Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : LCL638+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : run_E %s %d THM

% Computer : n028.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 03:00:18 PM UTC 2026

% Result   : Theorem 0.38s 0.63s
% Output   : Proof 0.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem    : LCL638+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03  % Command    : run_E %s %d THM
% 0.09/0.36  % Computer : n028.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit   : 300
% 0.09/0.36  % WCLimit    : 300
% 0.09/0.36  % DateTime   : Fri Sep  4 13:49:00 UTC 2026
% 0.13/0.36  % CPUTime    : 
% 0.38/0.63  % SZS status Theorem
% 0.38/0.63  % SZS output start Proof
% 0.38/0.63  tff(r1_type, type, (
% 0.38/0.63     r1: ( $i * $i ) > $o)).
% 0.38/0.63  tff(tptp_fun_X_4_type, type, (
% 0.38/0.63     tptp_fun_X_4: $i > $i)).
% 0.38/0.63  tff(tptp_fun_Y_12_type, type, (
% 0.38/0.63     tptp_fun_Y_12: $i)).
% 0.38/0.63  tff(p1_type, type, (
% 0.38/0.63     p1: $i > $o)).
% 0.38/0.63  tff(tptp_fun_X_2_type, type, (
% 0.38/0.63     tptp_fun_X_2: $i > $i)).
% 0.38/0.63  tff(tptp_fun_X_0_type, type, (
% 0.38/0.63     tptp_fun_X_0: $i)).
% 0.38/0.63  tff(tptp_fun_Y_1_type, type, (
% 0.38/0.63     tptp_fun_Y_1: $i > $i)).
% 0.38/0.63  tff(tptp_fun_Y_13_type, type, (
% 0.38/0.63     tptp_fun_Y_13: $i > $i)).
% 0.38/0.63  tff(tptp_fun_X_11_type, type, (
% 0.38/0.63     tptp_fun_X_11: $i)).
% 0.38/0.63  tff(tptp_fun_Y_10_type, type, (
% 0.38/0.63     tptp_fun_Y_10: $i)).
% 0.38/0.63  tff(tptp_fun_X_9_type, type, (
% 0.38/0.63     tptp_fun_X_9: $i)).
% 0.38/0.63  tff(tptp_fun_Y_8_type, type, (
% 0.38/0.63     tptp_fun_Y_8: $i)).
% 0.38/0.63  tff(tptp_fun_Y_3_type, type, (
% 0.38/0.63     tptp_fun_Y_3: $i > $i)).
% 0.38/0.63  tff(tptp_fun_X_7_type, type, (
% 0.38/0.63     tptp_fun_X_7: $i > $i)).
% 0.38/0.63  tff(tptp_fun_X_6_type, type, (
% 0.38/0.63     tptp_fun_X_6: $i > $i)).
% 0.38/0.63  tff(tptp_fun_Y_5_type, type, (
% 0.38/0.63     tptp_fun_Y_5: $i > $i)).
% 0.38/0.63  tff(1,assumption,(~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))), introduced(assumption)).
% 0.38/0.63  tff(2,plain,
% 0.38/0.63      ((p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12)))) | r1(Y!12, tptp_fun_X_2(Y!12))),
% 0.38/0.63      inference(tautology,[status(thm)],[])).
% 0.38/0.63  tff(3,plain,
% 0.38/0.63      (r1(Y!12, tptp_fun_X_2(Y!12))),
% 0.38/0.63      inference(unit_resolution,[status(thm)],[2, 1])).
% 0.38/0.63  tff(4,plain,
% 0.38/0.63      ((p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12)))) | (~p1(tptp_fun_X_2(Y!12)))),
% 0.38/0.63      inference(tautology,[status(thm)],[])).
% 0.38/0.63  tff(5,plain,
% 0.38/0.63      (~p1(tptp_fun_X_2(Y!12))),
% 0.38/0.63      inference(unit_resolution,[status(thm)],[4, 1])).
% 0.38/0.63  tff(6,plain,
% 0.38/0.63      (^[X: $i] : refl((p1(X) | (~r1(Y!12, X))) <=> (p1(X) | (~r1(Y!12, X))))),
% 0.38/0.63      inference(bind,[status(th)],[])).
% 0.38/0.63  tff(7,plain,
% 0.38/0.63      (![X: $i] : (p1(X) | (~r1(Y!12, X))) <=> ![X: $i] : (p1(X) | (~r1(Y!12, X)))),
% 0.38/0.63      inference(quant_intro,[status(thm)],[6])).
