%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL672+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:34 PM UTC 2026
% Result : Theorem 13.19s 13.44s
% Output : Proof 13.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL672+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.34 % Computer : n027.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 4 20:30:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 13.19/13.44 % SZS status Theorem
% 13.19/13.44 % SZS output start Proof
% 13.19/13.44 tff(p1_type, type, (
% 13.19/13.44 p1: $i > $o)).
% 13.19/13.44 tff(tptp_fun_Y_6_type, type, (
% 13.19/13.44 tptp_fun_Y_6: $i > $i)).
% 13.19/13.44 tff(tptp_fun_X_22_type, type, (
% 13.19/13.44 tptp_fun_X_22: $i)).
% 13.19/13.44 tff(r1_type, type, (
% 13.19/13.44 r1: ( $i * $i ) > $o)).
% 13.19/13.44 tff(tptp_fun_X_17_type, type, (
% 13.19/13.44 tptp_fun_X_17: $i)).
% 13.19/13.44 tff(tptp_fun_Y_14_type, type, (
% 13.19/13.44 tptp_fun_Y_14: $i)).
% 13.19/13.44 tff(tptp_fun_Y_8_type, type, (
% 13.19/13.44 tptp_fun_Y_8: $i)).
% 13.19/13.44 tff(p2_type, type, (
% 13.19/13.44 p2: $i > $o)).
% 13.19/13.44 tff(tptp_fun_X_10_type, type, (
% 13.19/13.44 tptp_fun_X_10: $i)).
% 13.19/13.44 tff(tptp_fun_Y_25_type, type, (
% 13.19/13.44 tptp_fun_Y_25: $i > $i)).
% 13.19/13.44 tff(tptp_fun_X_0_type, type, (
% 13.19/13.44 tptp_fun_X_0: $i)).
% 13.19/13.44 tff(tptp_fun_X_24_type, type, (
% 13.19/13.44 tptp_fun_X_24: $i > $i)).
% 13.19/13.44 tff(tptp_fun_X_4_type, type, (
% 13.19/13.44 tptp_fun_X_4: $i > $i)).
% 13.19/13.44 tff(tptp_fun_X_23_type, type, (
% 13.19/13.44 tptp_fun_X_23: $i > $i)).
% 13.19/13.44 tff(tptp_fun_Y_20_type, type, (
% 13.19/13.44 tptp_fun_Y_20: $i)).
% 13.19/13.44 tff(tptp_fun_X_21_type, type, (
% 13.19/13.44 tptp_fun_X_21: $i)).
% 13.19/13.44 tff(tptp_fun_Y_19_type, type, (
% 13.19/13.44 tptp_fun_Y_19: $i)).
% 13.19/13.44 tff(tptp_fun_Y_18_type, type, (
% 13.19/13.44 tptp_fun_Y_18: $i)).
% 13.19/13.44 tff(tptp_fun_X_16_type, type, (
% 13.19/13.44 tptp_fun_X_16: $i)).
% 13.19/13.44 tff(tptp_fun_X_15_type, type, (
% 13.19/13.44 tptp_fun_X_15: $i)).
% 13.19/13.44 tff(tptp_fun_X_11_type, type, (
% 13.19/13.44 tptp_fun_X_11: $i)).
% 13.19/13.44 tff(tptp_fun_Y_13_type, type, (
% 13.19/13.44 tptp_fun_Y_13: $i)).
% 13.19/13.44 tff(tptp_fun_Y_12_type, type, (
% 13.19/13.44 tptp_fun_Y_12: $i)).
% 13.19/13.44 tff(tptp_fun_X_9_type, type, (
% 13.19/13.44 tptp_fun_X_9: $i)).
% 13.19/13.44 tff(tptp_fun_X_7_type, type, (
% 13.19/13.44 tptp_fun_X_7: $i > $i)).
% 13.19/13.44 tff(tptp_fun_Y_5_type, type, (
% 13.19/13.44 tptp_fun_Y_5: $i > $i)).
% 13.19/13.44 tff(tptp_fun_Y_3_type, type, (
% 13.19/13.44 tptp_fun_Y_3: $i > $i)).
% 13.19/13.44 tff(tptp_fun_Y_2_type, type, (
% 13.19/13.44 tptp_fun_Y_2: $i)).
% 13.19/13.44 tff(tptp_fun_Y_1_type, type, (
% 13.19/13.44 tptp_fun_Y_1: $i)).
% 13.19/13.44 tff(1,assumption,(![X: $i] : (p2(X) | (~r1(Y!8, X)))), introduced(assumption)).
% 13.19/13.44 tff(2,plain,
% 13.19/13.44 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))))),
% 13.19/13.45 inference(rewrite,[status(thm)],[])).
% 13.19/13.45 tff(3,plain,
% 13.19/13.45 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))),
% 13.19/13.45 inference(rewrite,[status(thm)],[])).
% 13.19/13.45 tff(4,plain,
% 13.19/13.45 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | p1(Y)) <=> (p1(Y) | (~r1(X!0, Y))))),
% 13.19/13.45 inference(bind,[status(th)],[])).
% 13.19/13.45 tff(5,plain,
% 13.19/13.45 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 13.19/13.45 inference(quant_intro,[status(thm)],[4])).
% 13.19/13.46 tff(6,plain,
% 13.19/13.46 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))))),
% 13.19/13.46 inference(bind,[status(th)],[])).
% 13.19/13.46 tff(7,plain,
% 13.19/13.46 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))),
% 13.19/13.46 inference(quant_intro,[status(thm)],[6])).
% 13.19/13.46 tff(8,plain,
% 13.19/13.46 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.19/13.46 inference(monotonicity,[status(thm)],[7, 5])).
% 13.19/13.46 tff(9,plain,
% 13.19/13.46 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))),
% 13.19/13.46 inference(transitivity,[status(thm)],[8, 3])).
% 13.19/13.46 tff(10,plain,
% 13.19/13.46 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))),
% 13.19/13.46 inference(rewrite,[status(thm)],[])).
% 13.19/13.46 tff(11,plain,
% 13.19/13.46 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))),
% 13.19/13.46 inference(bind,[status(th)],[])).
% 13.19/13.46 tff(12,plain,
% 13.19/13.46 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))),
% 13.19/13.46 inference(quant_intro,[status(thm)],[11])).
% 13.19/13.46 tff(13,plain,
% 13.19/13.46 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.19/13.46 inference(monotonicity,[status(thm)],[12, 5])).
% 13.19/13.46 tff(14,plain,
% 13.19/13.46 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))),
% 13.19/13.46 inference(transitivity,[status(thm)],[13, 10])).
% 13.19/13.46 tff(15,plain,
% 13.19/13.46 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))))),
% 13.19/13.46 inference(rewrite,[status(thm)],[])).
% 13.19/13.46 tff(16,plain,
% 13.19/13.46 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) <=> ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) <=> ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), ((![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))), rewrite((![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), ((![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))))),
% 13.19/13.47 inference(bind,[status(th)],[])).
% 13.19/13.47 tff(17,plain,
% 13.19/13.47 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))),
% 13.19/13.47 inference(quant_intro,[status(thm)],[16])).
% 13.19/13.47 tff(18,plain,
% 13.19/13.47 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.19/13.48 inference(monotonicity,[status(thm)],[17, 5])).
% 13.19/13.48 tff(19,plain,
% 13.19/13.48 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))))),
% 13.19/13.48 inference(transitivity,[status(thm)],[18, 15])).
% 13.19/13.48 tff(20,plain,
% 13.19/13.48 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))),
% 13.19/13.48 inference(rewrite,[status(thm)],[])).
% 13.19/13.48 tff(21,plain,
% 13.19/13.48 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) <=> ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) <=> ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), ((![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))), rewrite((![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), ((![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))),
% 13.19/13.48 inference(bind,[status(th)],[])).
% 13.19/13.48 tff(22,plain,
% 13.19/13.48 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))),
% 13.19/13.48 inference(quant_intro,[status(thm)],[21])).
% 13.19/13.48 tff(23,plain,
% 13.19/13.48 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.19/13.48 inference(monotonicity,[status(thm)],[22, 5])).
% 13.19/13.48 tff(24,plain,
% 13.19/13.48 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))),
% 13.19/13.48 inference(transitivity,[status(thm)],[23, 20])).
% 13.19/13.48 tff(25,plain,
% 13.19/13.48 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))))),
% 13.19/13.48 inference(rewrite,[status(thm)],[])).
% 13.19/13.48 tff(26,plain,
% 13.19/13.48 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))), (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))))),
% 13.19/13.49 inference(bind,[status(th)],[])).
% 13.19/13.49 tff(27,plain,
% 13.19/13.49 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))),
% 13.19/13.49 inference(quant_intro,[status(thm)],[26])).
% 13.19/13.49 tff(28,plain,
% 13.19/13.49 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.19/13.49 inference(monotonicity,[status(thm)],[27, 5])).
% 13.19/13.49 tff(29,plain,
% 13.19/13.49 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))))),
% 13.19/13.49 inference(transitivity,[status(thm)],[28, 25])).
% 13.19/13.49 tff(30,plain,
% 13.19/13.49 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))),
% 13.19/13.49 inference(rewrite,[status(thm)],[])).
