%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL640+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n017.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 03:00:19 PM UTC 2026
% Result : Theorem 0.21s 0.50s
% Output : Proof 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL640+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 01:24:23 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 % SZS output start Proof
% 0.21/0.50 tff(p1_type, type, (
% 0.21/0.50 p1: $i > $o)).
% 0.21/0.50 tff(tptp_fun_X_7_type, type, (
% 0.21/0.50 tptp_fun_X_7: $i > $i)).
% 0.21/0.50 tff(tptp_fun_X_5_type, type, (
% 0.21/0.50 tptp_fun_X_5: $i)).
% 0.21/0.50 tff(r1_type, type, (
% 0.21/0.50 r1: ( $i * $i ) > $o)).
% 0.21/0.50 tff(tptp_fun_Y_6_type, type, (
% 0.21/0.50 tptp_fun_Y_6: $i > $i)).
% 0.21/0.50 tff(tptp_fun_Y_3_type, type, (
% 0.21/0.50 tptp_fun_Y_3: $i)).
% 0.21/0.50 tff(tptp_fun_X_4_type, type, (
% 0.21/0.50 tptp_fun_X_4: $i)).
% 0.21/0.50 tff(tptp_fun_Y_15_type, type, (
% 0.21/0.50 tptp_fun_Y_15: $i > $i)).
% 0.21/0.50 tff(tptp_fun_X_14_type, type, (
% 0.21/0.50 tptp_fun_X_14: $i > $i)).
% 0.21/0.50 tff(tptp_fun_X_11_type, type, (
% 0.21/0.50 tptp_fun_X_11: $i > $i)).
% 0.21/0.50 tff(tptp_fun_Y_10_type, type, (
% 0.21/0.50 tptp_fun_Y_10: $i > $i)).
% 0.21/0.50 tff(tptp_fun_X_9_type, type, (
% 0.21/0.50 tptp_fun_X_9: $i > $i)).
% 0.21/0.50 tff(tptp_fun_X_12_type, type, (
% 0.21/0.50 tptp_fun_X_12: $i > $i)).
% 0.21/0.50 tff(tptp_fun_Y_13_type, type, (
% 0.21/0.50 tptp_fun_Y_13: $i > $i)).
% 0.21/0.50 tff(tptp_fun_X_0_type, type, (
% 0.21/0.50 tptp_fun_X_0: $i)).
% 0.21/0.50 tff(tptp_fun_Y_8_type, type, (
% 0.21/0.50 tptp_fun_Y_8: $i > $i)).
% 0.21/0.50 tff(tptp_fun_X_2_type, type, (
% 0.21/0.50 tptp_fun_X_2: $i)).
% 0.21/0.50 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.50 tptp_fun_Y_1: $i)).
% 0.21/0.50 tff(1,assumption,(![X: $i] : (p1(X) | (~r1(Y!3, X)))), introduced(assumption)).
% 0.21/0.50 tff(2,plain,
% 0.21/0.50 (((r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))) <=> (r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(3,plain,
% 0.21/0.51 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(4,plain,
% 0.21/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.51 tff(5,plain,
% 0.21/0.51 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~r1(tptp_fun_Y_8(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(6,plain,
% 0.21/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~r1(tptp_fun_Y_8(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.51 tff(7,plain,
% 0.21/0.51 (((r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))))) <=> (r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(8,plain,
% 0.21/0.51 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) <=> ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(9,plain,
% 0.21/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.51 tff(10,plain,
% 0.21/0.51 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~r1(tptp_fun_Y_8(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(11,plain,
% 0.21/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~r1(tptp_fun_Y_8(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.51 tff(12,plain,
% 0.21/0.51 ((r1(X!0, Y!1) & (r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))) <=> (r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(13,plain,
% 0.21/0.52 ((r1(Y!1, X!2) & (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))) <=> (r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(14,plain,
% 0.21/0.52 ((r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))) <=> (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(15,plain,
% 0.21/0.52 ((r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) <=> (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(16,plain,
% 0.21/0.52 ((r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))) <=> (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[15])).
% 0.21/0.52 tff(17,plain,
% 0.21/0.52 ((r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))) <=> (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[16, 14])).
% 0.21/0.52 tff(18,plain,
% 0.21/0.52 ((r1(Y!1, X!2) & (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))) <=> (r1(Y!1, X!2) & (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[17])).
% 0.21/0.52 tff(19,plain,
% 0.21/0.52 ((r1(Y!1, X!2) & (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))) <=> (r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[18, 13])).
% 0.21/0.52 tff(20,plain,
% 0.21/0.52 ((r1(X!0, Y!1) & (r1(Y!1, X!2) & (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))))) <=> (r1(X!0, Y!1) & (r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[19])).
% 0.21/0.52 tff(21,plain,
% 0.21/0.52 ((r1(X!0, Y!1) & (r1(Y!1, X!2) & (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))))) <=> (r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[20, 12])).
% 0.21/0.52 tff(22,plain,
% 0.21/0.52 (((r1(X!0, Y!1) & (r1(Y!1, X!2) & (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~r1(tptp_fun_Y_8(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))))) <=> ((r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[21, 11, 9])).
% 0.21/0.52 tff(23,plain,
% 0.21/0.52 (((r1(X!0, Y!1) & (r1(Y!1, X!2) & (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~r1(tptp_fun_Y_8(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))))) <=> (r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[22, 7])).