% 0.38/0.63  tff(8,plain,
% 0.38/0.63      ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(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] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))) & (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_4(Y)))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(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] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_4(Y))))),
% 0.38/0.63      inference(rewrite,[status(thm)],[])).
% 0.38/0.63  tff(9,plain,
% 0.38/0.63      (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y)))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y)))))),
% 0.38/0.64      inference(bind,[status(th)],[])).
% 0.38/0.64  tff(10,plain,
% 0.38/0.64      (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y)))),
% 0.38/0.64      inference(quant_intro,[status(thm)],[9])).
% 0.38/0.64  tff(11,plain,
% 0.38/0.64      (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y)) <=> (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))) <=> ((~r1(X!0, Y)) | (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))), rewrite(((~r1(X!0, Y)) | (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y)))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))) <=> (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y)))))),
% 0.38/0.64      inference(bind,[status(th)],[])).
% 0.38/0.64  tff(12,plain,
% 0.38/0.64      (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))) <=> ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y)))),
% 0.38/0.64      inference(quant_intro,[status(thm)],[11])).
% 0.38/0.64  tff(13,plain,
% 0.38/0.64      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.38/0.64      inference(bind,[status(th)],[])).
% 0.38/0.64  tff(14,plain,
% 0.38/0.64      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.38/0.64      inference(quant_intro,[status(thm)],[13])).
% 0.38/0.64  tff(15,plain,
% 0.38/0.64      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | p1(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))),
% 0.38/0.64      inference(bind,[status(th)],[])).
% 0.38/0.64  tff(16,plain,
% 0.38/0.64      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | p1(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))),
% 0.38/0.64      inference(quant_intro,[status(thm)],[15])).
% 0.38/0.64  tff(17,plain,
% 0.38/0.64      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))),
% 0.38/0.64      inference(bind,[status(th)],[])).
% 0.38/0.64  tff(18,plain,
% 0.38/0.64      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))),
% 0.38/0.64      inference(quant_intro,[status(thm)],[17])).
% 0.38/0.64  tff(19,plain,
% 0.38/0.64      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.38/0.64      inference(bind,[status(th)],[])).
% 0.38/0.64  tff(20,plain,
% 0.38/0.64      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.38/0.64      inference(quant_intro,[status(thm)],[19])).
% 0.38/0.64  tff(21,plain,
% 0.38/0.64      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.38/0.64      inference(bind,[status(th)],[])).
% 0.38/0.64  tff(22,plain,
% 0.38/0.64      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.38/0.64      inference(quant_intro,[status(thm)],[21])).
% 0.38/0.64  tff(23,plain,
% 0.38/0.64      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | p1(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 0.38/0.64      inference(bind,[status(th)],[])).
% 0.38/0.64  tff(24,plain,
% 0.38/0.64      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | p1(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.38/0.64      inference(quant_intro,[status(thm)],[23])).
% 0.38/0.64  tff(25,plain,
% 0.38/0.64      ((r1(X!0, Y!8) & (r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.38/0.64      inference(rewrite,[status(thm)],[])).
% 0.38/0.64  tff(26,plain,
% 0.38/0.64      ((r1(Y!8, X!9) & (r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.38/0.64      inference(rewrite,[status(thm)],[])).
% 0.38/0.64  tff(27,plain,
% 0.38/0.64      ((r1(X!9, Y!10) & (r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.38/0.64      inference(rewrite,[status(thm)],[])).
% 0.38/0.64  tff(28,plain,
% 0.38/0.64      ((r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.38/0.64      inference(rewrite,[status(thm)],[])).
% 0.38/0.64  tff(29,plain,
% 0.38/0.64      (((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))) <=> ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.38/0.64      inference(rewrite,[status(thm)],[])).
% 0.38/0.64  tff(30,plain,
% 0.38/0.64      ((r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))),
% 0.38/0.64      inference(monotonicity,[status(thm)],[29])).
% 0.38/0.64  tff(31,plain,
% 0.38/0.64      ((r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.38/0.64      inference(transitivity,[status(thm)],[30, 28])).
% 0.38/0.64  tff(32,plain,
% 0.38/0.64      ((r1(X!9, Y!10) & (r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))) <=> (r1(X!9, Y!10) & (r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))),
% 0.38/0.64      inference(monotonicity,[status(thm)],[31])).
% 0.38/0.64  tff(33,plain,
% 0.38/0.64      ((r1(X!9, Y!10) & (r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))) <=> (r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.38/0.64      inference(transitivity,[status(thm)],[32, 27])).