% 13.19/13.49 tff(31,plain,
% 13.19/13.49 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))), (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))),
% 13.19/13.50 inference(bind,[status(th)],[])).
% 13.19/13.50 tff(32,plain,
% 13.19/13.50 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.29/13.50 inference(quant_intro,[status(thm)],[31])).
% 13.29/13.50 tff(33,plain,
% 13.29/13.50 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.50 inference(monotonicity,[status(thm)],[32, 5])).
% 13.29/13.50 tff(34,plain,
% 13.29/13.50 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))),
% 13.29/13.50 inference(transitivity,[status(thm)],[33, 30])).
% 13.29/13.50 tff(35,plain,
% 13.29/13.50 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))))),
% 13.29/13.50 inference(rewrite,[status(thm)],[])).
% 13.29/13.50 tff(36,plain,
% 13.29/13.50 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X))) <=> ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ((~r1(Y, X)) | ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), rewrite(((~r1(Y, X)) | ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) <=> ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))))),
% 13.29/13.50 inference(bind,[status(th)],[])).
% 13.29/13.50 tff(37,plain,
% 13.29/13.50 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))),
% 13.29/13.51 inference(quant_intro,[status(thm)],[36])).
% 13.29/13.51 tff(38,plain,
% 13.29/13.51 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.51 inference(monotonicity,[status(thm)],[37, 5])).
% 13.29/13.51 tff(39,plain,
% 13.29/13.51 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))))),
% 13.29/13.51 inference(transitivity,[status(thm)],[38, 35])).
% 13.29/13.51 tff(40,plain,
% 13.29/13.51 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))),
% 13.29/13.51 inference(rewrite,[status(thm)],[])).
% 13.29/13.51 tff(41,plain,
% 13.29/13.51 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X))) <=> ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ((~r1(Y, X)) | ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), rewrite(((~r1(Y, X)) | ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) <=> ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))),
% 13.29/13.51 inference(bind,[status(th)],[])).
% 13.29/13.51 tff(42,plain,
% 13.29/13.51 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))),
% 13.29/13.51 inference(quant_intro,[status(thm)],[41])).
% 13.29/13.51 tff(43,plain,
% 13.29/13.51 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.51 inference(monotonicity,[status(thm)],[42, 5])).
% 13.29/13.51 tff(44,plain,
% 13.29/13.51 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))),
% 13.29/13.51 inference(transitivity,[status(thm)],[43, 40])).
% 13.29/13.51 tff(45,plain,
% 13.29/13.51 ((r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.51 inference(rewrite,[status(thm)],[])).
% 13.29/13.51 tff(46,plain,
% 13.29/13.51 ((r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.51 inference(rewrite,[status(thm)],[])).
% 13.29/13.51 tff(47,plain,
% 13.29/13.51 ((r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.51 inference(rewrite,[status(thm)],[])).
% 13.29/13.51 tff(48,plain,
% 13.29/13.51 ((r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.51 inference(rewrite,[status(thm)],[])).
% 13.29/13.51 tff(49,plain,
% 13.29/13.51 ((r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.52 inference(rewrite,[status(thm)],[])).
% 13.29/13.52 tff(50,plain,
% 13.29/13.52 ((r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y))) <=> (r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.52 inference(rewrite,[status(thm)],[])).
% 13.29/13.52 tff(51,plain,
% 13.29/13.52 ((~((~r1(Y!20, X!21)) | p1(X!21))) <=> (~((~r1(Y!20, X!21)) | p1(X!21)))),
% 13.29/13.52 inference(rewrite,[status(thm)],[])).
% 13.29/13.52 tff(52,plain,
% 13.29/13.52 ((r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))) <=> (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 13.29/13.52 inference(monotonicity,[status(thm)],[51, 50])).
% 13.29/13.52 tff(53,plain,
% 13.29/13.52 ((r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))) <=> (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.52 inference(transitivity,[status(thm)],[52, 49])).
% 13.29/13.52 tff(54,plain,
% 13.29/13.52 ((~((~r1(X!17, Y!18)) | p1(Y!18))) <=> (~((~r1(X!17, Y!18)) | p1(Y!18)))),
% 13.29/13.52 inference(rewrite,[status(thm)],[])).
% 13.29/13.52 tff(55,plain,
% 13.29/13.52 ((r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y))))) <=> (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 13.29/13.52 inference(monotonicity,[status(thm)],[54, 53])).
% 13.29/13.52 tff(56,plain,
% 13.29/13.52 ((r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y))))) <=> (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.52 inference(transitivity,[status(thm)],[55, 48])).
% 13.29/13.52 tff(57,plain,
% 13.29/13.52 ((~((~r1(Y!14, X!15)) | p1(X!15))) <=> (~((~r1(Y!14, X!15)) | p1(X!15)))),
% 13.29/13.52 inference(rewrite,[status(thm)],[])).
% 13.29/13.52 tff(58,plain,
% 13.29/13.52 ((r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))) <=> (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 13.29/13.52 inference(monotonicity,[status(thm)],[57, 56])).
% 13.29/13.52 tff(59,plain,
% 13.29/13.52 ((r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))) <=> (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.52 inference(transitivity,[status(thm)],[58, 47])).
% 13.29/13.52 tff(60,plain,
% 13.29/13.52 ((~((~r1(X!11, Y!12)) | p1(Y!12))) <=> (~((~r1(X!11, Y!12)) | p1(Y!12)))),
% 13.29/13.52 inference(rewrite,[status(thm)],[])).
% 13.29/13.52 tff(61,plain,
% 13.29/13.52 ((r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y))))))) <=> (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 13.29/13.52 inference(monotonicity,[status(thm)],[60, 59])).
% 13.29/13.52 tff(62,plain,
% 13.29/13.52 ((r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y))))))) <=> (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.52 inference(transitivity,[status(thm)],[61, 46])).
% 13.29/13.52 tff(63,plain,
% 13.29/13.52 ((~((~r1(Y!8, X!9)) | p1(X!9))) <=> (~((~r1(Y!8, X!9)) | p1(X!9)))),
% 13.29/13.52 inference(rewrite,[status(thm)],[])).
% 13.29/13.52 tff(64,plain,
% 13.29/13.52 ((r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 13.29/13.52 inference(monotonicity,[status(thm)],[63, 62])).
% 13.29/13.52 tff(65,plain,
% 13.29/13.52 ((r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.29/13.52 inference(transitivity,[status(thm)],[64, 45])).
% 13.29/13.52 tff(66,plain,
% 13.29/13.52 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))))),
% 13.29/13.53 inference(rewrite,[status(thm)],[])).
% 13.29/13.53 tff(67,plain,
% 13.29/13.53 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))))),
% 13.29/13.53 inference(bind,[status(th)],[])).
% 13.29/13.53 tff(68,plain,
% 13.29/13.53 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))),
% 13.29/13.53 inference(quant_intro,[status(thm)],[67])).
% 13.29/13.53 tff(69,plain,
% 13.29/13.53 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.54 inference(monotonicity,[status(thm)],[68, 5])).
% 13.29/13.54 tff(70,plain,
% 13.29/13.54 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))))),
% 13.29/13.54 inference(transitivity,[status(thm)],[69, 66])).
% 13.29/13.54 tff(71,plain,
% 13.29/13.54 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))),
% 13.29/13.54 inference(rewrite,[status(thm)],[])).
% 13.29/13.54 tff(72,plain,
% 13.29/13.54 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))),
% 13.29/13.54 inference(bind,[status(th)],[])).
% 13.29/13.54 tff(73,plain,
% 13.29/13.54 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))),
% 13.29/13.54 inference(quant_intro,[status(thm)],[72])).
% 13.29/13.54 tff(74,plain,
% 13.29/13.54 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.54 inference(monotonicity,[status(thm)],[73, 5])).
% 13.29/13.54 tff(75,plain,
% 13.29/13.54 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))),
% 13.29/13.54 inference(transitivity,[status(thm)],[74, 71])).
% 13.29/13.54 tff(76,plain,
% 13.29/13.54 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.54 inference(rewrite,[status(thm)],[])).
% 13.29/13.54 tff(77,plain,
% 13.29/13.54 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.54 inference(monotonicity,[status(thm)],[5])).
% 13.29/13.54 tff(78,plain,
% 13.29/13.54 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.54 inference(transitivity,[status(thm)],[77, 76])).
% 13.29/13.54 tff(79,plain,
% 13.29/13.54 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))))),
% 13.29/13.54 inference(rewrite,[status(thm)],[])).
% 13.29/13.54 tff(80,plain,
% 13.29/13.54 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) <=> ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))), rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))))),
% 13.29/13.56 inference(bind,[status(th)],[])).
% 13.29/13.56 tff(81,plain,
% 13.29/13.56 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))),
% 13.29/13.56 inference(quant_intro,[status(thm)],[80])).
% 13.29/13.56 tff(82,plain,
% 13.29/13.56 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.56 inference(monotonicity,[status(thm)],[81, 5])).
% 13.29/13.56 tff(83,plain,
% 13.29/13.56 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))))),
% 13.29/13.56 inference(transitivity,[status(thm)],[82, 79])).
