%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL658+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:27 PM UTC 2026
% Result : Theorem 0.22s 0.47s
% Output : Proof 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL658+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n028.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 4 18:14:30 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.22/0.47 % SZS status Theorem
% 0.22/0.47 % SZS output start Proof
% 0.22/0.47 tff(p1_type, type, (
% 0.22/0.47 p1: $i > $o)).
% 0.22/0.47 tff(tptp_fun_Y_1_type, type, (
% 0.22/0.47 tptp_fun_Y_1: $i > $i)).
% 0.22/0.47 tff(tptp_fun_X_6_type, type, (
% 0.22/0.47 tptp_fun_X_6: $i)).
% 0.22/0.47 tff(r1_type, type, (
% 0.22/0.47 r1: ( $i * $i ) > $o)).
% 0.22/0.47 tff(tptp_fun_Y_4_type, type, (
% 0.22/0.47 tptp_fun_Y_4: $i)).
% 0.22/0.47 tff(tptp_fun_X_8_type, type, (
% 0.22/0.47 tptp_fun_X_8: $i > $i)).
% 0.22/0.47 tff(tptp_fun_Y_7_type, type, (
% 0.22/0.47 tptp_fun_Y_7: $i > $i)).
% 0.22/0.47 tff(tptp_fun_X_3_type, type, (
% 0.22/0.47 tptp_fun_X_3: $i)).
% 0.22/0.47 tff(tptp_fun_Y_2_type, type, (
% 0.22/0.47 tptp_fun_Y_2: $i)).
% 0.22/0.47 tff(tptp_fun_X_0_type, type, (
% 0.22/0.47 tptp_fun_X_0: $i)).
% 0.22/0.47 tff(tptp_fun_X_12_type, type, (
% 0.22/0.47 tptp_fun_X_12: $i > $i)).
% 0.22/0.47 tff(tptp_fun_Y_14_type, type, (
% 0.22/0.47 tptp_fun_Y_14: $i > $i)).
% 0.22/0.47 tff(tptp_fun_X_13_type, type, (
% 0.22/0.47 tptp_fun_X_13: $i > $i)).
% 0.22/0.47 tff(tptp_fun_X_9_type, type, (
% 0.22/0.47 tptp_fun_X_9: $i > $i)).
% 0.22/0.47 tff(tptp_fun_X_10_type, type, (
% 0.22/0.47 tptp_fun_X_10: $i > $i)).
% 0.22/0.47 tff(tptp_fun_Y_11_type, type, (
% 0.22/0.47 tptp_fun_Y_11: $i > $i)).
% 0.22/0.47 tff(tptp_fun_X_5_type, type, (
% 0.22/0.47 tptp_fun_X_5: $i)).
% 0.22/0.47 tff(1,assumption,(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))), introduced(assumption)).
% 0.22/0.47 tff(2,plain,
% 0.22/0.47 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(3,plain,
% 0.22/0.47 (^[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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_10(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))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) <=> ((~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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(4,plain,
% 0.22/0.47 (![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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_10(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))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) <=> ![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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.47 tff(5,plain,
% 0.22/0.47 (((r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(6,plain,
% 0.22/0.47 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~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)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(7,plain,
% 0.22/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.47 tff(8,plain,
% 0.22/0.47 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(9,plain,
% 0.22/0.47 ((r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(10,plain,
% 0.22/0.47 ((r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) <=> (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(11,plain,
% 0.22/0.47 ((r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) <=> (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(12,plain,
% 0.22/0.47 ((r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) <=> (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[11])).
% 0.22/0.47 tff(13,plain,
% 0.22/0.47 ((r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) <=> (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[12, 10])).
% 0.22/0.47 tff(14,plain,
% 0.22/0.47 ((r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))) <=> (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[13])).
% 0.22/0.48 tff(15,plain,
% 0.22/0.48 ((r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[14, 9])).
% 0.22/0.48 tff(16,plain,
% 0.22/0.48 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) <=> (r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[15])).
% 0.22/0.48 tff(17,plain,
% 0.22/0.48 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[16, 8])).
% 0.22/0.48 tff(18,plain,
% 0.22/0.48 (((r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) <=> ((r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[17, 7])).
% 0.22/0.48 tff(19,plain,
% 0.22/0.48 (((r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(Y)))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[18, 5])).
% 0.22/0.48 tff(20,plain,
% 0.22/0.48 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ((r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_10(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))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))))))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[19, 4])).
% 0.22/0.48 tff(21,plain,
% 0.22/0.48 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ((r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & (r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_10(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))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_12(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[20, 2])).