% 0.38/0.64  tff(34,plain,
% 0.38/0.64      ((r1(Y!8, X!9) & (r1(X!9, Y!10) & (r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))))) <=> (r1(Y!8, X!9) & (r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))),
% 0.38/0.64      inference(monotonicity,[status(thm)],[33])).
% 0.38/0.64  tff(35,plain,
% 0.38/0.64      ((r1(Y!8, X!9) & (r1(X!9, Y!10) & (r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))))) <=> (r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.38/0.64      inference(transitivity,[status(thm)],[34, 26])).
% 0.38/0.64  tff(36,plain,
% 0.38/0.64      ((r1(X!0, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & (r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))))) <=> (r1(X!0, Y!8) & (r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))),
% 0.38/0.64      inference(monotonicity,[status(thm)],[35])).
% 0.38/0.64  tff(37,plain,
% 0.38/0.64      ((r1(X!0, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & (r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))))) <=> (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.38/0.64      inference(transitivity,[status(thm)],[36, 25])).
% 0.38/0.64  tff(38,plain,
% 0.38/0.64      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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))))))))))))),
% 0.38/0.64      inference(bind,[status(th)],[])).
% 0.38/0.64  tff(39,plain,
% 0.38/0.64      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![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)) | ![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(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X)))))))))))),
% 0.38/0.64      inference(quant_intro,[status(thm)],[38])).
% 0.38/0.64  tff(40,plain,
% 0.38/0.64      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(41,plain,
% 0.38/0.65      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[40])).
% 0.38/0.65  tff(42,plain,
% 0.38/0.65      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(43,plain,
% 0.38/0.65      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[42])).
% 0.38/0.65  tff(44,plain,
% 0.38/0.65      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~p1(X))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(45,plain,
% 0.38/0.65      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~p1(X))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X))))))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[44])).
% 0.38/0.65  tff(46,plain,
% 0.38/0.65      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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))))))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(47,plain,
% 0.38/0.65      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)))))))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[46])).
% 0.38/0.65  tff(48,plain,
% 0.38/0.65      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(49,plain,
% 0.38/0.65      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[48])).
% 0.38/0.65  tff(50,plain,
% 0.38/0.65      (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))) <=> (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))), rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(51,plain,
% 0.38/0.65      (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[50])).
% 0.38/0.65  tff(52,plain,
% 0.38/0.65      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(53,plain,
% 0.38/0.65      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[52])).
% 0.38/0.65  tff(54,plain,
% 0.38/0.65      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~p1(X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(55,plain,
% 0.38/0.65      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~p1(X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X))))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[54])).
% 0.38/0.65  tff(56,plain,
% 0.38/0.65      (^[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)))))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(57,plain,
% 0.38/0.65      (![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)))))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[56])).
% 0.38/0.65  tff(58,plain,
% 0.38/0.65      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(59,plain,
% 0.38/0.65      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[58])).
% 0.38/0.65  tff(60,plain,
% 0.38/0.65      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))))),
% 0.38/0.65      inference(bind,[status(th)],[])).
% 0.38/0.65  tff(61,plain,
% 0.38/0.65      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.38/0.65      inference(quant_intro,[status(thm)],[60])).
% 0.38/0.65  tff(62,plain,
% 0.38/0.65      ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~p1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~p1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))))) & (r1(X!0, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & (r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | p1(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | p1(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_4(Y)))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(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] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))) & (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_4(Y))))),
% 0.38/0.66      inference(monotonicity,[status(thm)],[61, 59, 57, 55, 53, 51, 49, 47, 45, 43, 41, 39, 37, 24, 22, 20, 18, 16, 14, 12, 10])).
% 0.38/0.66  tff(63,plain,
% 0.38/0.66      ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~p1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~p1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))))) & (r1(X!0, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & (r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | p1(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | p1(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_4(Y)))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(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] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_4(Y))))),
% 0.38/0.67      inference(transitivity,[status(thm)],[62, 8])).
% 0.38/0.67  tff(64,plain,
% 0.38/0.67      (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))),
% 0.38/0.67      inference(rewrite,[status(thm)],[])).
% 0.38/0.67  tff(65,plain,
% 0.38/0.67      ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))),
% 0.38/0.68      inference(rewrite,[status(thm)],[])).
