TSTP Solution File: LCL664+1.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL664+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 04:57:37 EDT 2022
% Result : Theorem 0.19s 0.56s
% Output : Proof 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL664+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 23:31:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.56 % SZS status Theorem
% 0.19/0.56 % SZS output start Proof
% 0.19/0.56 tff(r1_type, type, (
% 0.19/0.56 r1: ( $i * $i ) > $o)).
% 0.19/0.56 tff(tptp_fun_X_19_type, type, (
% 0.19/0.56 tptp_fun_X_19: $i > $i)).
% 0.19/0.56 tff(tptp_fun_Y_11_type, type, (
% 0.19/0.56 tptp_fun_Y_11: $i > $i)).
% 0.19/0.56 tff(tptp_fun_X_8_type, type, (
% 0.19/0.56 tptp_fun_X_8: $i > $i)).
% 0.19/0.56 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.56 tptp_fun_Y_3: $i)).
% 0.19/0.56 tff(p54_type, type, (
% 0.19/0.56 p54: $i > $o)).
% 0.19/0.56 tff(p41_type, type, (
% 0.19/0.56 p41: $i > $o)).
% 0.19/0.56 tff(p34_type, type, (
% 0.19/0.56 p34: $i > $o)).
% 0.19/0.56 tff(p21_type, type, (
% 0.19/0.56 p21: $i > $o)).
% 0.19/0.56 tff(tptp_fun_X_0_type, type, (
% 0.19/0.56 tptp_fun_X_0: $i)).
% 0.19/0.56 tff(p12_type, type, (
% 0.19/0.56 p12: $i > $o)).
% 0.19/0.56 tff(p52_type, type, (
% 0.19/0.56 p52: $i > $o)).
% 0.19/0.56 tff(tptp_fun_Y_23_type, type, (
% 0.19/0.56 tptp_fun_Y_23: $i > $i)).
% 0.19/0.56 tff(p46_type, type, (
% 0.19/0.56 p46: $i > $o)).
% 0.19/0.56 tff(p44_type, type, (
% 0.19/0.56 p44: $i > $o)).
% 0.19/0.56 tff(p42_type, type, (
% 0.19/0.56 p42: $i > $o)).
% 0.19/0.56 tff(tptp_fun_Y_28_type, type, (
% 0.19/0.56 tptp_fun_Y_28: $i > $i)).
% 0.19/0.56 tff(tptp_fun_X_27_type, type, (
% 0.19/0.56 tptp_fun_X_27: $i > $i)).
% 0.19/0.56 tff(p36_type, type, (
% 0.19/0.56 p36: $i > $o)).
% 0.19/0.56 tff(p32_type, type, (
% 0.19/0.56 p32: $i > $o)).
% 0.19/0.56 tff(p55_type, type, (
% 0.19/0.56 p55: $i > $o)).
% 0.19/0.56 tff(tptp_fun_Y_24_type, type, (
% 0.19/0.56 tptp_fun_Y_24: $i > $i)).
% 0.19/0.56 tff(p45_type, type, (
% 0.19/0.56 p45: $i > $o)).
% 0.19/0.56 tff(p53_type, type, (
% 0.19/0.56 p53: $i > $o)).
% 0.19/0.56 tff(tptp_fun_Y_22_type, type, (
% 0.19/0.56 tptp_fun_Y_22: $i > $i)).
% 0.19/0.56 tff(p51_type, type, (
% 0.19/0.56 p51: $i > $o)).
% 0.19/0.56 tff(tptp_fun_Y_21_type, type, (
% 0.19/0.56 tptp_fun_Y_21: $i > $i)).
% 0.19/0.56 tff(tptp_fun_X_26_type, type, (
% 0.19/0.56 tptp_fun_X_26: $i > $i)).
% 0.19/0.56 tff(p43_type, type, (
% 0.19/0.56 p43: $i > $o)).
% 0.19/0.56 tff(tptp_fun_X_25_type, type, (
% 0.19/0.56 tptp_fun_X_25: $i > $i)).
% 0.19/0.56 tff(tptp_fun_Y_20_type, type, (
% 0.19/0.56 tptp_fun_Y_20: $i > $i)).
% 0.19/0.56 tff(p26_type, type, (
% 0.19/0.56 p26: $i > $o)).
% 0.19/0.56 tff(p24_type, type, (
% 0.19/0.56 p24: $i > $o)).
% 0.19/0.56 tff(p22_type, type, (
% 0.19/0.56 p22: $i > $o)).
% 0.19/0.56 tff(tptp_fun_X_17_type, type, (
% 0.19/0.56 tptp_fun_X_17: $i > $i)).
% 0.19/0.56 tff(p35_type, type, (
% 0.19/0.56 p35: $i > $o)).
% 0.19/0.56 tff(tptp_fun_X_16_type, type, (
% 0.19/0.56 tptp_fun_X_16: $i > $i)).
% 0.19/0.56 tff(p33_type, type, (
% 0.19/0.56 p33: $i > $o)).
% 0.19/0.56 tff(tptp_fun_Y_18_type, type, (
% 0.19/0.56 tptp_fun_Y_18: $i > $i)).