% 0.22/0.48 tff(22,plain,
% 0.22/0.48 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (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)) | (~![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] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![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)))))) | (~![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)))))))))) & (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] : (p1(Y) | (~r1(X, Y)))) | ![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] : ((~r1(Y, X)) | (~p1(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] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (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)) | (~![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] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![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)))))) | (~![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)))))))))) & (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] : (p1(Y) | (~r1(X, Y)))) | ![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] : ((~r1(Y, X)) | (~p1(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)))))))))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(23,plain,
% 0.22/0.49 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (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)) | (~![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] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![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)))))) | (~![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)))))))))) & (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] : (p1(Y) | (~r1(X, Y)))) | ![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] : ((~r1(Y, X)) | (~p1(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] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (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)) | (~![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] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![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)))))) | (~![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)))))))))) & (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] : (p1(Y) | (~r1(X, Y)))) | ![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] : ((~r1(Y, X)) | (~p1(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)))))))))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(24,plain,
% 0.22/0.49 ((~?[X: $i] : (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((((((![X: $i] : ((~r1(Y, X)) | 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (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)) | (~![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] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![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)))))) | (~![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)))))))))) & (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] : (p1(Y) | (~r1(X, Y)))) | ![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] : ((~r1(Y, X)) | (~p1(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))))))))))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(25,plain,
% 0.22/0.49 ((~(~?[X: $i] : (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((((((![X: $i] : ((~r1(Y, X)) | 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (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)) | (~![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] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![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)))))) | (~![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)))))))))) & (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] : (p1(Y) | (~r1(X, Y)))) | ![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] : ((~r1(Y, X)) | (~p1(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)))))))))))))))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[24])).
% 0.22/0.49 tff(26,plain,
% 0.22/0.49 ((~(~?[X: $i] : (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((((((![X: $i] : ((~r1(Y, X)) | 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (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)) | (~![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] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![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)))))) | (~![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)))))))))) & (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] : (p1(Y) | (~r1(X, Y)))) | ![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] : ((~r1(Y, X)) | (~p1(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)))))))))))))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[25, 23])).
% 0.22/0.50 tff(27,axiom,(~(~?[X: $i] : (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((((((![X: $i] : ((~r1(Y, X)) | 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.22/0.50 tff(28,plain,
% 0.22/0.50 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (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)) | (~![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] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![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)))))) | (~![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)))))))))) & (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] : (p1(Y) | (~r1(X, Y)))) | ![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] : ((~r1(Y, X)) | (~p1(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)))))))))))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.22/0.50 tff(29,plain,
% 0.22/0.50 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (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)) | (~![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] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![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)))))) | (~![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)))))))))) & (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] : (p1(Y) | (~r1(X, Y)))) | ![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] : ((~r1(Y, X)) | (~p1(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)))))))))))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.22/0.50 tff(30,plain,
% 0.22/0.50 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~(p1(X!5) | (~r1(Y!4, X!5)))) & r1(Y!4, X!6) & ![Y: $i] : (p1(Y) | (~r1(X!6, Y))) & ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_9(Y)) | (~r1(Y, tptp_fun_X_9(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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.22/0.50 tff(31,plain,
% 0.22/0.50 (r1(X!0, Y!2)),
% 0.22/0.50 inference(and_elim,[status(thm)],[30])).
% 0.22/0.50 tff(32,plain,
% 0.22/0.50 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(33,plain,
% 0.22/0.50 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[32])).
% 0.22/0.50 tff(34,plain,
% 0.22/0.50 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(35,plain,
% 0.22/0.50 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[34])).
% 0.22/0.50 tff(36,plain,
% 0.22/0.50 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[35, 33])).
% 0.22/0.50 tff(37,plain,
% 0.22/0.50 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.22/0.50 inference(and_elim,[status(thm)],[30])).
% 0.22/0.50 tff(38,plain,
% 0.22/0.50 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.22/0.50 tff(39,plain,
% 0.22/0.50 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(40,plain,
% 0.22/0.50 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(41,plain,
% 0.22/0.50 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.22/0.51 tff(42,plain,
% 0.22/0.51 (![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[41, 38, 31])).
% 0.22/0.51 tff(43,plain,
% 0.22/0.51 (r1(Y!2, X!3)),
% 0.22/0.51 inference(and_elim,[status(thm)],[30])).
% 0.22/0.51 tff(44,plain,
% 0.22/0.51 (((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ((~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | (~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(45,plain,
% 0.22/0.51 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ((~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(46,plain,
% 0.22/0.51 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | (~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.22/0.51 tff(47,plain,
% 0.22/0.51 (![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[46, 43, 42])).
% 0.22/0.51 tff(48,plain,
% 0.22/0.51 (r1(X!3, Y!4)),
% 0.22/0.51 inference(and_elim,[status(thm)],[30])).