% 13.29/13.56 tff(84,plain,
% 13.29/13.56 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))))),
% 13.29/13.56 inference(rewrite,[status(thm)],[])).
% 13.29/13.56 tff(85,plain,
% 13.29/13.56 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))), (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))))),
% 13.29/13.57 inference(bind,[status(th)],[])).
% 13.29/13.57 tff(86,plain,
% 13.29/13.57 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))),
% 13.29/13.57 inference(quant_intro,[status(thm)],[85])).
% 13.29/13.57 tff(87,plain,
% 13.29/13.57 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.57 inference(monotonicity,[status(thm)],[86, 5])).
% 13.29/13.57 tff(88,plain,
% 13.29/13.57 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))))),
% 13.29/13.58 inference(transitivity,[status(thm)],[87, 84])).
% 13.29/13.58 tff(89,plain,
% 13.29/13.58 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 13.29/13.58 inference(rewrite,[status(thm)],[])).
% 13.29/13.58 tff(90,plain,
% 13.29/13.58 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) <=> ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))), rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))),
% 13.29/13.58 inference(bind,[status(th)],[])).
% 13.29/13.58 tff(91,plain,
% 13.29/13.58 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 13.29/13.58 inference(quant_intro,[status(thm)],[90])).
% 13.29/13.58 tff(92,plain,
% 13.29/13.58 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.58 inference(monotonicity,[status(thm)],[91, 5])).
% 13.29/13.58 tff(93,plain,
% 13.29/13.58 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 13.29/13.58 inference(transitivity,[status(thm)],[92, 89])).
% 13.29/13.58 tff(94,plain,
% 13.29/13.58 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))),
% 13.29/13.58 inference(rewrite,[status(thm)],[])).
% 13.29/13.58 tff(95,plain,
% 13.29/13.58 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))), (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))),
% 13.29/13.59 inference(bind,[status(th)],[])).
% 13.29/13.59 tff(96,plain,
% 13.29/13.59 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))),
% 13.29/13.59 inference(quant_intro,[status(thm)],[95])).
% 13.29/13.59 tff(97,plain,
% 13.29/13.59 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.59 inference(monotonicity,[status(thm)],[96, 5])).
% 13.29/13.59 tff(98,plain,
% 13.29/13.59 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))))),
% 13.29/13.59 inference(transitivity,[status(thm)],[97, 94])).
% 13.29/13.59 tff(99,plain,
% 13.29/13.59 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 13.29/13.59 inference(rewrite,[status(thm)],[])).
% 13.29/13.59 tff(100,plain,
% 13.29/13.59 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) <=> ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))), rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 13.29/13.59 inference(bind,[status(th)],[])).
% 13.29/13.59 tff(101,plain,
% 13.29/13.59 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))),
% 13.29/13.59 inference(quant_intro,[status(thm)],[100])).
% 13.29/13.59 tff(102,plain,
% 13.29/13.59 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.59 inference(monotonicity,[status(thm)],[101, 5])).
% 13.29/13.59 tff(103,plain,
% 13.29/13.59 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 13.29/13.59 inference(transitivity,[status(thm)],[102, 99])).
% 13.29/13.59 tff(104,plain,
% 13.29/13.59 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 13.29/13.59 inference(rewrite,[status(thm)],[])).
% 13.29/13.59 tff(105,plain,
% 13.29/13.59 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 13.29/13.59 inference(bind,[status(th)],[])).
% 13.29/13.59 tff(106,plain,
% 13.29/13.59 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 13.29/13.59 inference(quant_intro,[status(thm)],[105])).
% 13.29/13.60 tff(107,plain,
% 13.29/13.60 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.29/13.60 inference(monotonicity,[status(thm)],[106, 5])).
% 13.29/13.60 tff(108,plain,
% 13.29/13.60 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 13.29/13.60 inference(transitivity,[status(thm)],[107, 104])).
% 13.29/13.60 tff(109,plain,
% 13.29/13.60 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))))),
% 13.29/13.60 inference(rewrite,[status(thm)],[])).
% 13.29/13.60 tff(110,plain,
% 13.29/13.60 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) <=> ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) <=> ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), ((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))) | (~p1(Y))))), rewrite((![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), ((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), rewrite(((~r1(X, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) <=> ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))))),
% 13.39/13.61 inference(bind,[status(th)],[])).
% 13.39/13.61 tff(111,plain,
% 13.39/13.61 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))),
% 13.39/13.61 inference(quant_intro,[status(thm)],[110])).
% 13.39/13.61 tff(112,plain,
% 13.39/13.61 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.39/13.61 inference(monotonicity,[status(thm)],[111, 5])).
% 13.39/13.61 tff(113,plain,
% 13.39/13.61 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))))),
% 13.39/13.61 inference(transitivity,[status(thm)],[112, 109])).
% 13.39/13.61 tff(114,plain,
% 13.39/13.61 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))),
% 13.39/13.61 inference(rewrite,[status(thm)],[])).
% 13.39/13.61 tff(115,plain,
% 13.39/13.61 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) <=> ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) <=> ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), ((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))) | (~p1(Y))))), rewrite((![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), ((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), rewrite(((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))),
% 13.39/13.61 inference(bind,[status(th)],[])).
% 13.39/13.61 tff(116,plain,
% 13.39/13.61 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))),
% 13.39/13.61 inference(quant_intro,[status(thm)],[115])).
% 13.39/13.61 tff(117,plain,
% 13.39/13.61 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.39/13.61 inference(monotonicity,[status(thm)],[116, 5])).
% 13.39/13.61 tff(118,plain,
% 13.39/13.61 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))),
% 13.39/13.61 inference(transitivity,[status(thm)],[117, 114])).
% 13.39/13.61 tff(119,plain,
% 13.39/13.61 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.39/13.61 inference(rewrite,[status(thm)],[])).
% 13.39/13.61 tff(120,plain,
% 13.39/13.61 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) <=> ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) <=> ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), ((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))) | (~p1(Y))))), rewrite((![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), ((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), rewrite(((~r1(X, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) <=> ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))),
% 13.39/13.62 inference(bind,[status(th)],[])).
% 13.39/13.62 tff(121,plain,
% 13.39/13.62 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))),
% 13.39/13.62 inference(quant_intro,[status(thm)],[120])).
% 13.39/13.62 tff(122,plain,
% 13.39/13.62 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.39/13.62 inference(monotonicity,[status(thm)],[121, 5])).
% 13.39/13.62 tff(123,plain,
% 13.39/13.62 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.39/13.62 inference(transitivity,[status(thm)],[122, 119])).
% 13.39/13.62 tff(124,plain,
% 13.39/13.62 ((~((~r1(X!0, Y!1)) | p1(Y!1))) <=> (~((~r1(X!0, Y!1)) | p1(Y!1)))),
% 13.39/13.62 inference(rewrite,[status(thm)],[])).
% 13.39/13.62 tff(125,plain,
% 13.39/13.62 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y)))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))))),
% 13.39/13.63 inference(monotonicity,[status(thm)],[124, 123, 118, 113, 108, 103, 98, 93, 88, 83, 78, 75, 70, 65, 44, 39, 34, 29, 24, 19, 14, 9])).
% 13.39/13.63 tff(126,plain,
% 13.39/13.63 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y)))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))))),
% 13.39/13.65 inference(transitivity,[status(thm)],[125, 2])).
% 13.39/13.65 tff(127,plain,
% 13.39/13.65 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : 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((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | 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((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))),
% 13.39/13.66 inference(rewrite,[status(thm)],[])).
% 13.39/13.66 tff(128,plain,
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(p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | 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(~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : 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(~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))),
% 13.39/13.67 inference(rewrite,[status(thm)],[])).
% 13.39/13.67 tff(129,plain,
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(~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | 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p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : 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Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : 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((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 13.39/13.69 inference(rewrite,[status(thm)],[])).
% 13.39/13.69 tff(130,plain,
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p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : 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Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : 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(p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 13.49/13.70 inference(monotonicity,[status(thm)],[129])).
% 13.49/13.70 tff(131,plain,
% 13.49/13.70 ((~(~?[X: $i] : (~(((((((((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | 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p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : 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| p2(X))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : 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Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, 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X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))),
% 13.49/13.71 inference(transitivity,[status(thm)],[130, 128])).
% 13.49/13.71 tff(132,axiom,(~(~?[X: $i] : (~(((((((((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : 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((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
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(p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))),
% 13.49/13.73 inference(modus_ponens,[status(thm)],[132, 131])).
% 13.49/13.73 tff(134,plain,
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(p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))),
% 13.49/13.73 inference(modus_ponens,[status(thm)],[133, 127])).
% 13.49/13.73 tff(135,plain,
% 13.49/13.73 ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X), X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))),
% 13.49/13.74 inference(modus_ponens,[status(thm)],[134, 126])).
% 13.49/13.74 tff(136,plain,
% 13.49/13.74 (~(p2(X!10) | (~r1(Y!8, X!10)))),
% 13.49/13.74 inference(and_elim,[status(thm)],[135])).
% 13.49/13.74 tff(137,plain,
% 13.49/13.74 (r1(Y!8, X!10)),
% 13.49/13.74 inference(or_elim,[status(thm)],[136])).