% 0.19/0.56 tff(p31_type, type, (
% 0.19/0.56 p31: $i > $o)).
% 0.19/0.56 tff(tptp_fun_X_15_type, type, (
% 0.19/0.56 tptp_fun_X_15: $i > $i)).
% 0.19/0.56 tff(p16_type, type, (
% 0.19/0.56 p16: $i > $o)).
% 0.19/0.56 tff(p14_type, type, (
% 0.19/0.56 p14: $i > $o)).
% 0.19/0.56 tff(tptp_fun_Y_12_type, type, (
% 0.19/0.56 tptp_fun_Y_12: $i > $i)).
% 0.19/0.56 tff(p25_type, type, (
% 0.19/0.56 p25: $i > $o)).
% 0.19/0.56 tff(tptp_fun_Y_10_type, type, (
% 0.19/0.56 tptp_fun_Y_10: $i > $i)).
% 0.19/0.56 tff(tptp_fun_Y_9_type, type, (
% 0.19/0.56 tptp_fun_Y_9: $i > $i)).
% 0.19/0.56 tff(tptp_fun_X_14_type, type, (
% 0.19/0.56 tptp_fun_X_14: $i > $i)).
% 0.19/0.56 tff(p23_type, type, (
% 0.19/0.56 p23: $i > $o)).
% 0.19/0.56 tff(tptp_fun_X_13_type, type, (
% 0.19/0.56 tptp_fun_X_13: $i > $i)).
% 0.19/0.56 tff(tptp_fun_X_7_type, type, (
% 0.19/0.56 tptp_fun_X_7: $i > $i)).
% 0.19/0.56 tff(p15_type, type, (
% 0.19/0.56 p15: $i > $o)).
% 0.19/0.56 tff(tptp_fun_X_6_type, type, (
% 0.19/0.56 tptp_fun_X_6: $i > $i)).
% 0.19/0.56 tff(p13_type, type, (
% 0.19/0.56 p13: $i > $o)).
% 0.19/0.56 tff(p11_type, type, (
% 0.19/0.56 p11: $i > $o)).
% 0.19/0.56 tff(tptp_fun_Y_5_type, type, (
% 0.19/0.56 tptp_fun_Y_5: $i)).
% 0.19/0.56 tff(tptp_fun_Y_4_type, type, (
% 0.19/0.56 tptp_fun_Y_4: $i)).
% 0.19/0.56 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.56 tptp_fun_Y_2: $i)).
% 0.19/0.56 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.56 tptp_fun_Y_1: $i > $i)).
% 0.19/0.56 tff(p56_type, type, (
% 0.19/0.56 p56: $i > $o)).
% 0.19/0.56 tff(1,plain,
% 0.19/0.56 (^[Y: $i] : refl((p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y))) <=> (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(2,plain,
% 0.19/0.56 (![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y))) <=> ![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.56 tff(3,plain,
% 0.19/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p56(Y) | (~r1(X, Y))))))) & ![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)))))))) & (~((~r1(X!0, Y!2)) | p11(Y!2))) & (~((~r1(X!0, Y!3)) | p12(Y!3))) & (~((~r1(X!0, Y!4)) | p13(Y!4))) & (~((~r1(X!0, Y!5)) | p15(Y!5))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p23(tptp_fun_X_6(Y)))) | (~(~p11(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_7(Y))) | p25(tptp_fun_X_7(Y)))) | (~(~p11(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~(~p12(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p23(tptp_fun_X_6(Y)))) | (~(~p13(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_7(Y))) | p25(tptp_fun_X_7(Y)))) | (~(~p13(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p23(tptp_fun_X_6(Y)))) | (~(~p15(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_7(Y))) | p25(tptp_fun_X_7(Y)))) | (~(~p15(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p31(tptp_fun_Y_9(X)))) | (~(~p21(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_10(X))) | p33(tptp_fun_Y_10(X)))) | (~(~p21(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~(~p21(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p35(tptp_fun_Y_12(X)))) | (~(~p21(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p22(tptp_fun_X_13(Y)))) | (~(~p14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_13(Y))) | p22(tptp_fun_X_13(Y)))) | (~(~p16(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p31(tptp_fun_Y_9(X)))) | (~(~p23(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_10(X))) | p33(tptp_fun_Y_10(X)))) | (~(~p23(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p35(tptp_fun_Y_12(X)))) | (~(~p23(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p24(tptp_fun_X_14(Y)))) | (~(~p14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_14(Y))) | p24(tptp_fun_X_14(Y)))) | (~(~p16(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p31(tptp_fun_Y_9(X)))) | (~(~p25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_10(X))) | p33(tptp_fun_Y_10(X)))) | (~(~p25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_12(X))) | p35(tptp_fun_Y_12(X)))) | (~(~p25(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p26(tptp_fun_X_15(Y)))) | (~(~p14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_15(Y))) | p26(tptp_fun_X_15(Y)))) | (~(~p16(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_16(Y))) | p43(tptp_fun_X_16(Y)))) | (~(~p31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_17(Y))) | p45(tptp_fun_X_17(Y)))) | (~(~p31(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_18(X))) | p32(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))) | p32(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))) | p32(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_16(Y))) | p43(tptp_fun_X_16(Y)))) | (~(~p33(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_17(Y))) | p45(tptp_fun_X_17(Y)))) | (~(~p33(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~(~p34(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~(~p22(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~(~p24(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~(~p26(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_16(Y))) | p43(tptp_fun_X_16(Y)))) | (~(~p35(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_17(Y))) | p45(tptp_fun_X_17(Y)))) | (~(~p35(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_20(X))) | p36(tptp_fun_Y_20(X)))) | (~(~p22(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_20(X))) | p36(tptp_fun_Y_20(X)))) | (~(~p24(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_20(X))) | p36(tptp_fun_Y_20(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_21(X))) | p51(tptp_fun_Y_21(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_22(X))) | p53(tptp_fun_Y_22(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_23(X))) | p54(tptp_fun_Y_23(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_24(X))) | p55(tptp_fun_Y_24(X)))) | (~(~p41(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_25(Y))) | p42(tptp_fun_X_25(Y)))) | (~(~p32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_25(Y))) | p42(tptp_fun_X_25(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_21(X))) | p51(tptp_fun_Y_21(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_22(X))) | p53(tptp_fun_Y