% 0.22/0.51 tff(49,plain,
% 0.22/0.51 (((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ((~r1(X!3, Y!4)) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) <=> ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~r1(X!3, Y!4)) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(50,plain,
% 0.22/0.51 ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ((~r1(X!3, Y!4)) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(51,plain,
% 0.22/0.51 ((~![Y: $i] : ((~r1(X!3, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~r1(X!3, Y!4)) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.22/0.51 tff(52,plain,
% 0.22/0.51 (![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[51, 48, 47])).
% 0.22/0.51 tff(53,plain,
% 0.22/0.51 (r1(Y!4, X!6)),
% 0.22/0.51 inference(and_elim,[status(thm)],[30])).
% 0.22/0.51 tff(54,plain,
% 0.22/0.51 (((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) | ![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) <=> ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) | ![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(55,plain,
% 0.22/0.51 ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) | ![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(56,plain,
% 0.22/0.51 ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) | ![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.22/0.51 tff(57,plain,
% 0.22/0.51 ((~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) | ![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[56, 53, 52])).
% 0.22/0.51 tff(58,plain,
% 0.22/0.51 (![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[57, 1])).
% 0.22/0.51 tff(59,assumption,(![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))), introduced(assumption)).
% 0.22/0.51 tff(60,assumption,(~((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))), introduced(assumption)).
% 0.22/0.51 tff(61,plain,
% 0.22/0.51 (((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))) | r1(X!6, tptp_fun_Y_7(X!6))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(62,plain,
% 0.22/0.51 (r1(X!6, tptp_fun_Y_7(X!6))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.22/0.51 tff(63,plain,
% 0.22/0.51 (((~![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!6, tptp_fun_Y_7(X!6))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X))))) <=> ((~![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(64,plain,
% 0.22/0.51 ((~![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!6, tptp_fun_Y_7(X!6))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(65,plain,
% 0.22/0.51 ((~![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.22/0.51 tff(66,plain,
% 0.22/0.51 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[65, 62, 59])).
% 0.22/0.51 tff(67,plain,
% 0.22/0.51 (((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))) | r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(68,plain,
% 0.22/0.51 (r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[67, 60])).
% 0.22/0.51 tff(69,plain,
% 0.22/0.51 (((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))) | (~p1(tptp_fun_X_8(X!6)))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(70,plain,
% 0.22/0.51 (~p1(tptp_fun_X_8(X!6))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[69, 60])).
% 0.22/0.51 tff(71,plain,
% 0.22/0.51 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))) | (p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(72,plain,
% 0.22/0.51 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))) | (p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(73,plain,
% 0.22/0.51 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!6), X)))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.22/0.51 tff(74,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[73, 70, 68, 66])).
% 0.22/0.51 tff(75,plain,(((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))) | (~![Y: $i] : ((~r1(X!6, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(76,plain,
% 0.22/0.51 ((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[75, 58])).
% 0.22/0.51 tff(77,assumption,(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))), introduced(assumption)).
% 0.22/0.51 tff(78,assumption,((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))), introduced(assumption)).
% 0.22/0.51 tff(79,plain,
% 0.22/0.51 (((~![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | ((~r1(Y!4, X!6)) | (~((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))))) <=> ((~![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (~r1(Y!4, X!6)) | (~((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(80,plain,
% 0.22/0.51 ((~![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | ((~r1(Y!4, X!6)) | (~((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6))))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(81,plain,
% 0.22/0.51 ((~![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (~r1(Y!4, X!6)) | (~((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.22/0.51 tff(82,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[81, 53, 78, 77])).
% 0.22/0.51 tff(83,plain,((~![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (~((~p1(tptp_fun_Y_7(X!6))) | (~r1(X!6, tptp_fun_Y_7(X!6))) | p1(tptp_fun_X_8(X!6)) | (~r1(tptp_fun_Y_7(X!6), tptp_fun_X_8(X!6)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(84,plain,
% 0.22/0.51 (~![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[83, 76])).
% 0.22/0.51 tff(85,assumption,(~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))), introduced(assumption)).
% 0.22/0.51 tff(86,plain,
% 0.22/0.51 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4)))) | r1(Y!4, tptp_fun_X_10(Y!4))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(87,plain,
% 0.22/0.51 (r1(Y!4, tptp_fun_X_10(Y!4))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.22/0.51 tff(88,assumption,(~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))), introduced(assumption)).
