57 inference(rewrite,[status(thm)],[])).
% 3.27/3.57 tff(316,plain,
% 3.27/3.57 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))) | ((~r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~((~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))) | ((~r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~((~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X))))))))),
% 3.27/3.57 inference(monotonicity,[status(thm)],[315])).
% 3.27/3.57 tff(317,plain,
% 3.27/3.57 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))) | ((~r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~((~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))) | (~r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~((~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))))))),
% 3.27/3.57 inference(transitivity,[status(thm)],[316, 314])).
% 3.27/3.57 tff(318,plain,
% 3.27/3.57 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))) | ((~r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~((~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))))))),
% 3.27/3.57 inference(quant_inst,[status(thm)],[])).
% 3.27/3.57 tff(319,plain,
% 3.27/3.57 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p54(X) | (~r1(Y, X)))) | (~![X: $i] : (p56(X) | (~r1(Y, X)))) | (~![X: $i] : (p52(X) | (~r1(Y, X)))))))) | (~r1(X!0, tptp_fun_Y_18(tptp_fun_X_15(X!10)))) | (~((~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X))))))),
% 3.27/3.57 inference(modus_ponens,[status(thm)],[318, 317])).
% 3.27/3.57 tff(320,plain,
% 3.27/3.57 (~((~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))))),
% 3.27/3.57 inference(unit_resolution,[status(thm)],[319, 313, 303])).
% 3.27/3.57 tff(321,plain,
% 3.27/3.57 (((~![X: $i] : (p52(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p56(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X))))) | ![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))),
% 3.27/3.57 inference(tautology,[status(thm)],[])).
% 3.27/3.57 tff(322,plain,
% 3.27/3.57 (![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))),
% 3.27/3.57 inference(unit_resolution,[status(thm)],[321, 320])).
% 3.27/3.57 tff(323,plain,
% 3.27/3.57 (((~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))))) <=> ((~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))))),
% 3.27/3.59 inference(rewrite,[status(thm)],[])).
% 3.27/3.59 tff(324,plain,
% 3.27/3.59 ((~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | (p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10)))))))),
% 3.27/3.59 inference(quant_inst,[status(thm)],[])).
% 3.27/3.59 tff(325,plain,
% 3.27/3.59 ((~![X: $i] : (p54(X) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), X)))) | p54(tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))) | (~r1(tptp_fun_Y_18(tptp_fun_X_15(X!10)), tptp_fun_Y_2(tptp_fun_X_26(tptp_fun_Y_18(tptp_fun_X_15(X!10))))))),
% 3.27/3.59 inference(modus_ponens,[status(thm)],[324, 323])).
% 3.27/3.59 tff(326,plain,
% 3.27/3.59 ($false),
% 3.27/3.59 inference(unit_resolution,[status(thm)],[325, 322, 289, 287])).
% 3.27/3.59 % SZS output end Proof
% 0.21/3.60 % E exiting
%------------------------------------------------------------------------------