%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL658+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:27 PM UTC 2026
% Result : Theorem 0.15s 0.41s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL658+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 09:10:01 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.15/0.41 % SZS status Theorem
% 0.15/0.41 % SZS output start Proof
% 0.15/0.41 tff(r1_type, type, (
% 0.15/0.41 r1: ( $i * $i ) > $o)).
% 0.15/0.41 tff(p1_type, type, (
% 0.15/0.41 p1: $i > $o)).
% 0.15/0.41 tff(tptp_fun_X_7_type, type, (
% 0.15/0.41 tptp_fun_X_7: $i > $i)).
% 0.15/0.41 tff(tptp_fun_Y_10_type, type, (
% 0.15/0.41 tptp_fun_Y_10: $i)).
% 0.15/0.41 tff(tptp_fun_X_8_type, type, (
% 0.15/0.41 tptp_fun_X_8: $i > $i)).
% 0.15/0.41 tff(tptp_fun_Y_4_type, type, (
% 0.15/0.41 tptp_fun_Y_4: $i > $i)).
% 0.15/0.41 tff(tptp_fun_Y_9_type, type, (
% 0.15/0.41 tptp_fun_Y_9: $i > $i)).
% 0.15/0.41 tff(tptp_fun_X_3_type, type, (
% 0.15/0.41 tptp_fun_X_3: $i > $i)).
% 0.15/0.41 tff(tptp_fun_X_5_type, type, (
% 0.15/0.41 tptp_fun_X_5: $i > $i)).
% 0.15/0.41 tff(tptp_fun_Y_6_type, type, (
% 0.15/0.41 tptp_fun_Y_6: $i > $i)).
% 0.15/0.41 tff(tptp_fun_X_12_type, type, (
% 0.15/0.41 tptp_fun_X_12: $i)).
% 0.15/0.41 tff(tptp_fun_X_2_type, type, (
% 0.15/0.41 tptp_fun_X_2: $i > $i)).
% 0.15/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.15/0.41 tptp_fun_Y_1: $i > $i)).
% 0.15/0.41 tff(tptp_fun_X_11_type, type, (
% 0.15/0.41 tptp_fun_X_11: $i)).
% 0.15/0.41 tff(tptp_fun_X_0_type, type, (
% 0.15/0.41 tptp_fun_X_0: $i)).
% 0.15/0.41 tff(1,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)).
% 0.15/0.41 tff(2,assumption,(~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))), introduced(assumption)).
% 0.15/0.41 tff(3,plain,
% 0.15/0.41 ((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))),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(4,plain,
% 0.15/0.41 (r1(X!12, tptp_fun_Y_6(X!12))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.15/0.41 tff(5,plain,
% 0.15/0.41 ((p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))) | (~p1(tptp_fun_Y_6(X!12)))),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(6,plain,
% 0.15/0.41 (~p1(tptp_fun_Y_6(X!12))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.15/0.41 tff(7,plain,
% 0.15/0.41 (^[Y: $i] : refl((p1(Y) | (~r1(X!12, Y))) <=> (p1(Y) | (~r1(X!12, Y))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(8,plain,
% 0.15/0.41 (![Y: $i] : (p1(Y) | (~r1(X!12, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!12, Y)))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[7])).
% 0.15/0.41 tff(9,plain,
% 0.15/0.41 ((![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))))))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(10,plain,
% 0.15/0.41 ((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))))))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(11,plain,
% 0.15/0.41 ((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))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(12,plain,
% 0.15/0.41 ((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))))))))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[11])).
% 0.15/0.41 tff(13,plain,
% 0.15/0.41 ((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))))))))),
% 0.15/0.41 inference(transitivity,[status(thm)],[12, 10])).
% 0.15/0.41 tff(14,plain,
% 0.15/0.41 (^[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))))))))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(15,plain,
% 0.15/0.41 (![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)))))))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.15/0.41 tff(16,plain,
% 0.15/0.41 ((![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)))))))))),
% 0.15/0.42 inference(monotonicity,[status(thm)],[15, 13])).
% 0.15/0.42 tff(17,plain,
% 0.15/0.42 ((![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))))))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[16, 9])).