% 0.22/0.51 tff(89,plain,
% 0.22/0.51 ((p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | r1(Y!4, tptp_fun_X_12(Y!4))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(90,plain,
% 0.22/0.51 (r1(Y!4, tptp_fun_X_12(Y!4))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.22/0.51 tff(91,plain,
% 0.22/0.51 ((p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~p1(tptp_fun_X_12(Y!4)))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(92,plain,
% 0.22/0.51 (~p1(tptp_fun_X_12(Y!4))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[91, 88])).
% 0.22/0.51 tff(93,plain,
% 0.22/0.51 (^[X: $i] : refl((p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) <=> (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(94,plain,
% 0.22/0.51 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) <=> ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[93])).
% 0.22/0.51 tff(95,plain,
% 0.22/0.51 (^[X: $i] : rewrite((p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) <=> (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(96,plain,
% 0.22/0.51 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) <=> ![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[95])).
% 0.22/0.51 tff(97,plain,
% 0.22/0.51 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))),
% 0.22/0.51 inference(and_elim,[status(thm)],[30])).
% 0.22/0.51 tff(98,plain,
% 0.22/0.51 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.22/0.51 tff(99,plain,
% 0.22/0.51 (![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.22/0.51 tff(100,plain,
% 0.22/0.51 (((~![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(101,plain,
% 0.22/0.51 ((~![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(102,plain,
% 0.22/0.51 ((~![X: $i] : (p1(X) | (~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.22/0.51 tff(103,plain,
% 0.22/0.51 (~((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[102, 99, 92, 90])).
% 0.22/0.51 tff(104,plain,
% 0.22/0.51 (((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))) | r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(105,plain,
% 0.22/0.51 (r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.22/0.51 tff(106,plain,
% 0.22/0.51 (((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))) | p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(107,plain,
% 0.22/0.51 (p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.22/0.51 tff(108,plain,
% 0.22/0.51 ((p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(109,plain,
% 0.22/0.51 (![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[108, 88])).
% 0.22/0.51 tff(110,plain,
% 0.22/0.51 (((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X))))) <=> ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(111,plain,
% 0.22/0.52 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(112,plain,
% 0.22/0.52 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.22/0.52 tff(113,plain,
% 0.22/0.52 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[112, 109, 107, 105])).
% 0.22/0.52 tff(114,plain,
% 0.22/0.52 (((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))) | r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(115,plain,
% 0.22/0.52 (r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[114, 103])).
% 0.22/0.52 tff(116,plain,
% 0.22/0.52 (((~p1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | (~r1(tptp_fun_X_12(Y!4), tptp_fun_Y_7(tptp_fun_X_12(Y!4)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))) | (~p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(117,plain,
% 0.22/0.52 (~p1(tptp_fun_X_8(tptp_fun_X_12(Y!4)))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[116, 103])).
% 0.22/0.52 tff(118,plain,
% 0.22/0.52 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))) | (p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(119,plain,
% 0.22/0.52 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))) | (p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4)))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(120,plain,
% 0.22/0.52 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), X)))) | p1(tptp_fun_X_8(tptp_fun_X_12(Y!4))) | (~r1(tptp_fun_Y_7(tptp_fun_X_12(Y!4)), tptp_fun_X_8(tptp_fun_X_12(Y!4))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.22/0.52 tff(121,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[120, 117, 115, 113])).
% 0.22/0.52 tff(122,plain,(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.52 tff(123,plain,
% 0.22/0.52 (^[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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(124,plain,
% 0.22/0.52 (![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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(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))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[123])).
% 0.22/0.52 tff(125,plain,
% 0.22/0.52 (^[Y: $i] : refl(((~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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(126,plain,
% 0.22/0.52 (![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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[125])).
% 0.22/0.52 tff(127,plain,
% 0.22/0.52 (^[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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(128,plain,
% 0.22/0.52 (![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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[127])).
% 0.22/0.52 tff(129,plain,
% 0.22/0.52 (![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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.22/0.53 inference(transitivity,[status(thm)],[128, 126])).
% 0.22/0.53 tff(130,plain,
% 0.22/0.53 (^[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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), 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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(131,plain,
% 0.22/0.53 (![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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), 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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[130])).
% 0.22/0.53 tff(132,plain,
% 0.22/0.53 (![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_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))))) | (r1(Y, tptp_fun_X_10(Y)) & p1(tptp_fun_X_10(Y)) & (~(p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(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)) | (r1(Y, tptp_fun_X_13(Y)) & p1(tptp_fun_X_13(Y)) & (~(p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~p1(tptp_fun_X_12(Y))) & r1(Y, tptp_fun_X_12(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))))),
% 0.22/0.53 inference(and_elim,[status(thm)],[30])).
% 0.22/0.53 tff(133,plain,
% 0.22/0.53 (![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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.22/0.53 tff(134,plain,
% 0.22/0.53 (![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)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_10(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_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_12(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.22/0.53 tff(135,plain,
% 0.22/0.53 (![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))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[134, 124])).