% 0.21/0.52 tff(24,plain,
% 0.21/0.52 ((((r1(X!0, Y!1) & (r1(Y!1, X!2) & (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~r1(tptp_fun_Y_8(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~r1(tptp_fun_Y_8(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))) <=> ((r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[23, 6, 4])).
% 0.21/0.52 tff(25,plain,
% 0.21/0.52 ((((r1(X!0, Y!1) & (r1(Y!1, X!2) & (r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & (r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~r1(tptp_fun_Y_8(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~r1(tptp_fun_Y_8(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_11(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))) <=> (r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[24, 2])).
% 0.21/0.53 tff(26,plain,
% 0.21/0.53 (?[X: $i] : (~((~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![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)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & (p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) <=> ?[X: $i] : (~((~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![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)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & (p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(27,plain,
% 0.21/0.53 ((~(~?[X: $i] : (~((~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![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)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & (p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))))) <=> ?[X: $i] : (~((~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![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)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & (p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(28,plain,
% 0.21/0.53 ((~?[X: $i] : (~(((~![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)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(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(Y))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))))))))) & ((p1(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)) | p1(X))) | (~p1(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))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~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))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(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)) | (((p1(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)) | p1(X))) | (~p1(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))))))))))) <=> (~?[X: $i] : (~((~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![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)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & (p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(29,plain,
% 0.21/0.54 ((~(~?[X: $i] : (~(((~![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)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(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(Y))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))))))))) & ((p1(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)) | p1(X))) | (~p1(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))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~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))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(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)) | (((p1(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)) | p1(X))) | (~p1(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)))))))))))) <=> (~(~?[X: $i] : (~((~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![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)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & (p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.54 tff(30,plain,
% 0.21/0.54 ((~(~?[X: $i] : (~(((~![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)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(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(Y))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))))))))) & ((p1(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)) | p1(X))) | (~p1(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))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~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))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(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)) | (((p1(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)) | p1(X))) | (~p1(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)))))))))))) <=> ?[X: $i] : (~((~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![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)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & (p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))),
% 0.21/0.55 inference(transitivity,[status(thm)],[29, 27])).
% 0.21/0.55 tff(31,axiom,(~(~?[X: $i] : (~(((~![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)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(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(Y))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(Y))))))))) & ((p1(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)) | p1(X))) | (~p1(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))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~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))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(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)) | (((p1(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)) | p1(X))) | (~p1(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)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.21/0.55 tff(32,plain,
% 0.21/0.55 (?[X: $i] : (~((~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![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)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & (p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.55 tff(33,plain,
% 0.21/0.55 (?[X: $i] : (~((~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![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)) | ((p1(X) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & (p1(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)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.21/0.55 tff(34,plain,
% 0.21/0.55 (r1(X!0, Y!1) & r1(Y!1, X!2) & r1(X!2, Y!3) & (~(p1(X!4) | (~r1(Y!3, X!4)))) & r1(Y!3, X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))) & ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_8(X))) & r1(X, tptp_fun_Y_8(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_8(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.21/0.55 tff(35,plain,
% 0.21/0.55 (~(p1(X!4) | (~r1(Y!3, X!4)))),
% 0.21/0.55 inference(and_elim,[status(thm)],[34])).
% 0.21/0.55 tff(36,plain,
% 0.21/0.55 (r1(Y!3, X!4)),
% 0.21/0.55 inference(or_elim,[status(thm)],[35])).
% 0.21/0.55 tff(37,plain,
% 0.21/0.55 (~p1(X!4)),
% 0.21/0.55 inference(or_elim,[status(thm)],[35])).
% 0.21/0.55 tff(38,plain,
% 0.21/0.55 (((~![X: $i] : (p1(X) | (~r1(Y!3, X)))) | (p1(X!4) | (~r1(Y!3, X!4)))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!3, X)))) | p1(X!4) | (~r1(Y!3, X!4)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(39,plain,
% 0.21/0.55 ((~![X: $i] : (p1(X) | (~r1(Y!3, X)))) | (p1(X!4) | (~r1(Y!3, X!4)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(40,plain,
% 0.21/0.55 ((~![X: $i] : (p1(X) | (~r1(Y!3, X)))) | p1(X!4) | (~r1(Y!3, X!4))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.55 tff(41,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[40, 37, 36, 1])).
% 0.21/0.55 tff(42,plain,(~![X: $i] : (p1(X) | (~r1(Y!3, X)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(43,assumption,(~(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))), introduced(assumption)).
% 0.21/0.55 tff(44,plain,
% 0.21/0.55 ((p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5)))) | r1(X!5, tptp_fun_Y_10(X!5))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(45,plain,
% 0.21/0.55 (r1(X!5, tptp_fun_Y_10(X!5))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.55 tff(46,plain,
% 0.21/0.55 ((p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5)))) | (~p1(tptp_fun_Y_10(X!5)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(47,plain,
% 0.21/0.55 (~p1(tptp_fun_Y_10(X!5))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.21/0.55 tff(48,plain,
% 0.21/0.55 (^[Y: $i] : refl((p1(Y) | (~r1(X!5, Y))) <=> (p1(Y) | (~r1(X!5, Y))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(49,plain,
% 0.21/0.55 (![Y: $i] : (p1(Y) | (~r1(X!5, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.55 tff(50,plain,
% 0.21/0.55 (![Y: $i] : (p1(Y) | (~r1(X!5, Y)))),
% 0.21/0.55 inference(and_elim,[status(thm)],[34])).