% 13.49/13.74 tff(138,plain,
% 13.49/13.74 (~p2(X!10)),
% 13.49/13.74 inference(or_elim,[status(thm)],[136])).
% 13.49/13.74 tff(139,plain,
% 13.49/13.74 (((~![X: $i] : (p2(X) | (~r1(Y!8, X)))) | (p2(X!10) | (~r1(Y!8, X!10)))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!8, X)))) | p2(X!10) | (~r1(Y!8, X!10)))),
% 13.49/13.74 inference(rewrite,[status(thm)],[])).
% 13.49/13.74 tff(140,plain,
% 13.49/13.74 ((~![X: $i] : (p2(X) | (~r1(Y!8, X)))) | (p2(X!10) | (~r1(Y!8, X!10)))),
% 13.49/13.74 inference(quant_inst,[status(thm)],[])).
% 13.49/13.74 tff(141,plain,
% 13.49/13.74 ((~![X: $i] : (p2(X) | (~r1(Y!8, X)))) | p2(X!10) | (~r1(Y!8, X!10))),
% 13.49/13.74 inference(modus_ponens,[status(thm)],[140, 139])).
% 13.49/13.74 tff(142,plain,
% 13.49/13.74 ($false),
% 13.49/13.74 inference(unit_resolution,[status(thm)],[141, 138, 137, 1])).
% 13.49/13.74 tff(143,plain,(~![X: $i] : (p2(X) | (~r1(Y!8, X)))), inference(lemma,lemma(discharge,[]))).
% 13.49/13.74 tff(144,assumption,(![X: $i] : (p1(X) | (~r1(Y!8, X)))), introduced(assumption)).
% 13.49/13.74 tff(145,plain,
% 13.49/13.74 (~((~r1(Y!8, X!9)) | p1(X!9))),
% 13.49/13.74 inference(and_elim,[status(thm)],[135])).
% 13.49/13.74 tff(146,plain,
% 13.49/13.74 (~p1(X!9)),
% 13.49/13.74 inference(or_elim,[status(thm)],[145])).
% 13.49/13.74 tff(147,plain,
% 13.49/13.74 (r1(Y!8, X!9)),
% 13.49/13.74 inference(or_elim,[status(thm)],[145])).
% 13.49/13.74 tff(148,plain,
% 13.49/13.74 (((~![X: $i] : (p1(X) | (~r1(Y!8, X)))) | (p1(X!9) | (~r1(Y!8, X!9)))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!8, X)))) | p1(X!9) | (~r1(Y!8, X!9)))),
% 13.49/13.74 inference(rewrite,[status(thm)],[])).
% 13.49/13.74 tff(149,plain,
% 13.49/13.74 ((~![X: $i] : (p1(X) | (~r1(Y!8, X)))) | (p1(X!9) | (~r1(Y!8, X!9)))),
% 13.49/13.74 inference(quant_inst,[status(thm)],[])).
% 13.49/13.74 tff(150,plain,
% 13.49/13.74 ((~![X: $i] : (p1(X) | (~r1(Y!8, X)))) | p1(X!9) | (~r1(Y!8, X!9))),
% 13.49/13.74 inference(modus_ponens,[status(thm)],[149, 148])).
% 13.49/13.74 tff(151,plain,
% 13.49/13.74 ($false),
% 13.49/13.74 inference(unit_resolution,[status(thm)],[150, 147, 146, 144])).
% 13.49/13.74 tff(152,plain,(~![X: $i] : (p1(X) | (~r1(Y!8, X)))), inference(lemma,lemma(discharge,[]))).
% 13.49/13.74 tff(153,assumption,(![Y: $i] : (p2(Y) | (~r1(X!0, Y)))), introduced(assumption)).
% 13.49/13.74 tff(154,plain,
% 13.49/13.74 (~(p2(Y!2) | (~r1(X!0, Y!2)))),
% 13.49/13.74 inference(and_elim,[status(thm)],[135])).
% 13.49/13.74 tff(155,plain,
% 13.49/13.74 (r1(X!0, Y!2)),
% 13.49/13.74 inference(or_elim,[status(thm)],[154])).
% 13.49/13.74 tff(156,plain,
% 13.49/13.74 (~p2(Y!2)),
% 13.49/13.74 inference(or_elim,[status(thm)],[154])).
% 13.49/13.74 tff(157,plain,
% 13.49/13.74 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(Y!2) | (~r1(X!0, Y!2)))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(Y!2) | (~r1(X!0, Y!2)))),
% 13.49/13.74 inference(rewrite,[status(thm)],[])).
% 13.49/13.74 tff(158,plain,
% 13.49/13.74 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(Y!2) | (~r1(X!0, Y!2)))),
% 13.49/13.74 inference(quant_inst,[status(thm)],[])).
% 13.49/13.74 tff(159,plain,
% 13.49/13.74 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(Y!2) | (~r1(X!0, Y!2))),
% 13.49/13.74 inference(modus_ponens,[status(thm)],[158, 157])).
% 13.49/13.74 tff(160,plain,
% 13.49/13.74 ($false),
% 13.49/13.74 inference(unit_resolution,[status(thm)],[159, 156, 155, 153])).
% 13.49/13.74 tff(161,plain,(~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))), inference(lemma,lemma(discharge,[]))).
% 13.49/13.74 tff(162,assumption,(![Y: $i] : (p1(Y) | (~r1(X!0, Y)))), introduced(assumption)).
% 13.49/13.74 tff(163,plain,
% 13.49/13.74 (~((~r1(X!0, Y!1)) | p1(Y!1))),
% 13.49/13.74 inference(and_elim,[status(thm)],[135])).
% 13.49/13.74 tff(164,plain,
% 13.49/13.74 (~p1(Y!1)),
% 13.49/13.74 inference(or_elim,[status(thm)],[163])).
% 13.49/13.74 tff(165,plain,
% 13.49/13.74 (r1(X!0, Y!1)),
% 13.49/13.74 inference(or_elim,[status(thm)],[163])).
% 13.49/13.74 tff(166,plain,
% 13.49/13.74 (((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | (p1(Y!1) | (~r1(X!0, Y!1)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | p1(Y!1) | (~r1(X!0, Y!1)))),
% 13.49/13.74 inference(rewrite,[status(thm)],[])).
% 13.49/13.74 tff(167,plain,
% 13.49/13.74 ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | (p1(Y!1) | (~r1(X!0, Y!1)))),
% 13.49/13.74 inference(quant_inst,[status(thm)],[])).
% 13.49/13.74 tff(168,plain,
% 13.49/13.74 ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | p1(Y!1) | (~r1(X!0, Y!1))),
% 13.49/13.74 inference(modus_ponens,[status(thm)],[167, 166])).
% 13.49/13.74 tff(169,plain,
% 13.49/13.74 ($false),
% 13.49/13.74 inference(unit_resolution,[status(thm)],[168, 165, 164, 162])).
% 13.49/13.74 tff(170,plain,(~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))), inference(lemma,lemma(discharge,[]))).
% 13.49/13.74 tff(171,plain,
% 13.49/13.74 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))),
% 13.49/13.74 inference(rewrite,[status(thm)],[])).
% 13.49/13.74 tff(172,plain,
% 13.49/13.74 (^[Y: $i] : rewrite((![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))),
% 13.49/13.74 inference(bind,[status(th)],[])).
% 13.49/13.74 tff(173,plain,
% 13.49/13.74 (![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(quant_intro,[status(thm)],[172])).
% 13.49/13.75 tff(174,plain,
% 13.49/13.75 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))),
% 13.49/13.75 inference(monotonicity,[status(thm)],[173])).
% 13.49/13.75 tff(175,plain,
% 13.49/13.75 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))),
% 13.49/13.75 inference(transitivity,[status(thm)],[174, 171])).
% 13.49/13.75 tff(176,plain,
% 13.49/13.75 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))),
% 13.49/13.75 inference(rewrite,[status(thm)],[])).
% 13.49/13.75 tff(177,plain,
% 13.49/13.75 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(and_elim,[status(thm)],[135])).
% 13.49/13.75 tff(178,plain,
% 13.49/13.75 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(modus_ponens,[status(thm)],[177, 176])).
% 13.49/13.75 tff(179,plain,
% 13.49/13.75 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(modus_ponens,[status(thm)],[178, 175])).
% 13.49/13.75 tff(180,plain,
% 13.49/13.75 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(unit_resolution,[status(thm)],[179, 170, 161])).
% 13.49/13.75 tff(181,plain,
% 13.49/13.75 (r1(X!0, Y!8)),
% 13.49/13.75 inference(and_elim,[status(thm)],[135])).
% 13.49/13.75 tff(182,plain,
% 13.49/13.75 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : (p1(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : (p1(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(rewrite,[status(thm)],[])).
% 13.49/13.75 tff(183,plain,
% 13.49/13.75 (((~r1(X!0, Y!8)) | ![X: $i] : (p1(X) | (~r1(Y!8, X))) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) <=> ((~r1(X!0, Y!8)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : (p1(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(rewrite,[status(thm)],[])).