_22(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_24(X))) | p55(tptp_fun_Y_24(X)))) | (~(~p43(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_26(Y))) | p44(tptp_fun_X_26(Y)))) | (~(~p32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_26(Y))) | p44(tptp_fun_X_26(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_21(X))) | p51(tptp_fun_Y_21(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_22(X))) | p53(tptp_fun_Y_22(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_24(X))) | p55(tptp_fun_Y_24(X)))) | (~(~p45(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_27(Y))) | p46(tptp_fun_X_27(Y)))) | (~(~p32(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_27(Y))) | p46(tptp_fun_X_27(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))) | p52(tptp_fun_Y_28(X)))) | (~(~p42(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))) | p52(tptp_fun_Y_28(X)))) | (~(~p44(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))) | p52(tptp_fun_Y_28(X)))) | (~(~p46(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_23(X))) | p54(tptp_fun_Y_23(X)))) | (~(~p42(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_23(X))) | p54(tptp_fun_Y_23(X)))) | (~(~p44(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_23(X))) | p54(tptp_fun_Y_23(X)))) | (~(~p46(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p52(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p56(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p46(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))))))))) & (~((~r1(X!0, Y!2)) | p11(Y!2))) & (~((~r1(X!0, Y!3)) | p12(Y!3))) & (~((~r1(X!0, Y!4)) | p13(Y!4))) & (~((~r1(X!0, Y!5)) | p15(Y!5))) & ![Y: $i] : (p11(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p23(tptp_fun_X_6(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p11(Y) | (~((~r1(Y, tptp_fun_X_7(Y))) | p25(tptp_fun_X_7(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p13(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p23(tptp_fun_X_6(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p13(Y) | (~((~r1(Y, tptp_fun_X_7(Y))) | p25(tptp_fun_X_7(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p15(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p23(tptp_fun_X_6(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p15(Y) | (~((~r1(Y, tptp_fun_X_7(Y))) | p25(tptp_fun_X_7(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_9(X))) | p31(tptp_fun_Y_9(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p33(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p35(tptp_fun_Y_12(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p22(tptp_fun_X_13(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p22(tptp_fun_X_13(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_9(X))) | p31(tptp_fun_Y_9(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p33(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p35(tptp_fun_Y_12(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p24(tptp_fun_X_14(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p24(tptp_fun_X_14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_9(X))) | p31(tptp_fun_Y_9(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p33(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p35(tptp_fun_Y_12(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p26(tptp_fun_X_15(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p26(tptp_fun_X_15(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_16(Y))) | p43(tptp_fun_X_16(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_17(Y))) | p45(tptp_fun_X_17(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p32(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))) | p32(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))) | p32(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_16(Y))) | p43(tptp_fun_X_16(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_17(Y))) | p45(tptp_fun_X_17(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_16(Y))) | p43(tptp_fun_X_16(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_17(Y))) | p45(tptp_fun_X_17(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_20(X))) | p36(tptp_fun_Y_20(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_20(X))) | p36(tptp_fun_Y_20(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_20(X))) | p36(tptp_fun_Y_20(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_21(X))) | p51(tptp_fun_Y_21(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_22(X))) | p53(tptp_fun_Y_22(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_23(X))) | p54(tptp_fun_Y_23(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_24(X))) | p55(tptp_fun_Y_24(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_25(Y))) | p42(tptp_fun_X_25(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_25(Y))) | p42(tptp_fun_X_25(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_21(X))) | p51(tptp_fun_Y_21(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_22(X))) | p53(tptp_fun_Y_22(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_24(X))) | p55(tptp_fun_Y_24(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p44(tptp_fun_X_26(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p44(tptp_fun_X_26(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_21(X))) | p51(tptp_fun_Y_21(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_22(X))) | p53(tptp_fun_Y_22(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_24(X))) | p55(tptp_fun_Y_24(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_27(Y))) | p46(tptp_fun_X_27(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_27(Y))) | p46(tptp_fun_X_27(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p52(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)) | p44(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p52(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)) | p46(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p52(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)) | p42(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p46(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p52(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))))),
% 0.51/0.57 inference(rewrite,[status(thm)],[])).