% 0.21/0.55 tff(51,plain,
% 0.21/0.55 (![Y: $i] : (p1(Y) | (~r1(X!5, Y)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.55 tff(52,plain,
% 0.21/0.55 (((~![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) | (p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) | p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(53,plain,
% 0.21/0.55 ((~![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) | (p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(54,plain,
% 0.21/0.55 ((~![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) | p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.55 tff(55,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[54, 51, 47, 45])).
% 0.21/0.55 tff(56,plain,(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(57,assumption,(![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))), introduced(assumption)).
% 0.21/0.55 tff(58,plain,
% 0.31/0.55 (r1(Y!3, X!5)),
% 0.31/0.55 inference(and_elim,[status(thm)],[34])).
% 0.31/0.55 tff(59,plain,
% 0.31/0.55 (((~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | ((~r1(Y!3, X!5)) | (~(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~r1(Y!3, X!5)) | (~(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))))),
% 0.31/0.55 inference(rewrite,[status(thm)],[])).
% 0.31/0.55 tff(60,plain,
% 0.31/0.55 ((~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | ((~r1(Y!3, X!5)) | (~(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))))),
% 0.31/0.55 inference(quant_inst,[status(thm)],[])).
% 0.31/0.55 tff(61,plain,
% 0.31/0.55 ((~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~r1(Y!3, X!5)) | (~(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5)))))),
% 0.31/0.55 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.31/0.55 tff(62,plain,
% 0.31/0.55 ($false),
% 0.31/0.55 inference(unit_resolution,[status(thm)],[61, 58, 57, 56])).
% 0.31/0.55 tff(63,plain,(~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.31/0.55 tff(64,assumption,(~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))), introduced(assumption)).
% 0.31/0.55 tff(65,plain,
% 0.31/0.55 ((p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | r1(Y!3, tptp_fun_X_11(Y!3))),
% 0.31/0.55 inference(tautology,[status(thm)],[])).
% 0.31/0.55 tff(66,plain,
% 0.31/0.55 (r1(Y!3, tptp_fun_X_11(Y!3))),
% 0.31/0.55 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.31/0.55 tff(67,plain,
% 0.31/0.55 ((p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~p1(tptp_fun_X_11(Y!3)))),
% 0.31/0.55 inference(tautology,[status(thm)],[])).
% 0.31/0.55 tff(68,plain,
% 0.31/0.55 (~p1(tptp_fun_X_11(Y!3))),
% 0.31/0.55 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.31/0.55 tff(69,plain,
% 0.31/0.55 (^[X: $i] : refl((p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) <=> (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))),
% 0.31/0.55 inference(bind,[status(th)],[])).
% 0.31/0.55 tff(70,plain,
% 0.31/0.55 (![X: $i] : (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) <=> ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))),
% 0.31/0.55 inference(quant_intro,[status(thm)],[69])).
% 0.31/0.55 tff(71,plain,
% 0.31/0.55 (^[X: $i] : rewrite((p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) <=> (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))),
% 0.31/0.55 inference(bind,[status(th)],[])).
% 0.31/0.55 tff(72,plain,
% 0.31/0.55 (![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) <=> ![X: $i] : (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))),
% 0.31/0.55 inference(quant_intro,[status(thm)],[71])).
% 0.31/0.55 tff(73,plain,
% 0.31/0.55 (![X: $i] : (p1(X) | (~r1(Y!3, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))))),
% 0.31/0.55 inference(and_elim,[status(thm)],[34])).
% 0.31/0.55 tff(74,plain,
% 0.31/0.55 (![X: $i] : (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))),
% 0.31/0.55 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.31/0.55 tff(75,plain,
% 0.31/0.55 (![X: $i] : (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))),
% 0.31/0.56 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.31/0.56 tff(76,plain,
% 0.31/0.56 (((~![X: $i] : (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3)))))))),
% 0.31/0.56 inference(rewrite,[status(thm)],[])).
% 0.31/0.56 tff(77,plain,
% 0.31/0.56 ((~![X: $i] : (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3)))))))),
% 0.31/0.56 inference(quant_inst,[status(thm)],[])).
% 0.31/0.56 tff(78,plain,
% 0.31/0.56 ((~![X: $i] : (p1(X) | (~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3))))))),
% 0.31/0.56 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.31/0.56 tff(79,plain,
% 0.31/0.56 (~((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3)))))),
% 0.31/0.56 inference(unit_resolution,[status(thm)],[78, 75, 68, 66])).
% 0.31/0.56 tff(80,plain,
% 0.31/0.56 (((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3))))) | r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))),
% 0.31/0.56 inference(tautology,[status(thm)],[])).
% 0.31/0.56 tff(81,plain,
% 0.31/0.56 (r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))),
% 0.31/0.56 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.31/0.56 tff(82,plain,
% 0.31/0.56 (((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3))))) | p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))),
% 0.31/0.56 inference(tautology,[status(thm)],[])).
% 0.31/0.56 tff(83,plain,
% 0.31/0.56 (p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))),
% 0.31/0.56 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.31/0.56 tff(84,plain,
% 0.31/0.56 ((p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.31/0.56 inference(tautology,[status(thm)],[])).
% 0.31/0.56 tff(85,plain,
% 0.31/0.56 (![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.31/0.56 inference(unit_resolution,[status(thm)],[84, 64])).
% 0.31/0.56 tff(86,plain,
% 0.31/0.56 (((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), X))))) <=> ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), X))))),
% 0.31/0.56 inference(rewrite,[status(thm)],[])).
% 0.31/0.56 tff(87,plain,
% 0.31/0.56 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), X))))),
% 0.31/0.56 inference(quant_inst,[status(thm)],[])).