% 13.49/13.75 tff(184,plain,
% 13.49/13.75 (^[X: $i] : rewrite(((~r1(Y!8, X)) | p1(X)) <=> (p1(X) | (~r1(Y!8, X))))),
% 13.49/13.75 inference(bind,[status(th)],[])).
% 13.49/13.75 tff(185,plain,
% 13.49/13.75 (![X: $i] : ((~r1(Y!8, X)) | p1(X)) <=> ![X: $i] : (p1(X) | (~r1(Y!8, X)))),
% 13.49/13.75 inference(quant_intro,[status(thm)],[184])).
% 13.49/13.75 tff(186,plain,
% 13.49/13.75 (((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) <=> ((~r1(X!0, Y!8)) | ![X: $i] : (p1(X) | (~r1(Y!8, X))) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(monotonicity,[status(thm)],[185])).
% 13.49/13.75 tff(187,plain,
% 13.49/13.75 (((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) <=> ((~r1(X!0, Y!8)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : (p1(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(transitivity,[status(thm)],[186, 183])).
% 13.49/13.75 tff(188,plain,
% 13.49/13.75 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : (p1(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))))),
% 13.49/13.75 inference(monotonicity,[status(thm)],[187])).
% 13.49/13.75 tff(189,plain,
% 13.49/13.75 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : (p1(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(transitivity,[status(thm)],[188, 182])).
% 13.49/13.75 tff(190,plain,
% 13.49/13.75 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))),
% 13.49/13.75 inference(quant_inst,[status(thm)],[])).
% 13.49/13.75 tff(191,plain,
% 13.49/13.75 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : (p1(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))),
% 13.49/13.75 inference(modus_ponens,[status(thm)],[190, 189])).
% 13.49/13.75 tff(192,plain,
% 13.49/13.75 (![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : (p1(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))),
% 13.49/13.75 inference(unit_resolution,[status(thm)],[191, 181, 180])).
% 13.49/13.75 tff(193,plain,
% 13.49/13.75 (![X: $i] : (p2(X) | (~r1(Y!8, X))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))),
% 13.49/13.75 inference(unit_resolution,[status(thm)],[192, 152])).
% 13.49/13.75 tff(194,plain,
% 13.49/13.75 (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))),
% 13.49/13.75 inference(unit_resolution,[status(thm)],[193, 143])).
% 13.49/13.75 tff(195,plain,
% 13.49/13.75 (r1(X!11, Y!14)),
% 13.49/13.75 inference(and_elim,[status(thm)],[135])).
% 13.49/13.75 tff(196,plain,
% 13.49/13.75 (r1(Y!8, X!11)),
% 13.49/13.75 inference(and_elim,[status(thm)],[135])).
% 13.49/13.75 tff(197,plain,
% 13.49/13.75 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 13.49/13.75 inference(rewrite,[status(thm)],[])).
% 13.49/13.75 tff(198,plain,
% 13.49/13.75 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(X, Y) & r1(Y, Z)) <=> (~((~r1(Y, Z)) | (~r1(X, Y))))), ((~(r1(X, Y) & r1(Y, Z))) <=> (~(~((~r1(Y, Z)) | (~r1(X, Y))))))), rewrite((~(~((~r1(Y, Z)) | (~r1(X, Y))))) <=> ((~r1(Y, Z)) | (~r1(X, Y)))), ((~(r1(X, Y) & r1(Y, Z))) <=> ((~r1(Y, Z)) | (~r1(X, Y))))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)))), rewrite((((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))))),
% 13.49/13.75 inference(bind,[status(th)],[])).
% 13.49/13.75 tff(199,plain,
% 13.49/13.75 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 13.49/13.75 inference(quant_intro,[status(thm)],[198])).
% 13.49/13.75 tff(200,plain,
% 13.49/13.75 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 13.49/13.75 inference(rewrite,[status(thm)],[])).
% 13.49/13.75 tff(201,plain,
% 13.49/13.75 (^[X: $i, Y: $i, Z: $i] : rewrite(((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)))),
% 13.49/13.75 inference(bind,[status(th)],[])).
% 13.49/13.75 tff(202,plain,
% 13.49/13.75 (![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 13.49/13.75 inference(quant_intro,[status(thm)],[201])).
% 13.49/13.75 tff(203,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity')).
% 13.49/13.75 tff(204,plain,
% 13.49/13.75 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 13.49/13.75 inference(modus_ponens,[status(thm)],[203, 202])).
% 13.49/13.75 tff(205,plain,
% 13.49/13.75 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 13.49/13.75 inference(modus_ponens,[status(thm)],[204, 200])).
% 13.49/13.75 tff(206,plain,(
% 13.49/13.75 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 13.49/13.75 inference(skolemize,[status(sab)],[205])).
% 13.49/13.75 tff(207,plain,
% 13.49/13.75 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 13.49/13.75 inference(modus_ponens,[status(thm)],[206, 199])).
% 13.49/13.75 tff(208,plain,
% 13.49/13.75 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 13.49/13.75 inference(modus_ponens,[status(thm)],[207, 197])).
% 13.49/13.75 tff(209,plain,
% 13.49/13.75 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, X!11)) | (~r1(X!11, Y!14)) | r1(Y!8, Y!14))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!11)) | (~r1(X!11, Y!14)) | r1(Y!8, Y!14))),
% 13.49/13.75 inference(rewrite,[status(thm)],[])).
% 13.49/13.75 tff(210,plain,
% 13.49/13.75 ((r1(Y!8, Y!14) | (~r1(X!11, Y!14)) | (~r1(Y!8, X!11))) <=> ((~r1(Y!8, X!11)) | (~r1(X!11, Y!14)) | r1(Y!8, Y!14))),
% 13.49/13.75 inference(rewrite,[status(thm)],[])).
% 13.49/13.75 tff(211,plain,
% 13.49/13.75 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, Y!14) | (~r1(X!11, Y!14)) | (~r1(Y!8, X!11)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!8, X!11)) | (~r1(X!11, Y!14)) | r1(Y!8, Y!14)))),
% 13.49/13.75 inference(monotonicity,[status(thm)],[210])).
% 13.49/13.75 tff(212,plain,
% 13.49/13.75 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, Y!14) | (~r1(X!11, Y!14)) | (~r1(Y!8, X!11)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!11)) | (~r1(X!11, Y!14)) | r1(Y!8, Y!14))),
% 13.49/13.75 inference(transitivity,[status(thm)],[211, 209])).
% 13.49/13.75 tff(213,plain,
% 13.49/13.75 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!8, Y!14) | (~r1(X!11, Y!14)) | (~r1(Y!8, X!11)))),
% 13.49/13.75 inference(quant_inst,[status(thm)],[])).
% 13.49/13.75 tff(214,plain,
% 13.49/13.75 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!8, X!11)) | (~r1(X!11, Y!14)) | r1(Y!8, Y!14)),
% 13.49/13.75 inference(modus_ponens,[status(thm)],[213, 212])).
% 13.49/13.75 tff(215,plain,
% 13.49/13.75 (r1(Y!8, Y!14)),
% 13.49/13.75 inference(unit_resolution,[status(thm)],[214, 208, 196, 195])).
% 13.49/13.75 tff(216,plain,
% 13.49/13.75 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) | ((~r1(Y!8, Y!14)) | ![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) | (~r1(Y!8, Y!14)) | ![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(217,plain,
% 13.49/13.76 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) | ((~r1(Y!8, Y!14)) | ![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))),
% 13.49/13.76 inference(quant_inst,[status(thm)],[])).
% 13.49/13.76 tff(218,plain,
% 13.49/13.76 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))) | (~r1(Y!8, Y!14)) | ![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))),
% 13.49/13.76 inference(modus_ponens,[status(thm)],[217, 216])).
% 13.49/13.76 tff(219,plain,
% 13.49/13.76 (![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[218, 215, 194])).
% 13.49/13.76 tff(220,assumption,(![X: $i] : (p1(X) | (~r1(X!17, X)))), introduced(assumption)).
% 13.49/13.76 tff(221,plain,
% 13.49/13.76 (~((~r1(X!17, Y!18)) | p1(Y!18))),
% 13.49/13.76 inference(and_elim,[status(thm)],[135])).
% 13.49/13.76 tff(222,plain,
% 13.49/13.76 (~p1(Y!18)),
% 13.49/13.76 inference(or_elim,[status(thm)],[221])).
% 13.49/13.76 tff(223,plain,
% 13.49/13.76 (r1(X!17, Y!18)),
% 13.49/13.76 inference(or_elim,[status(thm)],[221])).
% 13.49/13.76 tff(224,plain,
% 13.49/13.76 (((~![X: $i] : (p1(X) | (~r1(X!17, X)))) | (p1(Y!18) | (~r1(X!17, Y!18)))) <=> ((~![X: $i] : (p1(X) | (~r1(X!17, X)))) | p1(Y!18) | (~r1(X!17, Y!18)))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(225,plain,
% 13.49/13.76 ((~![X: $i] : (p1(X) | (~r1(X!17, X)))) | (p1(Y!18) | (~r1(X!17, Y!18)))),
% 13.49/13.76 inference(quant_inst,[status(thm)],[])).