% 0.38/0.68  tff(66,plain,
% 0.38/0.68      ((~?[X: $i] : (~((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(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)) | (~((~![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)) | (~((~![X: $i] : ((~r1(Y, 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)) | $false))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))),
% 0.38/0.69      inference(rewrite,[status(thm)],[])).
% 0.38/0.69  tff(67,plain,
% 0.38/0.69      ((~(~?[X: $i] : (~((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(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)) | (~((~![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)) | (~((~![X: $i] : ((~r1(Y, 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)) | $false))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))))),
% 0.38/0.70      inference(monotonicity,[status(thm)],[66])).
% 0.44/0.70  tff(68,plain,
% 0.44/0.70      ((~(~?[X: $i] : (~((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(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)) | (~((~![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)) | (~((~![X: $i] : ((~r1(Y, 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)) | $false))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))),
% 0.44/0.71      inference(transitivity,[status(thm)],[67, 65])).
% 0.44/0.71  tff(69,axiom,(~(~?[X: $i] : (~((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(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)) | (~((~![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)) | (~((~![X: $i] : ((~r1(Y, 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)) | $false))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.44/0.71  tff(70,plain,
% 0.44/0.71      (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))),
% 0.44/0.72      inference(modus_ponens,[status(thm)],[69, 68])).
% 0.44/0.72  tff(71,plain,
% 0.44/0.72      (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))),
% 0.44/0.72      inference(modus_ponens,[status(thm)],[70, 64])).
% 0.44/0.72  tff(72,plain,
% 0.44/0.72      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(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] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_5(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_5(X), X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_3(X))) | (~r1(X, tptp_fun_Y_3(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_4(Y)))),
% 0.44/0.72      inference(modus_ponens,[status(thm)],[71, 63])).
% 0.44/0.72  tff(73,plain,
% 0.44/0.72      (![X: $i] : (p1(X) | (~r1(Y!12, X)))),
% 0.44/0.72      inference(and_elim,[status(thm)],[72])).
% 0.44/0.72  tff(74,plain,
% 0.44/0.72      (![X: $i] : (p1(X) | (~r1(Y!12, X)))),
% 0.44/0.72      inference(modus_ponens,[status(thm)],[73, 7])).
% 0.44/0.72  tff(75,plain,
% 0.44/0.72      (((~![X: $i] : (p1(X) | (~r1(Y!12, X)))) | (p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!12, X)))) | p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))),
% 0.44/0.72      inference(rewrite,[status(thm)],[])).
% 0.44/0.72  tff(76,plain,
% 0.44/0.72      ((~![X: $i] : (p1(X) | (~r1(Y!12, X)))) | (p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))),
% 0.44/0.72      inference(quant_inst,[status(thm)],[])).
% 0.44/0.72  tff(77,plain,
% 0.44/0.72      ((~![X: $i] : (p1(X) | (~r1(Y!12, X)))) | p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12)))),
% 0.44/0.72      inference(modus_ponens,[status(thm)],[76, 75])).
% 0.44/0.72  tff(78,plain,
% 0.44/0.72      ($false),
% 0.44/0.72      inference(unit_resolution,[status(thm)],[77, 74, 5, 3])).
% 0.44/0.72  tff(79,plain,(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12)))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.72  tff(80,plain,
% 0.44/0.72      (r1(X!0, Y!8)),
% 0.44/0.72      inference(and_elim,[status(thm)],[72])).
% 0.44/0.72  tff(81,plain,
% 0.44/0.72      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.44/0.72      inference(bind,[status(th)],[])).
% 0.44/0.72  tff(82,plain,
% 0.44/0.72      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.44/0.72      inference(quant_intro,[status(thm)],[81])).
% 0.44/0.72  tff(83,plain,
% 0.44/0.72      (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 0.44/0.72      inference(bind,[status(th)],[])).
% 0.44/0.72  tff(84,plain,
% 0.44/0.72      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.44/0.72      inference(quant_intro,[status(thm)],[83])).
% 0.44/0.72  tff(85,plain,
% 0.44/0.72      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 0.44/0.72      inference(bind,[status(th)],[])).
% 0.44/0.72  tff(86,plain,
% 0.44/0.72      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.44/0.72      inference(quant_intro,[status(thm)],[85])).
% 0.44/0.72  tff(87,plain,
% 0.44/0.72      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.44/0.72      inference(transitivity,[status(thm)],[86, 84])).
% 0.44/0.72  tff(88,plain,
% 0.44/0.72      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.44/0.72      inference(and_elim,[status(thm)],[72])).