% 0.31/0.56 tff(88,plain,
% 0.31/0.56 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), X)))),
% 0.31/0.56 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.31/0.56 tff(89,plain,
% 0.31/0.56 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), X)))),
% 0.31/0.56 inference(unit_resolution,[status(thm)],[88, 85, 83, 81])).
% 0.31/0.56 tff(90,plain,
% 0.31/0.56 (((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3))))) | r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3)))),
% 0.31/0.56 inference(tautology,[status(thm)],[])).
% 0.31/0.56 tff(91,plain,
% 0.31/0.56 (r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3)))),
% 0.31/0.56 inference(unit_resolution,[status(thm)],[90, 79])).
% 0.31/0.56 tff(92,plain,
% 0.31/0.56 (((~p1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | (~r1(tptp_fun_X_11(Y!3), tptp_fun_Y_6(tptp_fun_X_11(Y!3)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3))))) | (~p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))))),
% 0.31/0.56 inference(tautology,[status(thm)],[])).
% 0.31/0.56 tff(93,plain,
% 0.31/0.56 (~p1(tptp_fun_X_7(tptp_fun_X_11(Y!3)))),
% 0.31/0.56 inference(unit_resolution,[status(thm)],[92, 79])).
% 0.31/0.56 tff(94,plain,
% 0.31/0.56 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), X)))) | (p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), X)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3)))))),
% 0.31/0.56 inference(rewrite,[status(thm)],[])).
% 0.31/0.56 tff(95,plain,
% 0.31/0.56 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), X)))) | (p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3)))))),
% 0.31/0.56 inference(quant_inst,[status(thm)],[])).
% 0.31/0.56 tff(96,plain,
% 0.31/0.56 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), X)))) | p1(tptp_fun_X_7(tptp_fun_X_11(Y!3))) | (~r1(tptp_fun_Y_6(tptp_fun_X_11(Y!3)), tptp_fun_X_7(tptp_fun_X_11(Y!3))))),
% 0.31/0.56 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.31/0.56 tff(97,plain,
% 0.31/0.56 ($false),
% 0.31/0.56 inference(unit_resolution,[status(thm)],[96, 93, 91, 89])).
% 0.31/0.56 tff(98,plain,(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.31/0.56 tff(99,plain,
% 0.31/0.56 (^[Y: $i] : rewrite(((~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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))))),
% 0.31/0.56 inference(bind,[status(th)],[])).
% 0.31/0.56 tff(100,plain,
% 0.31/0.56 (![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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.31/0.56 inference(quant_intro,[status(thm)],[99])).
% 0.31/0.56 tff(101,plain,
% 0.31/0.56 (^[Y: $i] : refl(((~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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))))),
% 0.31/0.56 inference(bind,[status(th)],[])).
% 0.31/0.56 tff(102,plain,
% 0.31/0.56 (![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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.31/0.56 inference(quant_intro,[status(thm)],[101])).
% 0.31/0.56 tff(103,plain,
% 0.31/0.56 (^[Y: $i] : rewrite(((~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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))))),
% 0.31/0.57 inference(bind,[status(th)],[])).
% 0.31/0.57 tff(104,plain,
% 0.31/0.57 (![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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.31/0.57 inference(quant_intro,[status(thm)],[103])).
% 0.31/0.57 tff(105,plain,
% 0.31/0.57 (![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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.31/0.57 inference(transitivity,[status(thm)],[104, 102])).
% 0.31/0.57 tff(106,plain,
% 0.31/0.57 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))))),
% 0.31/0.57 inference(bind,[status(th)],[])).
% 0.31/0.57 tff(107,plain,
% 0.31/0.57 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.31/0.57 inference(quant_intro,[status(thm)],[106])).
% 0.31/0.57 tff(108,plain,
% 0.31/0.57 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p1(tptp_fun_Y_6(X)) & (~(p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (r1(Y, tptp_fun_X_12(Y)) & p1(tptp_fun_X_12(Y)) & (~(p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | ((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) & (((~p1(tptp_fun_X_11(Y))) & r1(Y, tptp_fun_X_11(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & p1(tptp_fun_X_14(Y)) & (~(p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))),
% 0.31/0.57 inference(and_elim,[status(thm)],[34])).
% 0.31/0.57 tff(109,plain,
% 0.31/0.57 (![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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.31/0.57 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.31/0.57 tff(110,plain,
% 0.31/0.57 (![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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_11(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.31/0.57 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.31/0.57 tff(111,plain,
% 0.31/0.57 (![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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.31/0.57 inference(modus_ponens,[status(thm)],[110, 100])).
% 0.31/0.57 tff(112,plain,
% 0.31/0.57 (r1(X!0, Y!1)),
% 0.31/0.57 inference(and_elim,[status(thm)],[34])).
% 0.31/0.57 tff(113,plain,
% 0.31/0.57 (((~![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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))) | (~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.31/0.58 inference(rewrite,[status(thm)],[])).
% 0.31/0.58 tff(114,plain,
% 0.31/0.58 ((~![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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))),
% 0.31/0.58 inference(quant_inst,[status(thm)],[])).
% 0.31/0.58 tff(115,plain,
% 0.31/0.58 ((~![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_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))))) | (~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))),
% 0.31/0.58 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.31/0.58 tff(116,plain,
% 0.31/0.58 (![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))),
% 0.31/0.58 inference(unit_resolution,[status(thm)],[115, 112, 111])).
% 0.31/0.58 tff(117,plain,
% 0.31/0.58 (r1(Y!1, X!2)),
% 0.31/0.58 inference(and_elim,[status(thm)],[34])).