% 0.51/0.57 tff(4,plain,
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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)) | 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)) | 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] 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(~![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] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p21(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p35(Y)) & (~p21(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p22(X)) & (~p14(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p22(X)) & (~p16(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p31(Y)) & (~p23(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p33(Y)) & (~p23(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p35(Y)) & (~p23(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p24(X)) & (~p14(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p24(X)) & (~p16(Y)))))) | (~![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)) | (~(![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] : 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| (~(![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)) | p46(X)) & (~p32(Y)))))))) | (~![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)) | (~(![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)) | (~(![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)) & (~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)) & (~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)) & (~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)) & (~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))))))) | (~![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)))))))))),
% 0.51/0.57 inference(rewrite,[status(thm)],[])).
% 0.51/0.57 tff(5,plain,
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% 0.53/0.58 inference(rewrite,[status(thm)],[])).
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% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(7,plain,
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p11(Y)))))) <=> (~(~?[X: $i] : (~((~![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)))))))) | (~![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)) | p11(Y)) | ![Y: $i] : ((~r1(X, Y)) | p12(Y)) | ![Y: $i] : ((~r1(X, Y)) | p13(Y)) | ![Y: $i] : ((~r1(X, Y)) | p15(Y)) | (~![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] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p34(Y)) & (~p21(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p35(Y)) & (~p21(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p22(X)) & (~p14(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p22(X)) & 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| 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] 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(~(![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)) | p46(X)) & (~p32(Y)))))))) | (~![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)) | (~(![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)) | (~(![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)) & (~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)) & (~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)) & (~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)) & (~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))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))))))))),
% 0.53/0.60 inference(monotonicity,[status(thm)],[6])).
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$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)) | 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)) | 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)) | p46(X)) & (~p32(Y)))))))) | (~![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)) | (~(![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)) | (~(![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)) & (~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)) & (~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)) & (~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)) & (~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))))))) | (~![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)))))))))),
% 0.53/0.61 inference(transitivity,[status(thm)],[7, 5])).
% 0.53/0.61 tff(9,axiom,(~(~?[X: $i] : (~((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p56(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)) | p54(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)) | p54(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)) | p52(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)) | 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] : 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: ((~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)) | p46(X)) & (~p32(Y)))))))) | (~![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)) | (~(![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)) | (~(![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)) & (~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)) & (~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)) & (~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)) & (~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))))))) | (~![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)))))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.53/0.61 tff(11,plain,
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: ((~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)) | p46(X)) & (~p32(Y)))))))) | (~![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)) | (~(![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)) | (~(![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)) & (~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)) & (~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)) & (~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)) & (~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))))))) | (~![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)))))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.53/0.62 tff(12,plain,
% 0.53/0.62 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p56(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p46(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))))))))) & (~((~r1(X!0, Y!2)) | p11(Y!2))) & (~((~r1(X!0, Y!3)) | p12(Y!3))) & (~((~r1(X!0, Y!4)) | p13(Y!4))) & (~((~r1(X!0, Y!5)) | p15(Y!5))) & ![Y: $i] : (p11(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p23(tptp_fun_X_6(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p11(Y) | (~((~r1(Y, tptp_fun_X_7(Y))) | p25(tptp_fun_X_7(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p13(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p23(tptp_fun_X_6(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p13(Y) | (~((~r1(Y, tptp_fun_X_7(Y))) | p25(tptp_fun_X_7(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p15(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p23(tptp_fun_X_6(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : (p15(Y) | (~((~r1(Y, tptp_fun_X_7(Y))) | p25(tptp_fun_X_7(Y)))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_9(X))) | p31(tptp_fun_Y_9(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p33(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p35(tptp_fun_Y_12(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p22(tptp_fun_X_13(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p22(tptp_fun_X_13(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_9(X))) | p31(tptp_fun_Y_9(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p33(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p23(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p35(tptp_fun_Y_12(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p24(tptp_fun_X_14(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p24(tptp_fun_X_14(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_9(X))) | p31(tptp_fun_Y_9(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_10(X))) | p33(tptp_fun_Y_10(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p25(X) | (~((~r1(X, tptp_fun_Y_12(X))) | p35(tptp_fun_Y_12(X)))))) & ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p26(tptp_fun_X_15(Y))))) & ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_15(Y))) | p26(tptp_fun_X_15(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_16(Y))) | p43(tptp_fun_X_16(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p31(Y) | (~((~r1(Y, tptp_fun_X_17(Y))) | p45(tptp_fun_X_17(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_18(X))) | p32(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))) | p32(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))) | p32(tptp_fun_Y_18(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_16(Y))) | p43(tptp_fun_X_16(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p33(Y) | (~((~r1(Y, tptp_fun_X_17(Y))) | p45(tptp_fun_X_17(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_16(Y))) | p43(tptp_fun_X_16(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p35(Y) | (~((~r1(Y, tptp_fun_X_17(Y))) | p45(tptp_fun_X_17(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p22(X) | (~((~r1(X, tptp_fun_Y_20(X))) | p36(tptp_fun_Y_20(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p24(X) | (~((~r1(X, tptp_fun_Y_20(X))) | p36(tptp_fun_Y_20(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p26(X) | (~((~r1(X, tptp_fun_Y_20(X))) | p36(tptp_fun_Y_20(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_21(X))) | p51(tptp_fun_Y_21(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_22(X))) | p53(tptp_fun_Y_22(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_23(X))) | p54(tptp_fun_Y_23(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_24(X))) | p55(tptp_fun_Y_24(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_25(Y))) | p42(tptp_fun_X_25(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_25(Y))) | p42(tptp_fun_X_25(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_21(X))) | p51(tptp_fun_Y_21(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_22(X))) | p53(tptp_fun_Y_22(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_24(X))) | p55(tptp_fun_Y_24(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p44(tptp_fun_X_26(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_26(Y))) | p44(tptp_fun_X_26(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_21(X))) | p51(tptp_fun_Y_21(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_22(X))) | p53(tptp_fun_Y_22(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_24(X))) | p55(tptp_fun_Y_24(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p32(Y) | (~((~r1(Y, tptp_fun_X_27(Y))) | p46(tptp_fun_X_27(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p36(Y) | (~((~r1(Y, tptp_fun_X_27(Y))) | p46(tptp_fun_X_27(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p42(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p52(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)) | p44(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p52(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)) | p46(X) | (~((~r1(X, tptp_fun_Y_28(X))) | p52(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)) | p42(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p44(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p46(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p52(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.53/0.62 tff(13,plain,
% 0.53/0.62 (![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))),
% 0.53/0.62 inference(and_elim,[status(thm)],[12])).
% 0.53/0.62 tff(14,plain,
% 0.53/0.62 (![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.53/0.62 tff(15,plain,
% 0.53/0.62 (~((~r1(X!0, Y!3)) | p12(Y!3))),
% 0.53/0.62 inference(and_elim,[status(thm)],[12])).
% 0.53/0.62 tff(16,plain,
% 0.53/0.62 (~p12(Y!3)),
% 0.53/0.62 inference(or_elim,[status(thm)],[15])).
% 0.53/0.62 tff(17,plain,
% 0.53/0.62 (r1(X!0, Y!3)),
% 0.53/0.62 inference(or_elim,[status(thm)],[15])).
% 0.53/0.62 tff(18,plain,
% 0.53/0.62 (((~![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))) | ((~r1(X!0, Y!3)) | p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))))) <=> ((~![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))) | (~r1(X!0, Y!3)) | p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(19,plain,
% 0.53/0.62 ((p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))) | (~r1(X!0, Y!3))) <=> ((~r1(X!0, Y!3)) | p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(20,plain,
% 0.53/0.62 ((~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))) <=> (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(21,plain,
% 0.53/0.62 ((p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))) | (~r1(X!0, Y!3))) <=> (p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))) | (~r1(X!0, Y!3)))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[20])).
% 0.53/0.62 tff(22,plain,
% 0.53/0.62 ((p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))) | (~r1(X!0, Y!3))) <=> ((~r1(X!0, Y!3)) | p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))))),
% 0.53/0.62 inference(transitivity,[status(thm)],[21, 19])).
% 0.53/0.62 tff(23,plain,
% 0.53/0.62 (((~![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))) | (p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))) | (~r1(X!0, Y!3)))) <=> ((~![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))) | ((~r1(X!0, Y!3)) | p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3))))))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[22])).
% 0.53/0.62 tff(24,plain,
% 0.53/0.62 (((~![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))) | (p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))) | (~r1(X!0, Y!3)))) <=> ((~![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))) | (~r1(X!0, Y!3)) | p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))))),
% 0.53/0.62 inference(transitivity,[status(thm)],[23, 18])).
% 0.53/0.62 tff(25,plain,
% 0.53/0.62 ((~![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))) | (p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))) | (~r1(X!0, Y!3)))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(26,plain,
% 0.53/0.62 ((~![Y: $i] : (p12(Y) | (~((~r1(Y, tptp_fun_X_8(Y))) | p21(tptp_fun_X_8(Y)))) | (~r1(X!0, Y)))) | (~r1(X!0, Y!3)) | p12(Y!3) | (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.53/0.62 tff(27,plain,
% 0.53/0.62 (~((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[26, 17, 16, 14])).
% 0.53/0.62 tff(28,plain,
% 0.53/0.62 (((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3))) | r1(Y!3, tptp_fun_X_8(Y!3))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(29,plain,
% 0.53/0.62 (r1(Y!3, tptp_fun_X_8(Y!3))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.53/0.62 tff(30,plain,
% 0.53/0.62 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(31,plain,
% 0.53/0.62 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[30])).
% 0.53/0.62 tff(32,plain,
% 0.53/0.62 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(33,plain,
% 0.53/0.62 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[32])).
% 0.53/0.62 tff(34,plain,
% 0.53/0.62 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))),
% 0.53/0.62 inference(transitivity,[status(thm)],[33, 31])).
% 0.53/0.62 tff(35,plain,
% 0.53/0.62 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))),
% 0.53/0.62 inference(and_elim,[status(thm)],[12])).