% 0.44/0.72  tff(89,plain,
% 0.44/0.72      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.44/0.72      inference(modus_ponens,[status(thm)],[88, 87])).
% 0.44/0.72  tff(90,plain,
% 0.44/0.72      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.44/0.72      inference(modus_ponens,[status(thm)],[89, 82])).
% 0.44/0.72  tff(91,plain,
% 0.44/0.72      (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.44/0.73      inference(rewrite,[status(thm)],[])).
% 0.44/0.73  tff(92,plain,
% 0.44/0.73      ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.44/0.73      inference(quant_inst,[status(thm)],[])).
% 0.44/0.73  tff(93,plain,
% 0.44/0.73      ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.44/0.73      inference(modus_ponens,[status(thm)],[92, 91])).
% 0.44/0.73  tff(94,plain,
% 0.44/0.73      (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.44/0.73      inference(unit_resolution,[status(thm)],[93, 90, 80])).
% 0.44/0.73  tff(95,plain,
% 0.44/0.73      (r1(Y!8, X!9)),
% 0.44/0.73      inference(and_elim,[status(thm)],[72])).
% 0.44/0.73  tff(96,plain,
% 0.44/0.73      (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.44/0.73      inference(rewrite,[status(thm)],[])).
% 0.44/0.73  tff(97,plain,
% 0.44/0.73      ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.44/0.73      inference(quant_inst,[status(thm)],[])).
% 0.44/0.73  tff(98,plain,
% 0.44/0.73      ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.44/0.73      inference(modus_ponens,[status(thm)],[97, 96])).
% 0.44/0.73  tff(99,plain,
% 0.44/0.73      (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.44/0.73      inference(unit_resolution,[status(thm)],[98, 95, 94])).
% 0.44/0.73  tff(100,plain,
% 0.44/0.73      (r1(X!9, Y!10)),
% 0.44/0.73      inference(and_elim,[status(thm)],[72])).
% 0.44/0.73  tff(101,plain,
% 0.44/0.73      (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.44/0.73      inference(rewrite,[status(thm)],[])).
% 0.44/0.73  tff(102,plain,
% 0.44/0.73      ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.44/0.73      inference(quant_inst,[status(thm)],[])).
% 0.44/0.73  tff(103,plain,
% 0.44/0.73      ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.44/0.73      inference(modus_ponens,[status(thm)],[102, 101])).
% 0.44/0.73  tff(104,plain,
% 0.44/0.73      (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.44/0.73      inference(unit_resolution,[status(thm)],[103, 100, 99])).
% 0.44/0.73  tff(105,plain,
% 0.44/0.73      (r1(Y!10, X!11)),
% 0.44/0.73      inference(and_elim,[status(thm)],[72])).
% 0.44/0.73  tff(106,plain,
% 0.44/0.73      (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.44/0.73      inference(rewrite,[status(thm)],[])).
% 0.44/0.73  tff(107,plain,
% 0.44/0.73      ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.44/0.73      inference(quant_inst,[status(thm)],[])).
% 0.44/0.73  tff(108,plain,
% 0.44/0.73      ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.44/0.73      inference(modus_ponens,[status(thm)],[107, 106])).
% 0.44/0.73  tff(109,plain,
% 0.44/0.73      (![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.44/0.73      inference(unit_resolution,[status(thm)],[108, 105, 104])).
% 0.44/0.73  tff(110,plain,
% 0.44/0.73      (r1(X!11, Y!12)),
% 0.44/0.73      inference(and_elim,[status(thm)],[72])).
% 0.44/0.73  tff(111,plain,
% 0.44/0.73      (((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!11, Y!12)) | (~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!11, Y!12)) | (~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.44/0.73      inference(rewrite,[status(thm)],[])).
% 0.44/0.73  tff(112,plain,
% 0.44/0.73      ((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!11, Y!12)) | (~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.44/0.73      inference(quant_inst,[status(thm)],[])).
% 0.44/0.73  tff(113,plain,
% 0.44/0.73      ((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!11, Y!12)) | (~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.44/0.73      inference(modus_ponens,[status(thm)],[112, 111])).
% 0.44/0.73  tff(114,plain,
% 0.44/0.73      ((~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.44/0.73      inference(unit_resolution,[status(thm)],[113, 110, 109])).
% 0.44/0.73  tff(115,plain,
% 0.44/0.73      (![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.44/0.73      inference(unit_resolution,[status(thm)],[114, 79])).
% 0.44/0.73  tff(116,plain,
% 0.44/0.73      (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))))),
% 0.44/0.73      inference(bind,[status(th)],[])).