% 13.49/13.76 tff(226,plain,
% 13.49/13.76 ((~![X: $i] : (p1(X) | (~r1(X!17, X)))) | p1(Y!18) | (~r1(X!17, Y!18))),
% 13.49/13.76 inference(modus_ponens,[status(thm)],[225, 224])).
% 13.49/13.76 tff(227,plain,
% 13.49/13.76 ($false),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[226, 223, 222, 220])).
% 13.49/13.76 tff(228,plain,(~![X: $i] : (p1(X) | (~r1(X!17, X)))), inference(lemma,lemma(discharge,[]))).
% 13.49/13.76 tff(229,plain,
% 13.49/13.76 (r1(Y!14, X!17)),
% 13.49/13.76 inference(and_elim,[status(thm)],[135])).
% 13.49/13.76 tff(230,plain,
% 13.49/13.76 (((~![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ((~r1(Y!14, X!17)) | ![X: $i] : (p1(X) | (~r1(X!17, X))) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | (~r1(Y!14, X!17)) | ![X: $i] : (p1(X) | (~r1(X!17, X))) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(231,plain,
% 13.49/13.76 (((~r1(Y!14, X!17)) | ![X: $i] : (p1(X) | (~r1(X!17, X))) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> ((~r1(Y!14, X!17)) | ![X: $i] : (p1(X) | (~r1(X!17, X))) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(232,plain,
% 13.49/13.76 (^[X: $i] : rewrite(((~r1(X!17, X)) | p1(X)) <=> (p1(X) | (~r1(X!17, X))))),
% 13.49/13.76 inference(bind,[status(th)],[])).
% 13.49/13.76 tff(233,plain,
% 13.49/13.76 (![X: $i] : ((~r1(X!17, X)) | p1(X)) <=> ![X: $i] : (p1(X) | (~r1(X!17, X)))),
% 13.49/13.76 inference(quant_intro,[status(thm)],[232])).
% 13.49/13.76 tff(234,plain,
% 13.49/13.76 (((~r1(Y!14, X!17)) | ![X: $i] : ((~r1(X!17, X)) | p1(X)) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> ((~r1(Y!14, X!17)) | ![X: $i] : (p1(X) | (~r1(X!17, X))) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))),
% 13.49/13.76 inference(monotonicity,[status(thm)],[233])).
% 13.49/13.76 tff(235,plain,
% 13.49/13.76 (((~r1(Y!14, X!17)) | ![X: $i] : ((~r1(X!17, X)) | p1(X)) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) <=> ((~r1(Y!14, X!17)) | ![X: $i] : (p1(X) | (~r1(X!17, X))) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))),
% 13.49/13.76 inference(transitivity,[status(thm)],[234, 231])).
% 13.49/13.76 tff(236,plain,
% 13.49/13.76 (((~![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ((~r1(Y!14, X!17)) | ![X: $i] : ((~r1(X!17, X)) | p1(X)) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ((~r1(Y!14, X!17)) | ![X: $i] : (p1(X) | (~r1(X!17, X))) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))))),
% 13.49/13.76 inference(monotonicity,[status(thm)],[235])).
% 13.49/13.76 tff(237,plain,
% 13.49/13.76 (((~![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ((~r1(Y!14, X!17)) | ![X: $i] : ((~r1(X!17, X)) | p1(X)) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) <=> ((~![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | (~r1(Y!14, X!17)) | ![X: $i] : (p1(X) | (~r1(X!17, X))) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))),
% 13.49/13.76 inference(transitivity,[status(thm)],[236, 230])).
% 13.49/13.76 tff(238,plain,
% 13.49/13.76 ((~![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | ((~r1(Y!14, X!17)) | ![X: $i] : ((~r1(X!17, X)) | p1(X)) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))),
% 13.49/13.76 inference(quant_inst,[status(thm)],[])).
% 13.49/13.76 tff(239,plain,
% 13.49/13.76 ((~![Y: $i] : ((~r1(Y!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X))))))) | (~r1(Y!14, X!17)) | ![X: $i] : (p1(X) | (~r1(X!17, X))) | ![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))),
% 13.49/13.76 inference(modus_ponens,[status(thm)],[238, 237])).
% 13.49/13.76 tff(240,plain,
% 13.49/13.76 (![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[239, 229, 228, 219])).
% 13.49/13.76 tff(241,plain,
% 13.49/13.76 (r1(Y!20, X!22)),
% 13.49/13.76 inference(and_elim,[status(thm)],[135])).
% 13.49/13.76 tff(242,plain,
% 13.49/13.76 (r1(X!17, Y!20)),
% 13.49/13.76 inference(and_elim,[status(thm)],[135])).
% 13.49/13.76 tff(243,plain,
% 13.49/13.76 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!17, Y!20)) | (~r1(Y!20, X!22)) | r1(X!17, X!22))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!17, Y!20)) | (~r1(Y!20, X!22)) | r1(X!17, X!22))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(244,plain,
% 13.49/13.76 ((r1(X!17, X!22) | (~r1(Y!20, X!22)) | (~r1(X!17, Y!20))) <=> ((~r1(X!17, Y!20)) | (~r1(Y!20, X!22)) | r1(X!17, X!22))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(245,plain,
% 13.49/13.76 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!17, X!22) | (~r1(Y!20, X!22)) | (~r1(X!17, Y!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!17, Y!20)) | (~r1(Y!20, X!22)) | r1(X!17, X!22)))),
% 13.49/13.76 inference(monotonicity,[status(thm)],[244])).
% 13.49/13.76 tff(246,plain,
% 13.49/13.76 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!17, X!22) | (~r1(Y!20, X!22)) | (~r1(X!17, Y!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!17, Y!20)) | (~r1(Y!20, X!22)) | r1(X!17, X!22))),
% 13.49/13.76 inference(transitivity,[status(thm)],[245, 243])).
% 13.49/13.76 tff(247,plain,
% 13.49/13.76 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!17, X!22) | (~r1(Y!20, X!22)) | (~r1(X!17, Y!20)))),
% 13.49/13.76 inference(quant_inst,[status(thm)],[])).
% 13.49/13.76 tff(248,plain,
% 13.49/13.76 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!17, Y!20)) | (~r1(Y!20, X!22)) | r1(X!17, X!22)),
% 13.49/13.76 inference(modus_ponens,[status(thm)],[247, 246])).
% 13.49/13.76 tff(249,plain,
% 13.49/13.76 (r1(X!17, X!22)),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[248, 208, 242, 241])).
% 13.49/13.76 tff(250,plain,
% 13.49/13.76 (((~![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | ((~r1(X!17, X!22)) | (~((~r1(X!22, tptp_fun_Y_6(X!22))) | p1(tptp_fun_Y_6(X!22)))))) <=> ((~![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | (~r1(X!17, X!22)) | (~((~r1(X!22, tptp_fun_Y_6(X!22))) | p1(tptp_fun_Y_6(X!22)))))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(251,plain,
% 13.49/13.76 ((~![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | ((~r1(X!17, X!22)) | (~((~r1(X!22, tptp_fun_Y_6(X!22))) | p1(tptp_fun_Y_6(X!22)))))),
% 13.49/13.76 inference(quant_inst,[status(thm)],[])).
% 13.49/13.76 tff(252,plain,
% 13.49/13.76 ((~![X: $i] : ((~r1(X!17, X)) | (~((~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_Y_6(X)))))) | (~r1(X!17, X!22)) | (~((~r1(X!22, tptp_fun_Y_6(X!22))) | p1(tptp_fun_Y_6(X!22))))),
% 13.49/13.76 inference(modus_ponens,[status(thm)],[251, 250])).
% 13.49/13.76 tff(253,plain,
% 13.49/13.76 (~((~r1(X!22, tptp_fun_Y_6(X!22))) | p1(tptp_fun_Y_6(X!22)))),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[252, 249, 240])).
% 13.49/13.76 tff(254,plain,
% 13.49/13.76 (((~r1(X!22, tptp_fun_Y_6(X!22))) | p1(tptp_fun_Y_6(X!22))) | (~p1(tptp_fun_Y_6(X!22)))),
% 13.49/13.76 inference(tautology,[status(thm)],[])).
% 13.49/13.76 tff(255,plain,
% 13.49/13.76 (~p1(tptp_fun_Y_6(X!22))),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[254, 253])).
% 13.49/13.76 tff(256,plain,
% 13.49/13.76 (((~r1(X!22, tptp_fun_Y_6(X!22))) | p1(tptp_fun_Y_6(X!22))) | r1(X!22, tptp_fun_Y_6(X!22))),
% 13.49/13.76 inference(tautology,[status(thm)],[])).
% 13.49/13.76 tff(257,plain,
% 13.49/13.76 (r1(X!22, tptp_fun_Y_6(X!22))),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[256, 253])).
% 13.49/13.76 tff(258,assumption,(~(p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))))), introduced(assumption)).
% 13.49/13.76 tff(259,plain,
% 13.49/13.76 ((p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22))))) | (~p1(tptp_fun_X_4(tptp_fun_X_7(X!22))))),
% 13.49/13.76 inference(tautology,[status(thm)],[])).
% 13.49/13.76 tff(260,plain,
% 13.49/13.76 (~p1(tptp_fun_X_4(tptp_fun_X_7(X!22)))),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[259, 258])).