% 0.31/0.58 tff(118,plain,
% 0.31/0.58 (((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))) | ((~r1(Y!1, X!2)) | ![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))) | (~r1(Y!1, X!2)) | ![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))),
% 0.31/0.58 inference(rewrite,[status(thm)],[])).
% 0.31/0.58 tff(119,plain,
% 0.31/0.58 ((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))) | ((~r1(Y!1, X!2)) | ![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))),
% 0.31/0.58 inference(quant_inst,[status(thm)],[])).
% 0.31/0.58 tff(120,plain,
% 0.31/0.58 ((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))))) | (~r1(Y!1, X!2)) | ![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))),
% 0.31/0.58 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.31/0.58 tff(121,plain,
% 0.31/0.58 (![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))),
% 0.31/0.59 inference(unit_resolution,[status(thm)],[120, 117, 116])).
% 0.31/0.59 tff(122,plain,
% 0.31/0.59 (r1(X!2, Y!3)),
% 0.31/0.59 inference(and_elim,[status(thm)],[34])).
% 0.31/0.59 tff(123,plain,
% 0.31/0.59 (((~![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) | ((~r1(X!2, Y!3)) | (~((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3))))))))))) <=> ((~![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) | (~r1(X!2, Y!3)) | (~((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3))))))))))),
% 0.31/0.59 inference(rewrite,[status(thm)],[])).
% 0.31/0.59 tff(124,plain,
% 0.31/0.59 (((~r1(X!2, Y!3)) | (~((~(p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y!3)) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | ![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y!3))) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))))))) <=> ((~r1(X!2, Y!3)) | (~((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3))))))))))),
% 0.31/0.59 inference(rewrite,[status(thm)],[])).
% 0.31/0.59 tff(125,plain,
% 0.31/0.59 (((~![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) | ((~r1(X!2, Y!3)) | (~((~(p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y!3)) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | ![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y!3))) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) | ((~r1(X!2, Y!3)) | (~((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))))))))))),
% 0.31/0.59 inference(monotonicity,[status(thm)],[124])).
% 0.31/0.59 tff(126,plain,
% 0.31/0.59 (((~![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) | ((~r1(X!2, Y!3)) | (~((~(p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y!3)) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | ![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y!3))) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) | (~r1(X!2, Y!3)) | (~((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3))))))))))),
% 0.31/0.59 inference(transitivity,[status(thm)],[125, 123])).
% 0.31/0.59 tff(127,plain,
% 0.31/0.59 ((~![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) | ((~r1(X!2, Y!3)) | (~((~(p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y!3)) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | ![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y!3))) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))),
% 0.31/0.60 inference(quant_inst,[status(thm)],[])).
% 0.31/0.60 tff(128,plain,
% 0.31/0.60 ((~![Y: $i] : ((~r1(X!2, Y)) | (~((~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))) | (~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | (~((~p1(tptp_fun_X_12(Y))) | (~r1(Y, tptp_fun_X_12(Y))) | p1(tptp_fun_Y_13(Y)) | (~r1(tptp_fun_X_12(Y), tptp_fun_Y_13(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~((~(p1(tptp_fun_X_11(Y)) | (~r1(Y, tptp_fun_X_11(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))))))) | (~r1(X!2, Y!3)) | (~((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))))))))),
% 0.31/0.60 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.31/0.60 tff(129,plain,
% 0.31/0.60 (~((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3))))))))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[128, 122, 121])).
% 0.31/0.60 tff(130,plain,
% 0.31/0.60 (((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))))))) | ((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))),
% 0.31/0.60 inference(tautology,[status(thm)],[])).
% 0.31/0.60 tff(131,plain,
% 0.31/0.60 ((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.31/0.60 tff(132,plain,
% 0.31/0.60 ((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))),
% 0.31/0.60 inference(tautology,[status(thm)],[])).
% 0.31/0.60 tff(133,plain,
% 0.31/0.60 ((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.31/0.60 tff(134,plain,
% 0.31/0.60 (p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[133, 98])).
% 0.31/0.60 tff(135,plain,
% 0.31/0.60 (p1(Y!3)),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[134, 63])).
% 0.31/0.60 tff(136,assumption,(~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3))))), introduced(assumption)).
% 0.31/0.60 tff(137,plain,
% 0.31/0.60 (((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))) | r1(Y!3, tptp_fun_X_12(Y!3))),
% 0.31/0.60 inference(tautology,[status(thm)],[])).
% 0.31/0.60 tff(138,plain,
% 0.31/0.60 (r1(Y!3, tptp_fun_X_12(Y!3))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.31/0.60 tff(139,plain,
% 0.31/0.60 (((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))))))) | ((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))),
% 0.31/0.60 inference(tautology,[status(thm)],[])).
% 0.31/0.60 tff(140,plain,
% 0.31/0.60 ((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[139, 129])).
% 0.31/0.60 tff(141,plain,
% 0.31/0.60 ((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))),
% 0.31/0.60 inference(tautology,[status(thm)],[])).
% 0.31/0.60 tff(142,plain,
% 0.31/0.60 ((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.31/0.60 tff(143,plain,
% 0.31/0.60 (![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[142, 98])).
% 0.31/0.60 tff(144,plain,
% 0.31/0.60 (((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))) | ((~r1(Y!3, tptp_fun_X_12(Y!3))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))),
% 0.31/0.60 inference(rewrite,[status(thm)],[])).