% 0.44/0.73  tff(117,plain,
% 0.44/0.73      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))),
% 0.44/0.73      inference(quant_intro,[status(thm)],[116])).
% 0.44/0.73  tff(118,plain,
% 0.44/0.73      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))))),
% 0.44/0.73      inference(bind,[status(th)],[])).
% 0.44/0.73  tff(119,plain,
% 0.44/0.73      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))),
% 0.44/0.73      inference(quant_intro,[status(thm)],[118])).
% 0.44/0.73  tff(120,plain,
% 0.44/0.73      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))),
% 0.44/0.73      inference(transitivity,[status(thm)],[119, 117])).
% 0.44/0.73  tff(121,plain,
% 0.44/0.73      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))),
% 0.44/0.73      inference(and_elim,[status(thm)],[72])).
% 0.44/0.73  tff(122,plain,
% 0.44/0.73      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))),
% 0.44/0.73      inference(modus_ponens,[status(thm)],[121, 120])).
% 0.44/0.73  tff(123,plain,
% 0.44/0.73      (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))),
% 0.44/0.73      inference(rewrite,[status(thm)],[])).
% 0.44/0.73  tff(124,plain,
% 0.44/0.73      ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))),
% 0.44/0.74      inference(quant_inst,[status(thm)],[])).
% 0.44/0.74  tff(125,plain,
% 0.44/0.74      ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))),
% 0.44/0.74      inference(modus_ponens,[status(thm)],[124, 123])).
% 0.44/0.74  tff(126,plain,
% 0.44/0.74      (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))),
% 0.44/0.74      inference(unit_resolution,[status(thm)],[125, 122, 80])).
% 0.44/0.74  tff(127,plain,
% 0.44/0.74      (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))),
% 0.44/0.74      inference(rewrite,[status(thm)],[])).
% 0.44/0.74  tff(128,plain,
% 0.44/0.74      ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))),
% 0.44/0.74      inference(quant_inst,[status(thm)],[])).
% 0.44/0.74  tff(129,plain,
% 0.44/0.74      ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))),
% 0.44/0.74      inference(modus_ponens,[status(thm)],[128, 127])).
% 0.44/0.74  tff(130,plain,
% 0.44/0.74      (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))),
% 0.44/0.74      inference(unit_resolution,[status(thm)],[129, 95, 126])).
% 0.44/0.74  tff(131,plain,
% 0.44/0.74      (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))),
% 0.44/0.74      inference(rewrite,[status(thm)],[])).
% 0.44/0.74  tff(132,plain,
% 0.44/0.74      ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))),
% 0.44/0.74      inference(quant_inst,[status(thm)],[])).
% 0.44/0.74  tff(133,plain,
% 0.44/0.74      ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y)))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))),
% 0.44/0.74      inference(modus_ponens,[status(thm)],[132, 131])).
% 0.44/0.74  tff(134,plain,
% 0.44/0.74      (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))),
% 0.44/0.74      inference(unit_resolution,[status(thm)],[133, 100, 130])).
% 0.44/0.74  tff(135,plain,
% 0.44/0.74      (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_4(Y))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_4(Y))))),
% 0.44/0.74      inference(rewrite,[status(thm)],[])).
% 0.44/0.74  tff(136,plain,
% 0.44/0.74      ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_4(Y))))),
% 0.44/0.74      inference(quant_inst,[status(thm)],[])).
% 0.44/0.74  tff(137,plain,
% 0.44/0.74      ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_4(Y))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_4(Y)))),
% 0.44/0.74      inference(modus_ponens,[status(thm)],[136, 135])).
% 0.44/0.74  tff(138,plain,
% 0.44/0.74      (![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_4(Y)))),
% 0.44/0.74      inference(unit_resolution,[status(thm)],[137, 105, 134])).
% 0.44/0.74  tff(139,plain,
% 0.44/0.74      (((~![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_4(Y)))) | ((~r1(X!11, Y!12)) | r1(Y!12, tptp_fun_X_4(Y!12)))) <=> ((~![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_4(Y)))) | (~r1(X!11, Y!12)) | r1(Y!12, tptp_fun_X_4(Y!12)))),
% 0.44/0.74      inference(rewrite,[status(thm)],[])).
% 0.44/0.74  tff(140,plain,
% 0.44/0.74      ((~![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_4(Y)))) | ((~r1(X!11, Y!12)) | r1(Y!12, tptp_fun_X_4(Y!12)))),
% 0.44/0.74      inference(quant_inst,[status(thm)],[])).
