%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL640+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:19 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL640+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.35 % Computer : n008.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 5 13:37:09 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.45 % SZS status Theorem
% 0.12/0.45 % SZS output start Proof
% 0.12/0.45 tff(r1_type, type, (
% 0.12/0.45 r1: ( $i * $i ) > $o)).
% 0.12/0.45 tff(p1_type, type, (
% 0.12/0.45 p1: $i > $o)).
% 0.12/0.45 tff(tptp_fun_X_7_type, type, (
% 0.12/0.45 tptp_fun_X_7: $i > $i)).
% 0.12/0.45 tff(tptp_fun_Y_10_type, type, (
% 0.12/0.45 tptp_fun_Y_10: $i)).
% 0.12/0.45 tff(tptp_fun_X_8_type, type, (
% 0.12/0.45 tptp_fun_X_8: $i > $i)).
% 0.12/0.45 tff(tptp_fun_Y_4_type, type, (
% 0.12/0.45 tptp_fun_Y_4: $i > $i)).
% 0.12/0.45 tff(tptp_fun_Y_9_type, type, (
% 0.12/0.45 tptp_fun_Y_9: $i > $i)).
% 0.12/0.45 tff(tptp_fun_X_3_type, type, (
% 0.12/0.45 tptp_fun_X_3: $i > $i)).
% 0.12/0.45 tff(tptp_fun_X_5_type, type, (
% 0.12/0.45 tptp_fun_X_5: $i > $i)).
% 0.12/0.45 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.45 tptp_fun_Y_1: $i > $i)).
% 0.12/0.45 tff(tptp_fun_X_2_type, type, (
% 0.12/0.45 tptp_fun_X_2: $i > $i)).
% 0.12/0.45 tff(tptp_fun_X_12_type, type, (
% 0.12/0.45 tptp_fun_X_12: $i)).
% 0.12/0.45 tff(tptp_fun_Y_6_type, type, (
% 0.12/0.45 tptp_fun_Y_6: $i > $i)).
% 0.12/0.45 tff(tptp_fun_X_11_type, type, (
% 0.12/0.45 tptp_fun_X_11: $i)).
% 0.12/0.45 tff(tptp_fun_X_0_type, type, (
% 0.12/0.45 tptp_fun_X_0: $i)).
% 0.12/0.45 tff(1,assumption,(~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))), introduced(assumption)).
% 0.12/0.45 tff(2,plain,
% 0.12/0.45 ((p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))) | r1(X!12, tptp_fun_Y_6(X!12))),
% 0.12/0.45 inference(tautology,[status(thm)],[])).
% 0.12/0.45 tff(3,plain,
% 0.12/0.45 (r1(X!12, tptp_fun_Y_6(X!12))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.12/0.45 tff(4,plain,
% 0.12/0.45 ((p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))) | (~p1(tptp_fun_Y_6(X!12)))),
% 0.12/0.45 inference(tautology,[status(thm)],[])).
% 0.12/0.45 tff(5,plain,
% 0.12/0.45 (~p1(tptp_fun_Y_6(X!12))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.12/0.45 tff(6,plain,
% 0.12/0.45 (^[Y: $i] : refl((p1(Y) | (~r1(X!12, Y))) <=> (p1(Y) | (~r1(X!12, Y))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(7,plain,
% 0.12/0.45 (![Y: $i] : (p1(Y) | (~r1(X!12, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.45 tff(8,plain,
% 0.12/0.45 ((![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(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_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) & (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))) <=> (![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(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_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) & r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(9,plain,
% 0.12/0.45 ((r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & (r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) <=> (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(10,plain,
% 0.12/0.45 ((r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) <=> (r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(11,plain,
% 0.12/0.45 ((r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & (r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) <=> (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & (r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.12/0.45 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.45 tff(12,plain,
% 0.12/0.45 ((r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & (r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))) <=> (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.12/0.45 inference(transitivity,[status(thm)],[11, 9])).
% 0.12/0.45 tff(13,plain,
% 0.12/0.45 (^[Y: $i] : rewrite(((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(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_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(14,plain,
% 0.12/0.45 (![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(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_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.45 tff(15,plain,
% 0.12/0.45 ((![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & (r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))) <=> (![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(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_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) & (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))))),
% 0.12/0.46 inference(monotonicity,[status(thm)],[14, 12])).
% 0.12/0.46 tff(16,plain,
% 0.12/0.46 ((![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (p1(tptp_fun_X_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & (r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))) <=> (![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(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_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) & r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[15, 8])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 ((~?[X: $i] : (~((~![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)) | 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)))))))))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 ((~(~?[X: $i] : (~((~![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)) | 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))))))))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 ((~(~?[X: $i] : (~((~![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)) | 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))))))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[20, 18])).