% 0.31/0.60 tff(145,plain,
% 0.31/0.60 ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))) | ((~r1(Y!3, tptp_fun_X_12(Y!3))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))),
% 0.31/0.60 inference(quant_inst,[status(thm)],[])).
% 0.31/0.60 tff(146,plain,
% 0.31/0.60 ((~![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y)))))))) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))),
% 0.31/0.60 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.31/0.60 tff(147,plain,
% 0.31/0.60 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[146, 143, 138])).
% 0.31/0.60 tff(148,plain,
% 0.31/0.60 (((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))) | (~p1(tptp_fun_Y_13(Y!3)))),
% 0.31/0.60 inference(tautology,[status(thm)],[])).
% 0.31/0.60 tff(149,plain,
% 0.31/0.60 (~p1(tptp_fun_Y_13(Y!3))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[148, 136])).
% 0.31/0.60 tff(150,plain,
% 0.31/0.60 (((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))) | r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))),
% 0.31/0.60 inference(tautology,[status(thm)],[])).
% 0.31/0.60 tff(151,plain,
% 0.31/0.60 (r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[150, 136])).
% 0.31/0.60 tff(152,plain,
% 0.31/0.60 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))) | (p1(tptp_fun_Y_13(Y!3)) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3)))))))),
% 0.31/0.60 inference(rewrite,[status(thm)],[])).
% 0.31/0.60 tff(153,plain,
% 0.31/0.60 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))) | (p1(tptp_fun_Y_13(Y!3)) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3)))))))),
% 0.31/0.60 inference(quant_inst,[status(thm)],[])).
% 0.31/0.60 tff(154,plain,
% 0.31/0.60 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3))))))),
% 0.31/0.60 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.31/0.60 tff(155,plain,
% 0.31/0.60 (~((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3)))))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[154, 151, 149, 147])).
% 0.31/0.60 tff(156,plain,
% 0.31/0.60 (((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3))))) | r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))),
% 0.31/0.60 inference(tautology,[status(thm)],[])).
% 0.31/0.60 tff(157,plain,
% 0.31/0.60 (r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.31/0.60 tff(158,plain,
% 0.31/0.60 (((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3))))) | p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))),
% 0.31/0.60 inference(tautology,[status(thm)],[])).
% 0.31/0.60 tff(159,plain,
% 0.31/0.60 (p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[158, 155])).
% 0.31/0.60 tff(160,plain,
% 0.31/0.60 (((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3))))) | p1(tptp_fun_Y_13(Y!3))),
% 0.31/0.60 inference(tautology,[status(thm)],[])).
% 0.31/0.60 tff(161,plain,
% 0.31/0.60 ((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3))))),
% 0.31/0.60 inference(unit_resolution,[status(thm)],[160, 149])).
% 0.31/0.60 tff(162,plain,
% 0.31/0.60 (((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))) | ![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.31/0.61 inference(tautology,[status(thm)],[])).
% 0.31/0.61 tff(163,plain,
% 0.31/0.61 (![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.31/0.61 inference(unit_resolution,[status(thm)],[162, 136])).
% 0.31/0.61 tff(164,plain,
% 0.31/0.61 (((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X))))),
% 0.31/0.61 inference(rewrite,[status(thm)],[])).
% 0.31/0.61 tff(165,plain,
% 0.31/0.61 (((~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3)))))) | ![X: $i] : ((~r1(tptp_fun_Y_13(Y!3), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) <=> ((~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X))))),
% 0.31/0.61 inference(rewrite,[status(thm)],[])).
% 0.31/0.61 tff(166,plain,
% 0.31/0.61 (((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3)))))) | ![X: $i] : ((~r1(tptp_fun_Y_13(Y!3), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))))),
% 0.31/0.61 inference(monotonicity,[status(thm)],[165])).
% 0.31/0.61 tff(167,plain,
% 0.31/0.61 (((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3)))))) | ![X: $i] : ((~r1(tptp_fun_Y_13(Y!3), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X))))),
% 0.31/0.61 inference(transitivity,[status(thm)],[166, 164])).
% 0.31/0.61 tff(168,plain,
% 0.31/0.61 ((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3)))))) | ![X: $i] : ((~r1(tptp_fun_Y_13(Y!3), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.31/0.61 inference(quant_inst,[status(thm)],[])).
% 0.31/0.61 tff(169,plain,
% 0.31/0.61 ((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | (~((~p1(tptp_fun_Y_13(Y!3))) | p1(tptp_fun_X_9(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_9(tptp_fun_Y_13(Y!3)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))),
% 0.31/0.61 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.31/0.61 tff(170,plain,
% 0.31/0.61 (![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))),
% 0.31/0.61 inference(unit_resolution,[status(thm)],[169, 163, 151, 161])).
% 0.31/0.61 tff(171,plain,
% 0.31/0.61 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))) | ((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))) | (~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y))))),
% 0.31/0.61 inference(rewrite,[status(thm)],[])).
% 0.31/0.61 tff(172,plain,
% 0.31/0.61 (((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3))))) <=> ((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y))))),
% 0.31/0.61 inference(rewrite,[status(thm)],[])).
% 0.31/0.61 tff(173,plain,
% 0.31/0.61 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))) | ((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))) | ((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y)))))),
% 0.31/0.61 inference(monotonicity,[status(thm)],[172])).
% 0.31/0.61 tff(174,plain,
% 0.31/0.61 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))) | ((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))) | (~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y))))),
% 0.31/0.61 inference(transitivity,[status(thm)],[173, 171])).
% 0.31/0.61 tff(175,plain,
% 0.31/0.61 ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))) | ((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))))),
% 0.31/0.61 inference(quant_inst,[status(thm)],[])).