% 0.15/0.42 tff(18,plain,
% 0.15/0.42 (?[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))))))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(19,plain,
% 0.15/0.42 ((~(~?[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))))))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(20,plain,
% 0.15/0.42 ((~?[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)))))))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(21,plain,
% 0.15/0.42 ((~(~?[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))))))))))))),
% 0.15/0.42 inference(monotonicity,[status(thm)],[20])).
% 0.15/0.42 tff(22,plain,
% 0.15/0.42 ((~(~?[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))))))))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[21, 19])).
% 0.15/0.42 tff(23,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')).
% 0.15/0.42 tff(24,plain,
% 0.15/0.42 (?[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))))))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.15/0.42 tff(25,plain,
% 0.15/0.42 (?[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))))))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.15/0.42 tff(26,plain,
% 0.15/0.42 (![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)))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.15/0.42 tff(27,plain,
% 0.15/0.42 (![Y: $i] : (p1(Y) | (~r1(X!12, Y)))),
% 0.15/0.42 inference(and_elim,[status(thm)],[26])).
% 0.15/0.42 tff(28,plain,
% 0.15/0.42 (![Y: $i] : (p1(Y) | (~r1(X!12, Y)))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[27, 8])).
% 0.15/0.42 tff(29,plain,
% 0.15/0.42 (((~![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))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(30,plain,
% 0.15/0.42 ((~![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) | (p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(31,plain,
% 0.15/0.42 ((~![Y: $i] : (p1(Y) | (~r1(X!12, Y)))) | p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.15/0.42 tff(32,plain,
% 0.15/0.42 ($false),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[31, 28, 6, 4])).
% 0.15/0.42 tff(33,plain,(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.42 tff(34,assumption,(![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))), introduced(assumption)).
% 0.15/0.42 tff(35,plain,
% 0.15/0.42 (r1(Y!10, X!12)),
% 0.15/0.42 inference(and_elim,[status(thm)],[26])).
% 0.15/0.42 tff(36,plain,
% 0.15/0.42 (((~![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))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(37,plain,
% 0.15/0.42 ((~![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))))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(38,plain,
% 0.15/0.42 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))) | (~r1(Y!10, X!12)) | (~(p1(tptp_fun_Y_6(X!12)) | (~r1(X!12, tptp_fun_Y_6(X!12)))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.15/0.42 tff(39,plain,
% 0.15/0.42 ($false),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[38, 35, 34, 33])).
% 0.15/0.42 tff(40,plain,(~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_6(X)) | (~r1(X, tptp_fun_Y_6(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.42 tff(41,plain,
% 0.15/0.42 (r1(X!0, Y!10)),
% 0.15/0.42 inference(and_elim,[status(thm)],[26])).
% 0.15/0.42 tff(42,plain,
% 0.15/0.42 (^[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)))))) | (~((~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)) | (~((~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(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)))))))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(43,plain,
% 0.15/0.42 (![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)))))) | (~((~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)) | (~((~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(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))))))))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.15/0.42 tff(44,plain,
% 0.15/0.42 (^[Y: $i] : refl(((~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)))))) | (~((~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)) | (~((~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(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)))))))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(45,plain,
% 0.15/0.42 (![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)))))) | (~((~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)) | (~((~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(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))))))))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.15/0.42 tff(46,plain,
% 0.15/0.42 (^[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)))))) | (~((~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)) | (~((~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(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)))))))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(47,plain,
% 0.15/0.42 (![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)))))) | (~((~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)) | (~((~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(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))))))))))))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[46])).
% 0.15/0.43 tff(48,plain,
% 0.15/0.43 (![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)))))) | (~((~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)) | (~((~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(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))))))))))))),
% 0.15/0.43 inference(transitivity,[status(thm)],[47, 45])).
% 0.15/0.43 tff(49,plain,
% 0.15/0.43 (^[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)) | (~((~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(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)))))))))))))),
% 0.15/0.43 inference(bind,[status(th)],[])).
% 0.15/0.43 tff(50,plain,
% 0.15/0.43 (![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)) | (~((~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(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))))))))))))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[49])).
% 0.15/0.43 tff(51,plain,
% 0.15/0.43 (![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)))))))))))),
% 0.15/0.43 inference(and_elim,[status(thm)],[26])).