% 0.20/0.47 tff(22,axiom,(~(~?[X: $i] : (~((~![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)) | 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))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, 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] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[23, 17])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(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_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) & r1(X!0, Y!10) & (~(p1(X!11) | (~r1(Y!10, X!11)))) & r1(Y!10, X!12) & ![Y: $i] : (p1(Y) | (~r1(X!12, Y))) & ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[24, 16])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (![Y: $i] : (p1(Y) | (~r1(X!12, Y)))),
% 0.20/0.47 inference(and_elim,[status(thm)],[25])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (![Y: $i] : (p1(Y) | (~r1(X!12, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[26, 7])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (((~![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) | (p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) | p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 ((~![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) | (p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 ((~![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) | p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[30, 27, 5, 3])).
% 0.20/0.47 tff(32,plain,(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (r1(X!0, Y!10)),
% 0.20/0.47 inference(and_elim,[status(thm)],[25])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[39, 37])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (^[Y: $i] : rewrite(((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(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_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) <=> ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(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_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (![Y: $i] : ((~r1(X!0, 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)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | ((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) & (((~p1(tptp_fun_X_7(Y))) & r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(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_8(Y)) & r1(Y, tptp_fun_X_8(Y)) & (~(p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))),
% 0.20/0.48 inference(and_elim,[status(thm)],[25])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | ((~r1(X!0, Y!10)) | (~((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | (~r1(X!0, Y!10)) | (~((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (((~r1(X!0, Y!10)) | (~((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y!10, tptp_fun_X_3(Y!10))) | (~p1(tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))))))) <=> ((~r1(X!0, Y!10)) | (~((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | ((~r1(X!0, Y!10)) | (~((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y!10, tptp_fun_X_3(Y!10))) | (~p1(tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | ((~r1(X!0, Y!10)) | (~((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | ((~r1(X!0, Y!10)) | (~((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y!10, tptp_fun_X_3(Y!10))) | (~p1(tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | (~r1(X!0, Y!10)) | (~((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | ((~r1(X!0, Y!10)) | (~((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y!10)) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y!10, tptp_fun_X_3(Y!10))) | (~p1(tptp_fun_X_3(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y!10) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~((~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), 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_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))))))) | (~r1(X!0, Y!10)) | (~((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 (~((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[52, 46, 33])).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 (((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10)))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 (![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 (r1(Y!10, X!12)),
% 0.20/0.50 inference(and_elim,[status(thm)],[25])).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 (((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 ((~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[59, 56, 55])).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 (![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[60, 32])).
% 0.20/0.50 tff(62,assumption,(~((~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))) | p1(tptp_fun_X_2(X!12)) | (~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))))), introduced(assumption)).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 (((~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))) | p1(tptp_fun_X_2(X!12)) | (~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12)))) | r1(X!12, tptp_fun_Y_1(X!12))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 (r1(X!12, tptp_fun_Y_1(X!12))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 (((~![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!12, tptp_fun_Y_1(X!12))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(66,plain,
% 0.20/0.50 ((~![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!12, tptp_fun_Y_1(X!12))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 ((~![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[67, 64, 61])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 (((~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))) | p1(tptp_fun_X_2(X!12)) | (~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12)))) | (~p1(tptp_fun_X_2(X!12)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 (~p1(tptp_fun_X_2(X!12))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[69, 62])).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 (((~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))) | p1(tptp_fun_X_2(X!12)) | (~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12)))) | r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 (r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[71, 62])).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))) | (p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))) | (p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[75, 72, 70, 68])).
% 0.20/0.50 tff(77,plain,((~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))) | p1(tptp_fun_X_2(X!12)) | (~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(78,assumption,(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))), introduced(assumption)).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 (((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!10, X!12)) | (~((~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))) | p1(tptp_fun_X_2(X!12)) | (~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!10, X!12)) | (~((~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))) | p1(tptp_fun_X_2(X!12)) | (~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(80,plain,
% 0.20/0.50 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!10, X!12)) | (~((~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))) | p1(tptp_fun_X_2(X!12)) | (~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(81,plain,
% 0.20/0.50 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!10, X!12)) | (~((~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))) | p1(tptp_fun_X_2(X!12)) | (~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[81, 56, 78, 77])).
% 0.20/0.50 tff(83,plain,(~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(84,assumption,(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))), introduced(assumption)).
% 0.20/0.50 tff(85,assumption,(![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))), introduced(assumption)).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 (((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | ((~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(87,plain,
% 0.20/0.50 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | ((~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(88,plain,
% 0.20/0.50 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[88, 56, 85, 32])).