% 13.49/13.76 tff(261,plain,
% 13.49/13.76 (^[Y: $i] : refl((p1(Y) | (~r1(X!22, Y))) <=> (p1(Y) | (~r1(X!22, Y))))),
% 13.49/13.76 inference(bind,[status(th)],[])).
% 13.49/13.76 tff(262,plain,
% 13.49/13.76 (![Y: $i] : (p1(Y) | (~r1(X!22, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 13.49/13.76 inference(quant_intro,[status(thm)],[261])).
% 13.49/13.76 tff(263,plain,
% 13.49/13.76 (![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 13.49/13.76 inference(and_elim,[status(thm)],[135])).
% 13.49/13.76 tff(264,plain,
% 13.49/13.76 (![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 13.49/13.76 inference(modus_ponens,[status(thm)],[263, 262])).
% 13.49/13.76 tff(265,plain,
% 13.49/13.76 (((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | (p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22)))))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(266,plain,
% 13.49/13.76 ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | (p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22)))))),
% 13.49/13.76 inference(quant_inst,[status(thm)],[])).
% 13.49/13.76 tff(267,plain,
% 13.49/13.76 ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22))))),
% 13.49/13.76 inference(modus_ponens,[status(thm)],[266, 265])).
% 13.49/13.76 tff(268,plain,
% 13.49/13.76 (~r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22)))),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[267, 264, 260])).
% 13.49/13.76 tff(269,plain,
% 13.49/13.76 ((p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22))))) | r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))),
% 13.49/13.76 inference(tautology,[status(thm)],[])).
% 13.49/13.76 tff(270,plain,
% 13.49/13.76 (r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[269, 258])).
% 13.49/13.76 tff(271,plain,
% 13.49/13.76 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(272,plain,
% 13.49/13.76 ((r1(Y!14, Y!20) | (~r1(X!17, Y!20)) | (~r1(Y!14, X!17))) <=> ((~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(273,plain,
% 13.49/13.76 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, Y!20) | (~r1(X!17, Y!20)) | (~r1(Y!14, X!17)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20)))),
% 13.49/13.76 inference(monotonicity,[status(thm)],[272])).
% 13.49/13.76 tff(274,plain,
% 13.49/13.76 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, Y!20) | (~r1(X!17, Y!20)) | (~r1(Y!14, X!17)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20))),
% 13.49/13.76 inference(transitivity,[status(thm)],[273, 271])).
% 13.49/13.76 tff(275,plain,
% 13.49/13.76 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, Y!20) | (~r1(X!17, Y!20)) | (~r1(Y!14, X!17)))),
% 13.49/13.76 inference(quant_inst,[status(thm)],[])).
% 13.49/13.76 tff(276,plain,
% 13.49/13.76 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20)),
% 13.49/13.76 inference(modus_ponens,[status(thm)],[275, 274])).
% 13.49/13.76 tff(277,plain,
% 13.49/13.76 (r1(Y!14, Y!20)),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[276, 208, 229, 242])).
% 13.49/13.76 tff(278,plain,
% 13.49/13.76 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(279,plain,
% 13.49/13.76 ((r1(Y!14, X!22) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20))) <=> ((~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(280,plain,
% 13.49/13.76 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, X!22) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22)))),
% 13.49/13.76 inference(monotonicity,[status(thm)],[279])).
% 13.49/13.76 tff(281,plain,
% 13.49/13.76 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, X!22) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22))),
% 13.49/13.76 inference(transitivity,[status(thm)],[280, 278])).
% 13.49/13.76 tff(282,plain,
% 13.49/13.76 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, X!22) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)))),
% 13.49/13.76 inference(quant_inst,[status(thm)],[])).
% 13.49/13.76 tff(283,plain,
% 13.49/13.76 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22)),
% 13.49/13.76 inference(modus_ponens,[status(thm)],[282, 281])).
% 13.49/13.76 tff(284,plain,
% 13.49/13.76 (r1(Y!14, X!22)),
% 13.49/13.76 inference(unit_resolution,[status(thm)],[283, 208, 241, 277])).
% 13.49/13.76 tff(285,plain,
% 13.49/13.76 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.76 tff(286,plain,
% 13.49/13.76 ((r1(X!0, X!11) | (~r1(Y!8, X!11)) | (~r1(X!0, Y!8))) <=> ((~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11))),
% 13.49/13.76 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(287,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!11) | (~r1(Y!8, X!11)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11)))),
% 13.49/13.77 inference(monotonicity,[status(thm)],[286])).
% 13.49/13.77 tff(288,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!11) | (~r1(Y!8, X!11)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11))),
% 13.49/13.77 inference(transitivity,[status(thm)],[287, 285])).
% 13.49/13.77 tff(289,plain,
% 13.49/13.77 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!11) | (~r1(Y!8, X!11)) | (~r1(X!0, Y!8)))),
% 13.49/13.77 inference(quant_inst,[status(thm)],[])).
% 13.49/13.77 tff(290,plain,
% 13.49/13.77 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11)),
% 13.49/13.77 inference(modus_ponens,[status(thm)],[289, 288])).
% 13.49/13.77 tff(291,plain,
% 13.49/13.77 (r1(X!0, X!11)),
% 13.49/13.77 inference(unit_resolution,[status(thm)],[290, 208, 181, 196])).
% 13.49/13.77 tff(292,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(293,plain,
% 13.49/13.77 ((r1(X!0, Y!14) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11))) <=> ((~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(294,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!14) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14)))),
% 13.49/13.77 inference(monotonicity,[status(thm)],[293])).
% 13.49/13.77 tff(295,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!14) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14))),
% 13.49/13.77 inference(transitivity,[status(thm)],[294, 292])).
% 13.49/13.77 tff(296,plain,
% 13.49/13.77 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!14) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)))),
% 13.49/13.77 inference(quant_inst,[status(thm)],[])).
% 13.49/13.77 tff(297,plain,
% 13.49/13.77 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14)),
% 13.49/13.77 inference(modus_ponens,[status(thm)],[296, 295])).
% 13.49/13.77 tff(298,plain,
% 13.49/13.77 (r1(X!0, Y!14)),
% 13.49/13.77 inference(unit_resolution,[status(thm)],[297, 208, 195, 291])).
% 13.49/13.77 tff(299,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22)))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(300,plain,
% 13.49/13.77 ((r1(X!0, X!22) | (~r1(Y!14, X!22)) | (~r1(X!0, Y!14))) <=> ((~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22)))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(301,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!22) | (~r1(Y!14, X!22)) | (~r1(X!0, Y!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22))))),
% 13.49/13.77 inference(monotonicity,[status(thm)],[300])).
% 13.49/13.77 tff(302,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!22) | (~r1(Y!14, X!22)) | (~r1(X!0, Y!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22)))),
% 13.49/13.77 inference(transitivity,[status(thm)],[301, 299])).
% 13.49/13.77 tff(303,plain,
% 13.49/13.77 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!22) | (~r1(Y!14, X!22)) | (~r1(X!0, Y!14)))),
% 13.49/13.77 inference(quant_inst,[status(thm)],[])).
% 13.49/13.77 tff(304,plain,
% 13.49/13.77 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22))),
% 13.49/13.77 inference(modus_ponens,[status(thm)],[303, 302])).
% 13.49/13.77 tff(305,plain,
% 13.49/13.77 (r1(X!0, X!22)),
% 13.49/13.77 inference(unit_resolution,[status(thm)],[304, 208, 298, 284])).
% 13.49/13.77 tff(306,plain,
% 13.49/13.77 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(307,plain,
% 13.49/13.77 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(308,plain,
% 13.49/13.77 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 13.49/13.77 inference(and_elim,[status(thm)],[135])).
% 13.49/13.77 tff(309,plain,
% 13.49/13.77 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 13.49/13.77 inference(modus_ponens,[status(thm)],[308, 307])).
% 13.49/13.77 tff(310,plain,
% 13.49/13.77 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 13.49/13.77 inference(modus_ponens,[status(thm)],[309, 306])).
% 13.49/13.77 tff(311,plain,
% 13.49/13.77 (![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 13.49/13.77 inference(unit_resolution,[status(thm)],[310, 170, 161])).
% 13.49/13.77 tff(312,plain,
% 13.49/13.77 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!22)) | r1(X!22, tptp_fun_X_7(X!22)))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!22)) | r1(X!22, tptp_fun_X_7(X!22)))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(313,plain,
% 13.49/13.77 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!22)) | r1(X!22, tptp_fun_X_7(X!22)))),
% 13.49/13.77 inference(quant_inst,[status(thm)],[])).
% 13.49/13.77 tff(314,plain,
% 13.49/13.77 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!22)) | r1(X!22, tptp_fun_X_7(X!22))),
% 13.49/13.77 inference(modus_ponens,[status(thm)],[313, 312])).
% 13.49/13.77 tff(315,plain,
% 13.49/13.77 (r1(X!22, tptp_fun_X_7(X!22))),
% 13.49/13.77 inference(unit_resolution,[status(thm)],[314, 311, 305])).