% 0.53/0.62 tff(36,plain,
% 0.53/0.62 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.53/0.62 tff(37,plain,
% 0.53/0.62 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))) | (~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(38,plain,
% 0.53/0.62 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(39,plain,
% 0.53/0.62 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))))) | (~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.53/0.62 tff(40,plain,
% 0.53/0.62 (![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[39, 17, 36])).
% 0.53/0.62 tff(41,plain,
% 0.53/0.62 (((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(42,plain,
% 0.53/0.62 (((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))))) <=> ((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(43,plain,
% 0.53/0.62 (((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[42])).
% 0.53/0.63 tff(44,plain,
% 0.53/0.63 (((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[43, 41])).
% 0.53/0.63 tff(45,plain,
% 0.53/0.63 ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(46,plain,
% 0.53/0.63 ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y))))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.53/0.63 tff(47,plain,
% 0.53/0.63 (![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[46, 40, 29])).
% 0.53/0.63 tff(48,plain,
% 0.53/0.63 (((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3))) | (~p21(tptp_fun_X_8(Y!3)))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(49,plain,
% 0.53/0.63 (~p21(tptp_fun_X_8(Y!3))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[48, 27])).
% 0.53/0.63 tff(50,plain,
% 0.53/0.63 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))))),
% 0.53/0.63 inference(bind,[status(th)],[])).
% 0.53/0.63 tff(51,plain,
% 0.53/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))),
% 0.53/0.63 inference(quant_intro,[status(thm)],[50])).
% 0.53/0.63 tff(52,plain,
% 0.53/0.63 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))))),
% 0.53/0.63 inference(bind,[status(th)],[])).
% 0.53/0.63 tff(53,plain,
% 0.53/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))),
% 0.53/0.63 inference(quant_intro,[status(thm)],[52])).
% 0.53/0.63 tff(54,plain,
% 0.53/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[53, 51])).
% 0.53/0.63 tff(55,plain,
% 0.53/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))),
% 0.53/0.63 inference(and_elim,[status(thm)],[12])).
% 0.53/0.63 tff(56,plain,
% 0.53/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.53/0.63 tff(57,plain,
% 0.53/0.63 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))) | (~r1(X!0, Y!3)) | ![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(58,plain,
% 0.53/0.63 (((~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))))) <=> ((~r1(X!0, Y!3)) | ![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(59,plain,
% 0.53/0.63 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[58])).
% 0.53/0.63 tff(60,plain,
% 0.53/0.63 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))) | (~r1(X!0, Y!3)) | ![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[59, 57])).
% 0.53/0.63 tff(61,plain,
% 0.53/0.63 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(62,plain,
% 0.53/0.63 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X))))))) | (~r1(X!0, Y!3)) | ![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.53/0.63 tff(63,plain,
% 0.53/0.63 (![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[62, 17, 56])).
% 0.53/0.63 tff(64,plain,
% 0.53/0.63 (((~![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) <=> ((~![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))) | (~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(65,plain,
% 0.53/0.63 ((p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(Y!3, tptp_fun_X_8(Y!3)))) <=> ((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(66,plain,
% 0.53/0.63 ((~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) <=> (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(67,plain,
% 0.53/0.63 ((p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(Y!3, tptp_fun_X_8(Y!3)))) <=> (p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[66])).
% 0.53/0.63 tff(68,plain,
% 0.53/0.63 ((p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(Y!3, tptp_fun_X_8(Y!3)))) <=> ((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[67, 65])).
% 0.53/0.63 tff(69,plain,
% 0.53/0.63 (((~![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))) | (p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))))) <=> ((~![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[68])).
% 0.53/0.63 tff(70,plain,
% 0.53/0.63 (((~![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))) | (p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))))) <=> ((~![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))) | (~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[69, 64])).
% 0.53/0.63 tff(71,plain,
% 0.53/0.63 ((~![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))) | (p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(72,plain,
% 0.53/0.63 ((~![X: $i] : (p21(X) | (~((~r1(X, tptp_fun_Y_11(X))) | p34(tptp_fun_Y_11(X)))) | (~r1(Y!3, X)))) | (~r1(Y!3, tptp_fun_X_8(Y!3))) | p21(tptp_fun_X_8(Y!3)) | (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.53/0.63 tff(73,plain,
% 0.53/0.63 (~((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[72, 63, 29, 49])).
% 0.53/0.63 tff(74,plain,
% 0.53/0.63 (((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(75,plain,
% 0.53/0.63 (~p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.53/0.63 tff(76,plain,
% 0.53/0.63 (((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(77,plain,
% 0.53/0.63 (r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.53/0.63 tff(78,plain,
% 0.53/0.63 (((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))) | ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))) <=> ((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(79,plain,
% 0.53/0.63 ((p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) <=> ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(80,plain,
% 0.53/0.63 ((~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) <=> (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(81,plain,
% 0.53/0.63 ((p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) <=> (p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[80])).
% 0.53/0.63 tff(82,plain,
% 0.53/0.63 ((p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) <=> ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[81, 79])).
% 0.53/0.63 tff(83,plain,
% 0.53/0.63 (((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))) | (p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) <=> ((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))) | ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[82])).