% 0.44/0.74  tff(141,plain,
% 0.44/0.74      ((~![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_4(Y)))) | (~r1(X!11, Y!12)) | r1(Y!12, tptp_fun_X_4(Y!12))),
% 0.44/0.74      inference(modus_ponens,[status(thm)],[140, 139])).
% 0.44/0.74  tff(142,plain,
% 0.44/0.74      (r1(Y!12, tptp_fun_X_4(Y!12))),
% 0.44/0.74      inference(unit_resolution,[status(thm)],[141, 110, 138])).
% 0.44/0.74  tff(143,plain,
% 0.44/0.74      (((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!12, tptp_fun_X_4(Y!12))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_4(Y!12), Y))))) <=> ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!12, tptp_fun_X_4(Y!12))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_4(Y!12), Y))))),
% 0.44/0.74      inference(rewrite,[status(thm)],[])).
% 0.44/0.74  tff(144,plain,
% 0.44/0.74      ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!12, tptp_fun_X_4(Y!12))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_4(Y!12), Y))))),
% 0.44/0.74      inference(quant_inst,[status(thm)],[])).
% 0.44/0.74  tff(145,plain,
% 0.44/0.74      ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!12, tptp_fun_X_4(Y!12))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_4(Y!12), Y)))),
% 0.44/0.74      inference(modus_ponens,[status(thm)],[144, 143])).
% 0.44/0.74  tff(146,plain,
% 0.44/0.74      (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_4(Y!12), Y)))),
% 0.44/0.74      inference(unit_resolution,[status(thm)],[145, 142, 115])).
% 0.44/0.74  tff(147,plain,
% 0.44/0.74      (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))))),
% 0.44/0.74      inference(bind,[status(th)],[])).
% 0.44/0.74  tff(148,plain,
% 0.44/0.74      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.44/0.74      inference(quant_intro,[status(thm)],[147])).
% 0.44/0.74  tff(149,plain,
% 0.44/0.74      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))))),
% 0.44/0.74      inference(bind,[status(th)],[])).
% 0.44/0.74  tff(150,plain,
% 0.44/0.74      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.44/0.74      inference(quant_intro,[status(thm)],[149])).
% 0.44/0.74  tff(151,plain,
% 0.44/0.74      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.44/0.74      inference(transitivity,[status(thm)],[150, 148])).
% 0.44/0.74  tff(152,plain,
% 0.44/0.74      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.44/0.74      inference(and_elim,[status(thm)],[72])).
% 0.44/0.74  tff(153,plain,
% 0.44/0.74      (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.44/0.74      inference(modus_ponens,[status(thm)],[152, 151])).
% 0.44/0.74  tff(154,plain,
% 0.44/0.74      (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.44/0.74      inference(rewrite,[status(thm)],[])).
% 0.44/0.74  tff(155,plain,
% 0.44/0.74      ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.44/0.74      inference(quant_inst,[status(thm)],[])).
% 0.44/0.74  tff(156,plain,
% 0.44/0.74      ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.44/0.74      inference(modus_ponens,[status(thm)],[155, 154])).
% 0.44/0.74  tff(157,plain,
% 0.44/0.74      (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.44/0.74      inference(unit_resolution,[status(thm)],[156, 153, 80])).
% 0.44/0.74  tff(158,plain,
% 0.44/0.74      (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.44/0.74      inference(rewrite,[status(thm)],[])).
% 0.44/0.74  tff(159,plain,
% 0.44/0.74      ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.44/0.74      inference(quant_inst,[status(thm)],[])).
% 0.44/0.74  tff(160,plain,
% 0.44/0.74      ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.44/0.74      inference(modus_ponens,[status(thm)],[159, 158])).
% 0.44/0.74  tff(161,plain,
% 0.44/0.74      (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.44/0.74      inference(unit_resolution,[status(thm)],[160, 95, 157])).
% 0.44/0.74  tff(162,plain,
% 0.44/0.74      (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.44/0.74      inference(rewrite,[status(thm)],[])).
% 0.44/0.74  tff(163,plain,
% 0.44/0.74      ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.44/0.74      inference(quant_inst,[status(thm)],[])).
% 0.44/0.74  tff(164,plain,
% 0.44/0.74      ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.44/0.75      inference(modus_ponens,[status(thm)],[163, 162])).
% 0.44/0.75  tff(165,plain,
% 0.44/0.75      (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.44/0.75      inference(unit_resolution,[status(thm)],[164, 100, 161])).