% 0.22/0.53 tff(136,plain,
% 0.22/0.53 (((~![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))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(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))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(137,plain,
% 0.22/0.53 ((~![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))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(138,plain,
% 0.22/0.54 ((~![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))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))))) | (~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.22/0.54 tff(139,plain,
% 0.22/0.54 (![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[138, 31, 135])).
% 0.22/0.54 tff(140,plain,
% 0.22/0.54 (((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) | ((~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) | (~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(141,plain,
% 0.22/0.54 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) | ((~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(142,plain,
% 0.22/0.54 ((~![X: $i] : ((~r1(Y!2, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))))) | (~r1(Y!2, X!3)) | ![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.22/0.54 tff(143,plain,
% 0.22/0.54 (![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[142, 43, 139])).
% 0.22/0.54 tff(144,plain,
% 0.22/0.54 (((~![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | ((~r1(X!3, Y!4)) | (~((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | (~r1(X!3, Y!4)) | (~((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(145,plain,
% 0.22/0.55 (((~r1(X!3, Y!4)) | (~((~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~((~p1(tptp_fun_X_10(Y!4))) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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)))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))))))) <=> ((~r1(X!3, Y!4)) | (~((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(146,plain,
% 0.22/0.55 (((~![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | ((~r1(X!3, Y!4)) | (~((~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~((~p1(tptp_fun_X_10(Y!4))) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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)))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | ((~r1(X!3, Y!4)) | (~((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[145])).
% 0.22/0.55 tff(147,plain,
% 0.22/0.55 (((~![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | ((~r1(X!3, Y!4)) | (~((~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~((~p1(tptp_fun_X_10(Y!4))) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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)))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | (~r1(X!3, Y!4)) | (~((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.22/0.55 inference(transitivity,[status(thm)],[146, 144])).
% 0.22/0.55 tff(148,plain,
% 0.22/0.55 ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | ((~r1(X!3, Y!4)) | (~((~((~p1(Y!4)) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~((~p1(tptp_fun_X_10(Y!4))) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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)))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(149,plain,
% 0.22/0.55 ((~![Y: $i] : ((~r1(X!3, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~p1(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | p1(tptp_fun_Y_11(Y)) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_10(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)))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_12(Y)) | (~r1(Y, tptp_fun_X_12(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(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_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))))))) | (~r1(X!3, Y!4)) | (~((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.22/0.55 tff(150,plain,
% 0.22/0.55 (~((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[149, 48, 143])).
% 0.22/0.56 tff(151,plain,
% 0.22/0.56 (((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | ((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(152,plain,
% 0.22/0.56 ((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.22/0.56 tff(153,plain,
% 0.22/0.56 ((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(154,plain,
% 0.22/0.56 ((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.22/0.56 tff(155,plain,
% 0.22/0.56 (![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[154, 122])).
% 0.22/0.56 tff(156,plain,
% 0.22/0.56 (((~![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~r1(Y!4, tptp_fun_X_10(Y!4))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(157,plain,
% 0.22/0.56 ((~![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | ((~r1(Y!4, tptp_fun_X_10(Y!4))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(158,plain,
% 0.22/0.56 ((~![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y)))))))) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.22/0.56 tff(159,plain,
% 0.22/0.56 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[158, 155, 87])).
% 0.22/0.56 tff(160,plain,
% 0.22/0.56 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4)))) | (~p1(tptp_fun_Y_11(Y!4)))),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(161,plain,
% 0.22/0.56 (~p1(tptp_fun_Y_11(Y!4))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[160, 85])).
% 0.22/0.56 tff(162,plain,
% 0.22/0.56 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4)))) | r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(163,plain,
% 0.22/0.56 (r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[162, 85])).
% 0.22/0.56 tff(164,plain,
% 0.22/0.56 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | (p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~(p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~(p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))))),
% 0.32/0.56 inference(rewrite,[status(thm)],[])).
% 0.32/0.56 tff(165,plain,
% 0.32/0.56 ((p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4))))))) <=> (p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~(p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))))),
% 0.32/0.56 inference(rewrite,[status(thm)],[])).
% 0.32/0.56 tff(166,plain,
% 0.32/0.56 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | (p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | (p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~(p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4))))))))),
% 0.32/0.56 inference(monotonicity,[status(thm)],[165])).
% 0.32/0.56 tff(167,plain,
% 0.32/0.56 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | (p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~(p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))))),
% 0.32/0.56 inference(transitivity,[status(thm)],[166, 164])).