% 0.53/0.63 tff(84,plain,
% 0.53/0.63 (((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))) | (p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) <=> ((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[83, 78])).
% 0.53/0.63 tff(85,plain,
% 0.53/0.63 ((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))) | (p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(86,plain,
% 0.58/0.63 ((~![Y: $i] : (p34(Y) | (~((~r1(Y, tptp_fun_X_19(Y))) | p41(tptp_fun_X_19(Y)))) | (~r1(tptp_fun_X_8(Y!3), Y)))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | p34(tptp_fun_Y_11(tptp_fun_X_8(Y!3))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.58/0.63 tff(87,plain,
% 0.58/0.63 (~((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[86, 77, 75, 47])).
% 0.58/0.63 tff(88,plain,
% 0.58/0.63 (((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))),
% 0.58/0.63 inference(tautology,[status(thm)],[])).
% 0.58/0.63 tff(89,plain,
% 0.58/0.63 (r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.58/0.63 tff(90,plain,
% 0.58/0.63 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))))),
% 0.58/0.63 inference(bind,[status(th)],[])).
% 0.58/0.63 tff(91,plain,
% 0.58/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))),
% 0.58/0.63 inference(quant_intro,[status(thm)],[90])).
% 0.58/0.63 tff(92,plain,
% 0.58/0.63 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))))),
% 0.58/0.63 inference(bind,[status(th)],[])).
% 0.58/0.63 tff(93,plain,
% 0.58/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))),
% 0.58/0.63 inference(quant_intro,[status(thm)],[92])).
% 0.58/0.63 tff(94,plain,
% 0.58/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))),
% 0.58/0.63 inference(transitivity,[status(thm)],[93, 91])).
% 0.58/0.63 tff(95,plain,
% 0.58/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))),
% 0.58/0.63 inference(and_elim,[status(thm)],[12])).
% 0.58/0.63 tff(96,plain,
% 0.58/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.58/0.63 tff(97,plain,
% 0.58/0.63 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))) | (~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(98,plain,
% 0.58/0.63 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(99,plain,
% 0.58/0.63 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))))) | (~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.58/0.63 tff(100,plain,
% 0.58/0.63 (![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[99, 17, 96])).
% 0.58/0.63 tff(101,plain,
% 0.58/0.63 (((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(102,plain,
% 0.58/0.63 ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(103,plain,
% 0.58/0.63 ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.58/0.63 tff(104,plain,
% 0.58/0.63 (![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[103, 100, 29])).
% 0.58/0.63 tff(105,plain,
% 0.58/0.63 (((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))) | ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(106,plain,
% 0.58/0.63 ((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))) | ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(107,plain,
% 0.58/0.63 ((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.58/0.63 tff(108,plain,
% 0.58/0.63 (![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[107, 77, 104])).
% 0.58/0.63 tff(109,plain,
% 0.58/0.63 (((~![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))) | ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | ![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | ![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(110,plain,
% 0.58/0.63 (((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | ![Y: $i] : ((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)) | p54(Y))) <=> ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | ![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(111,plain,
% 0.58/0.63 (((~![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))) | ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | ![Y: $i] : ((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)) | p54(Y)))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))) | ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | ![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[110])).
% 0.58/0.64 tff(112,plain,
% 0.58/0.64 (((~![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))) | ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | ![Y: $i] : ((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)) | p54(Y)))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | ![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y))))),
% 0.58/0.64 inference(transitivity,[status(thm)],[111, 109])).
% 0.58/0.64 tff(113,plain,
% 0.58/0.64 ((~![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))) | ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | ![Y: $i] : ((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)) | p54(Y)))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(114,plain,
% 0.58/0.64 ((~![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | ![Y: $i] : ((~r1(X, Y)) | p54(Y)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | ![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.58/0.64 tff(115,plain,
% 0.58/0.64 (![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[114, 108, 89])).
% 0.58/0.64 tff(116,plain,
% 0.58/0.64 (((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))),
% 0.58/0.64 inference(tautology,[status(thm)],[])).
% 0.58/0.64 tff(117,plain,
% 0.58/0.64 (~p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[116, 87])).
% 0.58/0.64 tff(118,plain,
% 0.58/0.64 (^[Y: $i] : refl(((~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_23(X))) | p54(tptp_fun_Y_23(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_23(X))) | p54(tptp_fun_Y_23(X)))))))))),
% 0.58/0.64 inference(bind,[status(th)],[])).
% 0.58/0.64 tff(119,plain,
% 0.58/0.64 (![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_23(X))) | p54(tptp_fun_Y_23(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_23(X))) | p54(tptp_fun_Y_23(X))))))))),
% 0.58/0.64 inference(quant_intro,[status(thm)],[118])).
% 0.58/0.64 tff(120,plain,
% 0.58/0.64 (^[Y: $i] : rewrite(((~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_23(X))) | p54(tptp_fun_Y_23(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_23(X))) | p54(tptp_fun_Y_23(X)))))))))),
% 0.58/0.64 inference(bind,[status(th)],[])).