% 0.44/0.75  tff(166,plain,
% 0.44/0.75      (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.44/0.75      inference(rewrite,[status(thm)],[])).
% 0.44/0.75  tff(167,plain,
% 0.44/0.75      ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.44/0.75      inference(quant_inst,[status(thm)],[])).
% 0.44/0.75  tff(168,plain,
% 0.44/0.75      ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.44/0.75      inference(modus_ponens,[status(thm)],[167, 166])).
% 0.44/0.75  tff(169,plain,
% 0.44/0.75      (![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.44/0.75      inference(unit_resolution,[status(thm)],[168, 105, 165])).
% 0.44/0.75  tff(170,plain,
% 0.44/0.75      (~p1(Y!12)),
% 0.44/0.75      inference(and_elim,[status(thm)],[72])).
% 0.44/0.75  tff(171,plain,
% 0.44/0.75      (((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (p1(Y!12) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | p1(Y!12) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.44/0.75      inference(rewrite,[status(thm)],[])).
% 0.44/0.75  tff(172,plain,
% 0.44/0.75      ((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (p1(Y!12) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.44/0.75      inference(quant_inst,[status(thm)],[])).
% 0.44/0.75  tff(173,plain,
% 0.44/0.75      ((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | p1(Y!12) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.44/0.75      inference(modus_ponens,[status(thm)],[172, 171])).
% 0.44/0.75  tff(174,plain,
% 0.44/0.75      (![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.44/0.75      inference(unit_resolution,[status(thm)],[173, 170, 110, 169])).
% 0.44/0.75  tff(175,plain,
% 0.44/0.75      (((~![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!12, tptp_fun_X_4(Y!12))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12)))))))) <=> ((~![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!12, tptp_fun_X_4(Y!12))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12)))))))),
% 0.44/0.75      inference(rewrite,[status(thm)],[])).
% 0.44/0.75  tff(176,plain,
% 0.44/0.75      ((~![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!12, tptp_fun_X_4(Y!12))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12)))))))),
% 0.44/0.75      inference(quant_inst,[status(thm)],[])).
% 0.44/0.75  tff(177,plain,
% 0.44/0.75      ((~![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!12, tptp_fun_X_4(Y!12))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12))))))),
% 0.44/0.75      inference(modus_ponens,[status(thm)],[176, 175])).
% 0.44/0.75  tff(178,plain,
% 0.44/0.75      (~(p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12)))))),
% 0.44/0.75      inference(unit_resolution,[status(thm)],[177, 174, 142])).
% 0.44/0.75  tff(179,plain,
% 0.44/0.75      ((p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12))))) | r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12)))),
% 0.44/0.75      inference(tautology,[status(thm)],[])).
% 0.44/0.75  tff(180,plain,
% 0.44/0.75      (r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12)))),
% 0.44/0.75      inference(unit_resolution,[status(thm)],[179, 178])).
% 0.44/0.75  tff(181,plain,
% 0.44/0.75      ((p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12))))) | (~p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))))),
% 0.44/0.75      inference(tautology,[status(thm)],[])).
% 0.44/0.75  tff(182,plain,
% 0.44/0.75      (~p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12)))),
% 0.44/0.75      inference(unit_resolution,[status(thm)],[181, 178])).
% 0.44/0.75  tff(183,plain,
% 0.44/0.75      (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_4(Y!12), Y)))) | (p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_4(Y!12), Y)))) | p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12)))))),
% 0.44/0.75      inference(rewrite,[status(thm)],[])).
% 0.44/0.75  tff(184,plain,
% 0.44/0.75      ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_4(Y!12), Y)))) | (p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12)))))),
% 0.44/0.75      inference(quant_inst,[status(thm)],[])).
% 0.44/0.75  tff(185,plain,
% 0.44/0.75      ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_4(Y!12), Y)))) | p1(tptp_fun_Y_1(tptp_fun_X_4(Y!12))) | (~r1(tptp_fun_X_4(Y!12), tptp_fun_Y_1(tptp_fun_X_4(Y!12))))),
% 0.44/0.75      inference(modus_ponens,[status(thm)],[184, 183])).
% 0.44/0.75  tff(186,plain,
% 0.44/0.75      ($false),
% 0.44/0.75      inference(unit_resolution,[status(thm)],[185, 182, 180, 146])).
% 0.44/0.75  % SZS output end Proof
% 0.44/0.76  % E exiting
%------------------------------------------------------------------------------