% 0.20/0.50 tff(90,plain,(~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 (((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10)))) | ((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 ((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[91, 53])).
% 0.20/0.51 tff(93,plain,
% 0.20/0.51 ((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(94,plain,
% 0.20/0.51 ((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 ((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!10)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[94, 90])).
% 0.20/0.51 tff(96,plain,
% 0.20/0.51 (p1(Y!10)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[95, 84])).
% 0.20/0.51 tff(97,assumption,(![X: $i] : (p1(X) | (~r1(Y!10, X)))), introduced(assumption)).
% 0.20/0.51 tff(98,plain,
% 0.20/0.51 (~(p1(X!11) | (~r1(Y!10, X!11)))),
% 0.20/0.51 inference(and_elim,[status(thm)],[25])).
% 0.20/0.51 tff(99,plain,
% 0.20/0.51 (r1(Y!10, X!11)),
% 0.20/0.51 inference(or_elim,[status(thm)],[98])).
% 0.20/0.51 tff(100,plain,
% 0.20/0.51 (~p1(X!11)),
% 0.20/0.51 inference(or_elim,[status(thm)],[98])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 (((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | (p1(X!11) | (~r1(Y!10, X!11)))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | p1(X!11) | (~r1(Y!10, X!11)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(102,plain,
% 0.20/0.51 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | (p1(X!11) | (~r1(Y!10, X!11)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(103,plain,
% 0.20/0.51 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | p1(X!11) | (~r1(Y!10, X!11))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.51 tff(104,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[103, 100, 99, 97])).
% 0.20/0.51 tff(105,plain,(~![X: $i] : (p1(X) | (~r1(Y!10, X)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(106,plain,
% 0.20/0.51 (((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10)))) | (![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(107,plain,
% 0.20/0.51 (![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[106, 53])).
% 0.20/0.51 tff(108,plain,
% 0.20/0.51 ((~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10)))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 (![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 (![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[109, 105])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[110, 96, 83])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10)))) | r1(Y!10, tptp_fun_X_3(Y!10))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 (r1(Y!10, tptp_fun_X_3(Y!10))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 (((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!10, X))) | (~p1(Y!10)) | (~((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10))))))) | (~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X)))))) | p1(Y!10)))) | ((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 ((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[114, 53])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 ((~((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))))) | (~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 ((~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.51 tff(118,plain,
% 0.20/0.51 (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[117, 84])).
% 0.20/0.51 tff(119,plain,
% 0.20/0.51 (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~r1(Y!10, tptp_fun_X_3(Y!10))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | ((~r1(Y!10, tptp_fun_X_3(Y!10))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(121,plain,
% 0.20/0.51 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y)))))))) | (~r1(Y!10, tptp_fun_X_3(Y!10))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.51 tff(122,plain,
% 0.20/0.51 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[121, 118, 113])).
% 0.20/0.51 tff(123,plain,
% 0.20/0.51 (((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10)))) | (~p1(tptp_fun_Y_4(Y!10)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(124,plain,
% 0.20/0.51 (~p1(tptp_fun_Y_4(Y!10))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[123, 111])).
% 0.20/0.51 tff(125,plain,
% 0.20/0.51 (((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10)))) | r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(126,plain,
% 0.20/0.51 (r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[125, 111])).
% 0.20/0.51 tff(127,plain,
% 0.20/0.51 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | (p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(128,plain,
% 0.20/0.51 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | (p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(129,plain,
% 0.20/0.51 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!10), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p1(tptp_fun_X_8(Y))) | p1(tptp_fun_Y_9(Y)) | (~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))))))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.51 tff(130,plain,
% 0.20/0.51 (~((~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[129, 126, 124, 122])).
% 0.20/0.51 tff(131,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))) | p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(132,plain,
% 0.20/0.51 (p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.51 tff(133,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))) | r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(134,plain,
% 0.20/0.51 (r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[133, 130])).
% 0.20/0.51 tff(135,plain,
% 0.20/0.51 (((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10))))) | p1(tptp_fun_Y_4(Y!10))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(136,plain,
% 0.20/0.51 ((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[135, 124])).
% 0.20/0.51 tff(137,plain,
% 0.20/0.51 (((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | p1(tptp_fun_Y_4(Y!10)) | (~p1(tptp_fun_X_3(Y!10))) | (~r1(Y!10, tptp_fun_X_3(Y!10)))) | ![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(138,plain,
% 0.20/0.51 (![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[137, 111])).
% 0.20/0.51 tff(139,plain,
% 0.20/0.51 (((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10)))))) | ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10)))))) | ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10)))))) | ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(141,plain,
% 0.20/0.52 ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!10), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))) | (~((~p1(tptp_fun_Y_4(Y!10))) | p1(tptp_fun_X_5(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_5(tptp_fun_Y_4(Y!10)))))) | ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.52 tff(142,plain,
% 0.20/0.52 (![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[141, 138, 126, 136])).