% 0.32/0.56 tff(168,plain,
% 0.32/0.56 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | (p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))))),
% 0.32/0.56 inference(quant_inst,[status(thm)],[])).
% 0.32/0.56 tff(169,plain,
% 0.32/0.56 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_10(Y!4), Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~(p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4))))))),
% 0.32/0.56 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.32/0.56 tff(170,plain,
% 0.32/0.56 (~(p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[169, 163, 161, 159])).
% 0.32/0.56 tff(171,plain,
% 0.32/0.56 ((p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4))))) | r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))),
% 0.32/0.56 inference(tautology,[status(thm)],[])).
% 0.32/0.56 tff(172,plain,
% 0.32/0.56 (r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.32/0.56 tff(173,plain,
% 0.32/0.56 ((p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4))))) | p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))),
% 0.32/0.56 inference(tautology,[status(thm)],[])).
% 0.32/0.56 tff(174,plain,
% 0.32/0.56 (p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[173, 170])).
% 0.32/0.56 tff(175,plain,
% 0.32/0.56 (((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4))))) | p1(tptp_fun_Y_11(Y!4))),
% 0.32/0.56 inference(tautology,[status(thm)],[])).
% 0.32/0.56 tff(176,plain,
% 0.32/0.56 ((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4))))),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[175, 161])).
% 0.32/0.56 tff(177,plain,
% 0.32/0.56 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4)))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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)))))),
% 0.32/0.56 inference(tautology,[status(thm)],[])).
% 0.32/0.56 tff(178,plain,
% 0.32/0.56 (![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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)))))),
% 0.32/0.56 inference(unit_resolution,[status(thm)],[177, 85])).
% 0.32/0.56 tff(179,plain,
% 0.32/0.56 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X))))),
% 0.32/0.56 inference(rewrite,[status(thm)],[])).
% 0.32/0.56 tff(180,plain,
% 0.32/0.56 (((~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~r1(tptp_fun_Y_11(Y!4), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) <=> ((~r1(tptp_fun_X_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X))))),
% 0.32/0.57 inference(rewrite,[status(thm)],[])).
% 0.32/0.57 tff(181,plain,
% 0.32/0.57 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~r1(tptp_fun_Y_11(Y!4), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))))),
% 0.32/0.57 inference(monotonicity,[status(thm)],[180])).
% 0.32/0.57 tff(182,plain,
% 0.32/0.57 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~r1(tptp_fun_Y_11(Y!4), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X))))),
% 0.32/0.57 inference(transitivity,[status(thm)],[181, 179])).
% 0.32/0.57 tff(183,plain,
% 0.32/0.57 ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~r1(tptp_fun_Y_11(Y!4), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.32/0.57 inference(quant_inst,[status(thm)],[])).
% 0.32/0.57 tff(184,plain,
% 0.32/0.57 ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | (~((~p1(tptp_fun_Y_11(Y!4))) | p1(tptp_fun_X_9(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_9(tptp_fun_Y_11(Y!4)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))),
% 0.32/0.57 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.32/0.57 tff(185,plain,
% 0.32/0.57 (![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[184, 178, 163, 176])).
% 0.32/0.57 tff(186,plain,
% 0.32/0.57 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | ((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))))),
% 0.32/0.57 inference(rewrite,[status(thm)],[])).
% 0.32/0.57 tff(187,plain,
% 0.32/0.57 (((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4))))) <=> ((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))))),
% 0.32/0.57 inference(rewrite,[status(thm)],[])).
% 0.32/0.57 tff(188,plain,
% 0.32/0.57 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | ((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | ((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))))),
% 0.32/0.57 inference(monotonicity,[status(thm)],[187])).
% 0.32/0.57 tff(189,plain,
% 0.32/0.57 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | ((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))))),
% 0.32/0.57 inference(transitivity,[status(thm)],[188, 186])).
% 0.32/0.57 tff(190,plain,
% 0.32/0.57 ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | ((~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))))),
% 0.32/0.57 inference(quant_inst,[status(thm)],[])).
% 0.32/0.57 tff(191,plain,
% 0.32/0.57 ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_11(Y!4), X)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))),
% 0.32/0.57 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.32/0.57 tff(192,plain,
% 0.32/0.57 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[191, 185, 174, 172])).
% 0.32/0.57 tff(193,plain,
% 0.32/0.57 ((p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4))))) | r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))),
% 0.32/0.57 inference(tautology,[status(thm)],[])).
% 0.32/0.57 tff(194,plain,
% 0.32/0.57 (r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[193, 170])).
% 0.32/0.57 tff(195,plain,
% 0.32/0.57 ((p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))) | (~p1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)))) | (~r1(tptp_fun_Y_11(Y!4), tptp_fun_X_13(tptp_fun_Y_11(Y!4))))) | (~p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))))),
% 0.32/0.57 inference(tautology,[status(thm)],[])).