% 0.31/0.61 tff(176,plain,
% 0.31/0.61 ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_13(Y!3), X)))) | (~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y)))),
% 0.31/0.61 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.31/0.61 tff(177,plain,
% 0.31/0.61 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y)))),
% 0.31/0.61 inference(unit_resolution,[status(thm)],[176, 170, 159, 157])).
% 0.31/0.61 tff(178,plain,
% 0.31/0.61 (((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3))))) | r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3)))),
% 0.31/0.61 inference(tautology,[status(thm)],[])).
% 0.31/0.61 tff(179,plain,
% 0.31/0.61 (r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3)))),
% 0.31/0.61 inference(unit_resolution,[status(thm)],[178, 155])).
% 0.31/0.61 tff(180,plain,
% 0.31/0.61 (((~p1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | (~r1(tptp_fun_Y_13(Y!3), tptp_fun_X_14(tptp_fun_Y_13(Y!3)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3))))) | (~p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))))),
% 0.31/0.61 inference(tautology,[status(thm)],[])).
% 0.31/0.61 tff(181,plain,
% 0.31/0.61 (~p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3)))),
% 0.31/0.61 inference(unit_resolution,[status(thm)],[180, 155])).
% 0.31/0.61 tff(182,plain,
% 0.31/0.61 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y)))) | (p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3)))))),
% 0.31/0.61 inference(rewrite,[status(thm)],[])).
% 0.31/0.61 tff(183,plain,
% 0.31/0.61 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y)))) | (p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3)))))),
% 0.31/0.61 inference(quant_inst,[status(thm)],[])).
% 0.31/0.61 tff(184,plain,
% 0.31/0.61 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), Y)))) | p1(tptp_fun_Y_15(tptp_fun_Y_13(Y!3))) | (~r1(tptp_fun_X_14(tptp_fun_Y_13(Y!3)), tptp_fun_Y_15(tptp_fun_Y_13(Y!3))))),
% 0.31/0.61 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.31/0.61 tff(185,plain,
% 0.31/0.61 ($false),
% 0.31/0.61 inference(unit_resolution,[status(thm)],[184, 181, 179, 177])).
% 0.31/0.61 tff(186,plain,((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))), inference(lemma,lemma(discharge,[]))).
% 0.31/0.61 tff(187,plain,
% 0.31/0.61 (((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))))))) | (![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3))))))),
% 0.31/0.61 inference(tautology,[status(thm)],[])).
% 0.31/0.61 tff(188,plain,
% 0.31/0.61 (![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))))),
% 0.31/0.61 inference(unit_resolution,[status(thm)],[187, 129])).
% 0.31/0.61 tff(189,plain,
% 0.31/0.61 ((~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3))))))) | ![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))))),
% 0.31/0.61 inference(tautology,[status(thm)],[])).
% 0.31/0.61 tff(190,plain,
% 0.31/0.61 (![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))))),
% 0.31/0.61 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.31/0.61 tff(191,plain,
% 0.31/0.61 (![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))),
% 0.31/0.61 inference(unit_resolution,[status(thm)],[190, 186, 135, 42])).
% 0.31/0.61 tff(192,assumption,(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))), introduced(assumption)).
% 0.31/0.61 tff(193,assumption,((~p1(tptp_fun_Y_6(X!5))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5)))), introduced(assumption)).
% 0.31/0.61 tff(194,plain,
% 0.31/0.61 (((~![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | ((~r1(Y!3, X!5)) | (~((~p1(tptp_fun_Y_6(X!5))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5))))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (~r1(Y!3, X!5)) | (~((~p1(tptp_fun_Y_6(X!5))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5))))))),
% 0.31/0.61 inference(rewrite,[status(thm)],[])).
% 0.31/0.61 tff(195,plain,
% 0.31/0.61 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | ((~r1(Y!3, X!5)) | (~((~p1(tptp_fun_Y_6(X!5))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5))))))),
% 0.31/0.62 inference(quant_inst,[status(thm)],[])).
% 0.31/0.62 tff(196,plain,
% 0.31/0.62 ((~![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (~r1(Y!3, X!5)) | (~((~p1(tptp_fun_Y_6(X!5))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5)))))),
% 0.31/0.62 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.31/0.62 tff(197,plain,
% 0.31/0.62 ($false),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[196, 58, 193, 192])).
% 0.31/0.62 tff(198,plain,((~![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))))))) | (~((~p1(tptp_fun_Y_6(X!5))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5)))))), inference(lemma,lemma(discharge,[]))).
% 0.31/0.62 tff(199,plain,
% 0.31/0.62 (~((~p1(tptp_fun_Y_6(X!5))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5))))),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[198, 191])).
% 0.31/0.62 tff(200,plain,
% 0.31/0.62 (((~p1(tptp_fun_Y_6(X!5))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5)))) | (~p1(tptp_fun_X_7(X!5)))),
% 0.31/0.62 inference(tautology,[status(thm)],[])).
% 0.31/0.62 tff(201,plain,
% 0.31/0.62 (~p1(tptp_fun_X_7(X!5))),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.31/0.62 tff(202,plain,
% 0.31/0.62 (((~p1(tptp_fun_Y_6(X!5))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5)))) | r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5))),
% 0.31/0.62 inference(tautology,[status(thm)],[])).
% 0.31/0.62 tff(203,plain,
% 0.31/0.62 (r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5))),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[202, 199])).