% 0.20/0.52 tff(143,plain,
% 0.20/0.52 (((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y))))) <=> ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[145, 142, 134, 132])).
% 0.20/0.52 tff(147,plain,
% 0.20/0.52 (((~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))) | r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(148,plain,
% 0.20/0.52 (r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[147, 130])).
% 0.20/0.52 tff(149,plain,
% 0.20/0.52 (((~r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | (~p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))) | (~p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(150,plain,
% 0.20/0.52 (~p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[149, 130])).
% 0.20/0.52 tff(151,plain,
% 0.20/0.52 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))) | (p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(152,plain,
% 0.20/0.52 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))) | (p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(153,plain,
% 0.20/0.52 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.52 tff(154,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[153, 150, 148, 146])).
% 0.20/0.52 tff(155,plain,(~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(156,plain,
% 0.20/0.52 ((p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~p1(tptp_fun_X_7(Y!10)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(157,plain,
% 0.20/0.52 (~p1(tptp_fun_X_7(Y!10))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.20/0.52 tff(158,assumption,(~(p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))), introduced(assumption)).
% 0.20/0.52 tff(159,plain,
% 0.20/0.52 ((p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | r1(Y!10, tptp_fun_X_7(Y!10))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(160,plain,
% 0.20/0.52 (r1(Y!10, tptp_fun_X_7(Y!10))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.20/0.52 tff(161,assumption,(~p1(tptp_fun_X_7(Y!10))), introduced(assumption)).
% 0.20/0.52 tff(162,plain,
% 0.20/0.52 (^[X: $i] : refl((p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) <=> (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(163,plain,
% 0.20/0.52 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) <=> ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.52 tff(164,plain,
% 0.20/0.52 (^[X: $i] : rewrite((p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) <=> (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(165,plain,
% 0.20/0.52 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) <=> ![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.52 tff(166,plain,
% 0.20/0.52 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | (p1(tptp_fun_Y_1(X)) & r1(X, tptp_fun_Y_1(X)) & (~(p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X)))))))),
% 0.20/0.52 inference(and_elim,[status(thm)],[25])).
% 0.20/0.52 tff(167,plain,
% 0.20/0.52 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.52 tff(168,plain,
% 0.20/0.52 (![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.20/0.52 tff(169,plain,
% 0.20/0.52 (((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | (p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(170,plain,
% 0.20/0.52 ((p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10))))))) <=> (p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(171,plain,
% 0.20/0.52 (((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | (p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | (p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[170])).
% 0.20/0.52 tff(172,plain,
% 0.20/0.52 (((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | (p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[171, 169])).
% 0.20/0.52 tff(173,plain,
% 0.20/0.52 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | (p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(174,plain,
% 0.20/0.52 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)) | (~((~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))) | p1(tptp_fun_X_2(X)) | (~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))) | p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.52 tff(175,plain,
% 0.20/0.52 (~((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[174, 168, 161, 160])).
% 0.20/0.52 tff(176,plain,
% 0.20/0.52 (((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10))))) | r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(177,plain,
% 0.20/0.52 (r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.20/0.52 tff(178,plain,
% 0.20/0.52 (((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10))))) | p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(179,plain,
% 0.20/0.52 (p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[178, 175])).
% 0.20/0.52 tff(180,plain,
% 0.20/0.52 ((p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(181,plain,
% 0.20/0.52 (![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[180, 158])).
% 0.20/0.52 tff(182,plain,
% 0.20/0.52 (((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X))))) <=> ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(183,plain,
% 0.20/0.52 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(184,plain,
% 0.20/0.52 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.52 tff(185,plain,
% 0.20/0.52 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[184, 181, 179, 177])).
% 0.20/0.52 tff(186,plain,
% 0.20/0.52 (((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10))))) | (~p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(187,plain,
% 0.20/0.53 (~p1(tptp_fun_X_2(tptp_fun_X_7(Y!10)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[186, 175])).
% 0.20/0.53 tff(188,plain,
% 0.20/0.53 (((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10))))) | r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(189,plain,
% 0.20/0.53 (r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[188, 175])).
% 0.20/0.53 tff(190,plain,
% 0.20/0.53 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))) | (p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(191,plain,
% 0.20/0.53 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))) | (p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(192,plain,
% 0.20/0.53 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.53 tff(193,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[192, 189, 187, 185])).
% 0.20/0.53 tff(194,plain,((p1(tptp_fun_X_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | p1(tptp_fun_X_7(Y!10))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(195,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[194, 157, 155])).
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------