% 0.32/0.57 tff(196,plain,
% 0.32/0.57 (~p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[195, 170])).
% 0.32/0.57 tff(197,plain,
% 0.32/0.57 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))) | (p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))),
% 0.32/0.57 inference(rewrite,[status(thm)],[])).
% 0.32/0.57 tff(198,plain,
% 0.32/0.57 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))) | (p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4)))))),
% 0.32/0.57 inference(quant_inst,[status(thm)],[])).
% 0.32/0.57 tff(199,plain,
% 0.32/0.57 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), Y)))) | p1(tptp_fun_Y_14(tptp_fun_Y_11(Y!4))) | (~r1(tptp_fun_X_13(tptp_fun_Y_11(Y!4)), tptp_fun_Y_14(tptp_fun_Y_11(Y!4))))),
% 0.32/0.57 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.32/0.57 tff(200,plain,
% 0.32/0.57 ($false),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[199, 196, 194, 192])).
% 0.32/0.57 tff(201,plain,((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.32/0.57 tff(202,assumption,(![X: $i] : (p1(X) | (~r1(Y!4, X)))), introduced(assumption)).
% 0.32/0.57 tff(203,plain,
% 0.32/0.57 (~(p1(X!5) | (~r1(Y!4, X!5)))),
% 0.32/0.57 inference(and_elim,[status(thm)],[30])).
% 0.32/0.57 tff(204,plain,
% 0.32/0.57 (r1(Y!4, X!5)),
% 0.32/0.57 inference(or_elim,[status(thm)],[203])).
% 0.32/0.57 tff(205,plain,
% 0.32/0.57 (~p1(X!5)),
% 0.32/0.57 inference(or_elim,[status(thm)],[203])).
% 0.32/0.57 tff(206,plain,
% 0.32/0.57 (((~![X: $i] : (p1(X) | (~r1(Y!4, X)))) | (p1(X!5) | (~r1(Y!4, X!5)))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!4, X)))) | p1(X!5) | (~r1(Y!4, X!5)))),
% 0.32/0.57 inference(rewrite,[status(thm)],[])).
% 0.32/0.57 tff(207,plain,
% 0.32/0.57 ((~![X: $i] : (p1(X) | (~r1(Y!4, X)))) | (p1(X!5) | (~r1(Y!4, X!5)))),
% 0.32/0.57 inference(quant_inst,[status(thm)],[])).
% 0.32/0.57 tff(208,plain,
% 0.32/0.57 ((~![X: $i] : (p1(X) | (~r1(Y!4, X)))) | p1(X!5) | (~r1(Y!4, X!5))),
% 0.32/0.57 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.32/0.57 tff(209,plain,
% 0.32/0.57 ($false),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[208, 205, 204, 202])).
% 0.32/0.57 tff(210,plain,(~![X: $i] : (p1(X) | (~r1(Y!4, X)))), inference(lemma,lemma(discharge,[]))).
% 0.32/0.57 tff(211,plain,
% 0.32/0.57 (((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | (![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))),
% 0.32/0.57 inference(tautology,[status(thm)],[])).
% 0.32/0.57 tff(212,plain,
% 0.32/0.57 (![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4)))))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[211, 150])).
% 0.32/0.57 tff(213,plain,
% 0.32/0.57 ((~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | ![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4)))))),
% 0.32/0.57 inference(tautology,[status(thm)],[])).
% 0.32/0.57 tff(214,plain,
% 0.32/0.57 (![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4)))))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.32/0.57 tff(215,plain,
% 0.32/0.57 (![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | (~p1(Y!4))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[214, 210, 201])).
% 0.32/0.57 tff(216,plain,
% 0.32/0.57 (~p1(Y!4)),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[215, 84])).
% 0.32/0.57 tff(217,plain,
% 0.32/0.57 (((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!4, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))) | p1(tptp_fun_Y_14(Y)) | (~r1(tptp_fun_X_13(Y), tptp_fun_Y_14(Y))))))))) | (~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!4, X)) | (~((~p1(tptp_fun_Y_7(X))) | (~r1(X, tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!4, X))) | (~p1(Y!4)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!4), 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_10(Y!4), tptp_fun_Y_11(Y!4))) | p1(tptp_fun_Y_11(Y!4)) | (~r1(Y!4, tptp_fun_X_10(Y!4))) | (~p1(tptp_fun_X_10(Y!4))))))) | (~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | ((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.32/0.57 inference(tautology,[status(thm)],[])).
% 0.32/0.57 tff(218,plain,
% 0.32/0.57 ((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[217, 150])).