% 0.31/0.62 tff(204,plain,
% 0.31/0.62 (((~p1(tptp_fun_Y_6(X!5))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5)))) | r1(X!5, tptp_fun_Y_6(X!5))),
% 0.31/0.62 inference(tautology,[status(thm)],[])).
% 0.31/0.62 tff(205,plain,
% 0.31/0.62 (r1(X!5, tptp_fun_Y_6(X!5))),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[204, 199])).
% 0.31/0.62 tff(206,plain,
% 0.31/0.62 (((~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!3, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_14(Y))) | (~r1(Y, tptp_fun_X_14(Y))) | p1(tptp_fun_Y_15(Y)) | (~r1(tptp_fun_X_14(Y), tptp_fun_Y_15(Y))))))))) | (~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_11(Y!3)) | (~r1(Y!3, tptp_fun_X_11(Y!3))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_11(Y!3), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!3) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X)))))))) | (~(![X: $i] : ((~r1(Y!3, X)) | (~((~p1(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | p1(tptp_fun_X_7(X)) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!3, X))) | (~p1(Y!3)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_12(Y!3), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_12(Y!3), tptp_fun_Y_13(Y!3))) | p1(tptp_fun_Y_13(Y!3)) | (~r1(Y!3, tptp_fun_X_12(Y!3))) | (~p1(tptp_fun_X_12(Y!3)))))))) | ![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.31/0.62 inference(tautology,[status(thm)],[])).
% 0.31/0.62 tff(207,plain,
% 0.31/0.62 (![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[206, 129])).
% 0.31/0.62 tff(208,plain,
% 0.31/0.62 (((~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!3, X!5)) | (~(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))) | ![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) <=> ((~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!3, X!5)) | (~(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))) | ![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.31/0.62 inference(rewrite,[status(thm)],[])).
% 0.31/0.62 tff(209,plain,
% 0.31/0.62 ((~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!3, X!5)) | (~(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))) | ![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.31/0.62 inference(quant_inst,[status(thm)],[])).
% 0.31/0.62 tff(210,plain,
% 0.31/0.62 ((~![X: $i] : ((~r1(Y!3, X)) | (~(p1(tptp_fun_Y_10(X)) | (~r1(X, tptp_fun_Y_10(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!3, X!5)) | (~(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))) | ![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.31/0.62 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.31/0.62 tff(211,plain,
% 0.31/0.62 ((~(p1(tptp_fun_Y_10(X!5)) | (~r1(X!5, tptp_fun_Y_10(X!5))))) | ![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[210, 58, 207])).
% 0.31/0.62 tff(212,plain,
% 0.31/0.62 (![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[211, 56])).
% 0.31/0.62 tff(213,assumption,(~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))), introduced(assumption)).
% 0.31/0.62 tff(214,assumption,(![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))), introduced(assumption)).
% 0.31/0.62 tff(215,assumption,(r1(X!5, tptp_fun_Y_6(X!5))), introduced(assumption)).
% 0.31/0.62 tff(216,plain,
% 0.31/0.62 (((~![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!5, tptp_fun_Y_6(X!5))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X))))) <=> ((~![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X))))),
% 0.31/0.62 inference(rewrite,[status(thm)],[])).
% 0.31/0.62 tff(217,plain,
% 0.31/0.62 ((~![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!5, tptp_fun_Y_6(X!5))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X))))),
% 0.31/0.62 inference(quant_inst,[status(thm)],[])).
% 0.31/0.62 tff(218,plain,
% 0.31/0.62 ((~![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))),
% 0.31/0.62 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.31/0.62 tff(219,plain,
% 0.31/0.62 ($false),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[218, 215, 214, 213])).
% 0.31/0.62 tff(220,plain,((~![Y: $i] : ((~r1(X!5, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!5, tptp_fun_Y_6(X!5))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))), inference(lemma,lemma(discharge,[]))).
% 0.31/0.62 tff(221,plain,
% 0.31/0.62 ((~r1(X!5, tptp_fun_Y_6(X!5))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[220, 212])).
% 0.31/0.62 tff(222,plain,
% 0.31/0.62 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[221, 205])).
% 0.31/0.62 tff(223,assumption,(![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))), introduced(assumption)).
% 0.31/0.62 tff(224,assumption,(r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5))), introduced(assumption)).
% 0.31/0.62 tff(225,assumption,(~p1(tptp_fun_X_7(X!5))), introduced(assumption)).
% 0.31/0.62 tff(226,plain,
% 0.31/0.62 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))) | (p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5))))),
% 0.31/0.62 inference(rewrite,[status(thm)],[])).
% 0.31/0.62 tff(227,plain,
% 0.31/0.62 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))) | (p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5))))),
% 0.31/0.62 inference(quant_inst,[status(thm)],[])).
% 0.31/0.62 tff(228,plain,
% 0.31/0.62 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5)))),
% 0.31/0.62 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.31/0.62 tff(229,plain,
% 0.31/0.62 ($false),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[228, 225, 224, 223])).
% 0.31/0.62 tff(230,plain,((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_6(X!5), X)))) | p1(tptp_fun_X_7(X!5)) | (~r1(tptp_fun_Y_6(X!5), tptp_fun_X_7(X!5)))), inference(lemma,lemma(discharge,[]))).
% 0.31/0.62 tff(231,plain,
% 0.31/0.62 ($false),
% 0.31/0.62 inference(unit_resolution,[status(thm)],[230, 222, 203, 201])).
% 0.31/0.62 % SZS output end Proof
% 0.14/0.62 % E exiting
%------------------------------------------------------------------------------