% 0.58/0.64 tff(121,plain,
% 0.58/0.64 (![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_23(X))) | p54(tptp_fun_Y_23(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_23(X))) | p54(tptp_fun_Y_23(X))))))))),
% 0.58/0.64 inference(quant_intro,[status(thm)],[120])).
% 0.58/0.64 tff(122,plain,
% 0.58/0.64 (![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_23(X))) | p54(tptp_fun_Y_23(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_23(X))) | p54(tptp_fun_Y_23(X))))))))),
% 0.58/0.64 inference(transitivity,[status(thm)],[121, 119])).
% 0.58/0.64 tff(123,plain,
% 0.58/0.64 (![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_23(X))) | p54(tptp_fun_Y_23(X))))))))),
% 0.58/0.64 inference(and_elim,[status(thm)],[12])).
% 0.58/0.64 tff(124,plain,
% 0.58/0.64 (![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_23(X))) | p54(tptp_fun_Y_23(X))))))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.58/0.64 tff(125,plain,
% 0.58/0.64 (((~![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_23(X))) | p54(tptp_fun_Y_23(X))))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(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_23(X))) | p54(tptp_fun_Y_23(X))))))))) | (~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(126,plain,
% 0.58/0.64 ((~![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_23(X))) | p54(tptp_fun_Y_23(X))))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(127,plain,
% 0.58/0.64 ((~![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_23(X))) | p54(tptp_fun_Y_23(X))))))))) | (~r1(X!0, Y!3)) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.58/0.64 tff(128,plain,
% 0.58/0.64 (![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[127, 17, 124])).
% 0.58/0.64 tff(129,plain,
% 0.58/0.64 (((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(130,plain,
% 0.58/0.64 ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) | ((~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(131,plain,
% 0.58/0.64 ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))))) | (~r1(Y!3, tptp_fun_X_8(Y!3))) | ![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.58/0.64 tff(132,plain,
% 0.58/0.64 (![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[131, 128, 29])).
% 0.58/0.64 tff(133,plain,
% 0.58/0.64 (((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))) | ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(134,plain,
% 0.58/0.64 (((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))))) <=> ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(135,plain,
% 0.58/0.64 (((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))) | ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))) | ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[134])).
% 0.58/0.64 tff(136,plain,
% 0.58/0.64 (((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))) | ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X))))),
% 0.58/0.64 inference(transitivity,[status(thm)],[135, 133])).
% 0.58/0.64 tff(137,plain,
% 0.58/0.64 ((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))) | ((~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(138,plain,
% 0.58/0.64 ((~![Y: $i] : ((~r1(tptp_fun_X_8(Y!3), Y)) | ![X: $i] : ((~r1(Y, X)) | p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X))))))) | (~r1(tptp_fun_X_8(Y!3), tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | ![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.58/0.64 tff(139,plain,
% 0.58/0.64 (![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[138, 77, 132])).
% 0.58/0.64 tff(140,plain,
% 0.58/0.64 (((~![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))) | ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))))) <=> ((~![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(141,plain,
% 0.58/0.64 ((p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) <=> ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(142,plain,
% 0.58/0.64 ((~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) <=> (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(143,plain,
% 0.58/0.64 ((p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) <=> (p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[142])).
% 0.58/0.64 tff(144,plain,
% 0.58/0.64 ((p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) <=> ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))))),
% 0.58/0.64 inference(transitivity,[status(thm)],[143, 141])).
% 0.58/0.64 tff(145,plain,
% 0.58/0.64 (((~![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))) | (p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) <=> ((~![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))) | ((~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[144])).
% 0.58/0.64 tff(146,plain,
% 0.58/0.64 (((~![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))) | (p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) <=> ((~![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))))),
% 0.58/0.64 inference(transitivity,[status(thm)],[145, 140])).
% 0.58/0.64 tff(147,plain,
% 0.58/0.64 ((~![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))) | (p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(148,plain,
% 0.58/0.64 ((~![X: $i] : (p41(X) | (~((~r1(X, tptp_fun_Y_23(X))) | p54(tptp_fun_Y_23(X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), X)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_8(Y!3)), tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | p41(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))) | (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.58/0.64 tff(149,plain,
% 0.58/0.64 (~((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[148, 139, 89, 117])).
% 0.58/0.64 tff(150,plain,
% 0.58/0.64 (((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | (~p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(151,plain,
% 0.59/0.65 (~p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.59/0.65 tff(152,plain,
% 0.59/0.65 (((~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))) | r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(153,plain,
% 0.59/0.65 (r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.59/0.65 tff(154,plain,
% 0.59/0.65 (((~![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)))) | (p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))) <=> ((~![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(155,plain,
% 0.59/0.65 ((~![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)))) | (p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3)))))))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(156,plain,
% 0.59/0.65 ((~![Y: $i] : (p54(Y) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), Y)))) | p54(tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))) | (~r1(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))), tptp_fun_Y_23(tptp_fun_X_19(tptp_fun_Y_11(tptp_fun_X_8(Y!3))))))),
% 0.59/0.65 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.59/0.65 tff(157,plain,
% 0.59/0.65 ($false),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[156, 153, 151, 115])).
% 0.59/0.65 % SZS output end Proof
%------------------------------------------------------------------------------