% 0.32/0.57 tff(219,plain,
% 0.32/0.57 ((~((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.32/0.57 inference(tautology,[status(thm)],[])).
% 0.32/0.57 tff(220,plain,
% 0.32/0.57 ((~(p1(tptp_fun_X_12(Y!4)) | (~r1(Y!4, tptp_fun_X_12(Y!4))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_12(Y!4), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.32/0.57 tff(221,plain,
% 0.32/0.57 (p1(Y!4) | ![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[220, 122])).
% 0.32/0.57 tff(222,plain,
% 0.32/0.57 (![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[221, 216])).
% 0.32/0.57 tff(223,plain,
% 0.32/0.57 (((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))))) <=> ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))))),
% 0.32/0.57 inference(rewrite,[status(thm)],[])).
% 0.32/0.57 tff(224,plain,
% 0.32/0.57 ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))))),
% 0.32/0.57 inference(quant_inst,[status(thm)],[])).
% 0.32/0.57 tff(225,plain,
% 0.32/0.57 ((~![X: $i] : ((~r1(Y!4, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!4, X!6)) | (~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))))),
% 0.32/0.57 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.32/0.57 tff(226,plain,
% 0.32/0.57 ($false),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[225, 53, 222, 1])).
% 0.32/0.57 tff(227,plain,(~(p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))), inference(lemma,lemma(discharge,[]))).
% 0.32/0.57 tff(228,plain,
% 0.32/0.57 ((p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))) | (~p1(tptp_fun_Y_1(X!6)))),
% 0.32/0.57 inference(tautology,[status(thm)],[])).
% 0.32/0.57 tff(229,plain,
% 0.32/0.57 (~p1(tptp_fun_Y_1(X!6))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.32/0.57 tff(230,plain,
% 0.32/0.57 ((p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))) | r1(X!6, tptp_fun_Y_1(X!6))),
% 0.32/0.57 inference(tautology,[status(thm)],[])).
% 0.32/0.57 tff(231,plain,
% 0.32/0.57 (r1(X!6, tptp_fun_Y_1(X!6))),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.32/0.57 tff(232,assumption,(r1(X!6, tptp_fun_Y_1(X!6))), introduced(assumption)).
% 0.32/0.57 tff(233,assumption,(~p1(tptp_fun_Y_1(X!6))), introduced(assumption)).
% 0.32/0.57 tff(234,plain,
% 0.32/0.57 (^[Y: $i] : refl((p1(Y) | (~r1(X!6, Y))) <=> (p1(Y) | (~r1(X!6, Y))))),
% 0.32/0.57 inference(bind,[status(th)],[])).
% 0.32/0.57 tff(235,plain,
% 0.32/0.57 (![Y: $i] : (p1(Y) | (~r1(X!6, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!6, Y)))),
% 0.32/0.57 inference(quant_intro,[status(thm)],[234])).
% 0.32/0.57 tff(236,plain,
% 0.32/0.57 (![Y: $i] : (p1(Y) | (~r1(X!6, Y)))),
% 0.32/0.57 inference(and_elim,[status(thm)],[30])).
% 0.32/0.57 tff(237,plain,
% 0.32/0.57 (![Y: $i] : (p1(Y) | (~r1(X!6, Y)))),
% 0.32/0.57 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.32/0.57 tff(238,plain,
% 0.32/0.57 (((~![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) | (p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) | p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))),
% 0.32/0.57 inference(rewrite,[status(thm)],[])).
% 0.32/0.57 tff(239,plain,
% 0.32/0.57 ((~![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) | (p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6))))),
% 0.32/0.57 inference(quant_inst,[status(thm)],[])).
% 0.32/0.57 tff(240,plain,
% 0.32/0.57 ((~![Y: $i] : (p1(Y) | (~r1(X!6, Y)))) | p1(tptp_fun_Y_1(X!6)) | (~r1(X!6, tptp_fun_Y_1(X!6)))),
% 0.32/0.57 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.32/0.57 tff(241,plain,
% 0.32/0.57 ($false),
% 0.32/0.57 inference(unit_resolution,[status(thm)],[240, 237, 233, 232])).
% 0.32/0.57 tff(242,plain,((~r1(X!6, tptp_fun_Y_1(X!6))) | p1(tptp_fun_Y_1(X!6))), inference(lemma,lemma(discharge,[]))).
% 0.32/0.58 tff(243,plain,
% 0.32/0.58 ($false),
% 0.32/0.58 inference(unit_resolution,[status(thm)],[242, 231, 229])).
% 0.32/0.58 % SZS output end Proof
% 0.32/0.58 % E exiting
%------------------------------------------------------------------------------