% 13.49/13.77 tff(316,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22))))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(317,plain,
% 13.49/13.77 ((r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | (~r1(X!22, tptp_fun_X_7(X!22)))) <=> ((~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22))))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(318,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | (~r1(X!22, tptp_fun_X_7(X!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22)))))),
% 13.49/13.77 inference(monotonicity,[status(thm)],[317])).
% 13.49/13.77 tff(319,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | (~r1(X!22, tptp_fun_X_7(X!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22))))),
% 13.49/13.77 inference(transitivity,[status(thm)],[318, 316])).
% 13.49/13.77 tff(320,plain,
% 13.49/13.77 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | (~r1(X!22, tptp_fun_X_7(X!22))))),
% 13.49/13.77 inference(quant_inst,[status(thm)],[])).
% 13.49/13.77 tff(321,plain,
% 13.49/13.77 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_4(tptp_fun_X_7(X!22)))),
% 13.49/13.77 inference(modus_ponens,[status(thm)],[320, 319])).
% 13.49/13.77 tff(322,plain,
% 13.49/13.77 ($false),
% 13.49/13.77 inference(unit_resolution,[status(thm)],[321, 208, 315, 270, 268])).
% 13.49/13.77 tff(323,plain,(p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22))))), inference(lemma,lemma(discharge,[]))).
% 13.49/13.77 tff(324,assumption,(![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))), introduced(assumption)).
% 13.49/13.77 tff(325,plain,
% 13.49/13.77 (((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~(p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))))))) <=> ((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~(p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))))))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(326,plain,
% 13.49/13.77 (((~r1(X!22, tptp_fun_X_7(X!22))) | (~((~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_4(tptp_fun_X_7(X!22)))))) <=> ((~r1(X!22, tptp_fun_X_7(X!22))) | (~(p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))))))),
% 13.49/13.77 inference(rewrite,[status(thm)],[])).
% 13.49/13.77 tff(327,plain,
% 13.49/13.77 (((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~((~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_4(tptp_fun_X_7(X!22))))))) <=> ((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~(p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22))))))))),
% 13.49/13.77 inference(monotonicity,[status(thm)],[326])).
% 13.49/13.77 tff(328,plain,
% 13.49/13.77 (((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~((~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_4(tptp_fun_X_7(X!22))))))) <=> ((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~(p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))))))),
% 13.49/13.77 inference(transitivity,[status(thm)],[327, 325])).
% 13.49/13.77 tff(329,plain,
% 13.49/13.77 ((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~((~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_4(tptp_fun_X_7(X!22))))))),
% 13.49/13.77 inference(quant_inst,[status(thm)],[])).
% 13.49/13.77 tff(330,plain,
% 13.49/13.77 ((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~(p1(tptp_fun_X_4(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_4(tptp_fun_X_7(X!22))))))),
% 13.49/13.77 inference(modus_ponens,[status(thm)],[329, 328])).
% 13.49/13.77 tff(331,plain,
% 13.49/13.77 ($false),
% 13.49/13.77 inference(unit_resolution,[status(thm)],[330, 315, 324, 323])).
% 13.49/13.77 tff(332,plain,(~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))), inference(lemma,lemma(discharge,[]))).
% 13.49/13.77 tff(333,plain,
% 13.49/13.77 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20))),
% 13.49/13.78 inference(rewrite,[status(thm)],[])).
% 13.49/13.78 tff(334,plain,
% 13.49/13.78 ((r1(X!0, Y!20) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14))) <=> ((~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20))),
% 13.49/13.78 inference(rewrite,[status(thm)],[])).
% 13.49/13.78 tff(335,plain,
% 13.49/13.78 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!20) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20)))),
% 13.49/13.78 inference(monotonicity,[status(thm)],[334])).
% 13.49/13.78 tff(336,plain,
% 13.49/13.78 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!20) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20))),
% 13.49/13.78 inference(transitivity,[status(thm)],[335, 333])).
% 13.49/13.78 tff(337,plain,
% 13.49/13.78 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!20) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)))),
% 13.49/13.78 inference(quant_inst,[status(thm)],[])).
% 13.49/13.78 tff(338,plain,
% 13.49/13.78 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20)),
% 13.49/13.78 inference(modus_ponens,[status(thm)],[337, 336])).
% 13.49/13.78 tff(339,plain,
% 13.49/13.78 (r1(X!0, Y!20)),
% 13.49/13.78 inference(unit_resolution,[status(thm)],[338, 208, 277, 298])).
% 13.49/13.78 tff(340,plain,
% 13.49/13.78 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))))),
% 13.49/13.78 inference(rewrite,[status(thm)],[])).
% 13.49/13.78 tff(341,plain,
% 13.49/13.78 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 13.49/13.78 inference(and_elim,[status(thm)],[135])).
% 13.49/13.78 tff(342,plain,
% 13.49/13.78 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 13.49/13.78 inference(modus_ponens,[status(thm)],[341, 340])).
% 13.49/13.78 tff(343,plain,
% 13.49/13.78 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 13.49/13.78 inference(unit_resolution,[status(thm)],[342, 170, 161])).
% 13.49/13.78 tff(344,plain,
% 13.49/13.78 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, Y!20)) | ![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, Y!20)) | ![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 13.49/13.78 inference(rewrite,[status(thm)],[])).
% 13.49/13.78 tff(345,plain,
% 13.49/13.78 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | ((~r1(X!0, Y!20)) | ![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))),
% 13.49/13.78 inference(quant_inst,[status(thm)],[])).
% 13.49/13.78 tff(346,plain,
% 13.49/13.78 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))))) | (~r1(X!0, Y!20)) | ![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 13.49/13.78 inference(modus_ponens,[status(thm)],[345, 344])).
% 13.49/13.78 tff(347,plain,
% 13.49/13.78 (![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 13.49/13.78 inference(unit_resolution,[status(thm)],[346, 343, 339])).
% 13.49/13.78 tff(348,plain,
% 13.49/13.78 (((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | (~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.49/13.78 inference(rewrite,[status(thm)],[])).
% 13.49/13.78 tff(349,plain,
% 13.49/13.78 (((~r1(Y!20, X!22)) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.49/13.78 inference(rewrite,[status(thm)],[])).
% 13.49/13.78 tff(350,plain,
% 13.49/13.78 (^[Y: $i] : rewrite(((~r1(X!22, Y)) | p1(Y)) <=> (p1(Y) | (~r1(X!22, Y))))),
% 13.49/13.78 inference(bind,[status(th)],[])).
% 13.49/13.78 tff(351,plain,
% 13.49/13.78 (![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 13.49/13.78 inference(quant_intro,[status(thm)],[350])).
% 13.49/13.78 tff(352,plain,
% 13.49/13.78 (((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> ((~r1(Y!20, X!22)) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 13.49/13.78 inference(monotonicity,[status(thm)],[351])).
% 13.49/13.78 tff(353,plain,
% 13.49/13.78 (((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y)))))) <=> ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.49/13.78 inference(transitivity,[status(thm)],[352, 349])).
% 13.49/13.78 tff(354,plain,
% 13.49/13.78 (((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 13.49/13.78 inference(monotonicity,[status(thm)],[353])).
% 13.49/13.78 tff(355,plain,
% 13.49/13.78 (((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) <=> ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | (~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 13.49/13.78 inference(transitivity,[status(thm)],[354, 348])).
% 13.49/13.78 tff(356,plain,
% 13.49/13.78 ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))),
% 13.59/13.81 inference(quant_inst,[status(thm)],[])).
% 13.59/13.81 tff(357,plain,
% 13.59/13.81 ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))))) | (~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 13.59/13.81 inference(modus_ponens,[status(thm)],[356, 355])).
% 13.59/13.81 tff(358,plain,
% 13.59/13.81 (![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | p1(tptp_fun_X_4(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 13.59/13.81 inference(unit_resolution,[status(thm)],[357, 241, 347])).
% 13.59/13.81 tff(359,plain,
% 13.59/13.81 (![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 13.59/13.81 inference(unit_resolution,[status(thm)],[358, 332])).
% 13.59/13.81 tff(360,plain,
% 13.59/13.81 (((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | (p1(tptp_fun_Y_6(X!22)) | (~r1(X!22, tptp_fun_Y_6(X!22))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | p1(tptp_fun_Y_6(X!22)) | (~r1(X!22, tptp_fun_Y_6(X!22))))),
% 13.59/13.81 inference(rewrite,[status(thm)],[])).
% 13.59/13.81 tff(361,plain,
% 13.59/13.81 ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | (p1(tptp_fun_Y_6(X!22)) | (~r1(X!22, tptp_fun_Y_6(X!22))))),
% 13.59/13.81 inference(quant_inst,[status(thm)],[])).
% 13.59/13.81 tff(362,plain,
% 13.59/13.81 ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | p1(tptp_fun_Y_6(X!22)) | (~r1(X!22, tptp_fun_Y_6(X!22)))),
% 13.59/13.81 inference(modus_ponens,[status(thm)],[361, 360])).
% 13.59/13.81 tff(363,plain,
% 13.59/13.81 ($false),
% 13.59/13.81 inference(unit_resolution,[status(thm)],[362, 359, 257, 255])).
% 13.59/13.81 % SZS output end Proof
% 13.59/13.84 % E exiting
%------------------------------------------------------------------------------