% 0.15/0.43 tff(52,plain,
% 0.15/0.43 (![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)))))) | (~((~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))))))))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.15/0.43 tff(53,plain,
% 0.15/0.43 (![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)))))) | (~((~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))))))))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.15/0.43 tff(54,plain,
% 0.15/0.43 (![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)) | (~((~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(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))))))))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.15/0.43 tff(55,plain,
% 0.15/0.43 (((~![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)) | (~((~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(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)) | (~((~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))) | (~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)) | (~((~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(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)) | (~((~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))) | (~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))))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(56,plain,
% 0.15/0.43 (((~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)) | (~((~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(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)) | (~((~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))) | (~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))))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(57,plain,
% 0.15/0.43 (((~![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)) | (~((~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(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)) | (~((~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(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)) | (~((~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(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)) | (~((~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))) | (~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)))))))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[56])).
% 0.15/0.43 tff(58,plain,
% 0.15/0.43 (((~![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)) | (~((~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(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)) | (~((~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(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)) | (~((~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(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)) | (~((~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))) | (~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))))))),
% 0.15/0.43 inference(transitivity,[status(thm)],[57, 55])).
% 0.15/0.43 tff(59,plain,
% 0.15/0.43 ((~![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)) | (~((~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(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)) | (~((~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(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))))))))))))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(60,plain,
% 0.15/0.43 ((~![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)) | (~((~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(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)) | (~((~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))) | (~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)))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.15/0.43 tff(61,plain,
% 0.15/0.43 (~((~((~(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)) | (~((~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))) | (~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))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[60, 54, 41])).
% 0.15/0.43 tff(62,plain,
% 0.15/0.43 (((~((~(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)) | (~((~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))) | (~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))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(63,plain,
% 0.15/0.43 ((~(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)),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.15/0.43 tff(64,plain,
% 0.15/0.43 ((~((~(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)),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(65,plain,
% 0.15/0.43 ((~(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)),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.15/0.43 tff(66,plain,
% 0.15/0.43 ((~(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)),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[65, 40])).
% 0.15/0.43 tff(67,plain,
% 0.15/0.43 (p1(Y!10)),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[66, 1])).
% 0.15/0.43 tff(68,plain,
% 0.15/0.43 (((~((~(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)) | (~((~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))) | (~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)))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(69,plain,
% 0.15/0.44 (![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)))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[68, 61])).
% 0.15/0.44 tff(70,plain,
% 0.15/0.44 (((~![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)))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(71,plain,
% 0.15/0.44 ((~![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)))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(72,plain,
% 0.15/0.44 ((~![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))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.15/0.44 tff(73,plain,
% 0.15/0.44 ((~(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))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[72, 35, 69])).
% 0.15/0.44 tff(74,plain,
% 0.15/0.44 (![Y: $i] : ((~r1(X!12, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[73, 33])).
% 0.15/0.44 tff(75,assumption,(~((~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))), introduced(assumption)).
% 0.15/0.44 tff(76,plain,
% 0.15/0.44 (((~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))) | r1(X!12, tptp_fun_Y_1(X!12))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(77,plain,
% 0.15/0.44 (r1(X!12, tptp_fun_Y_1(X!12))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.15/0.44 tff(78,plain,
% 0.15/0.44 (((~![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))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(79,plain,
% 0.15/0.44 ((~![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))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(80,plain,
% 0.15/0.44 ((~![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)))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.15/0.44 tff(81,plain,
% 0.15/0.44 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[80, 77, 74])).
% 0.15/0.44 tff(82,plain,
% 0.15/0.44 (((~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))) | r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(83,plain,
% 0.15/0.44 (r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[82, 75])).
% 0.15/0.44 tff(84,plain,
% 0.15/0.44 (((~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))) | (~p1(tptp_fun_X_2(X!12)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(85,plain,
% 0.15/0.44 (~p1(tptp_fun_X_2(X!12))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[84, 75])).
% 0.15/0.44 tff(86,plain,
% 0.15/0.44 (((~![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))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(87,plain,
% 0.15/0.44 ((~![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))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(88,plain,
% 0.15/0.44 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(X!12), X)))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.15/0.44 tff(89,plain,
% 0.15/0.44 ($false),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[88, 85, 83, 81])).
% 0.15/0.44 tff(90,plain,((~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.44 tff(91,assumption,((~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))), introduced(assumption)).
% 0.15/0.44 tff(92,assumption,(![X: $i] : ((~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))))))), introduced(assumption)).
% 0.15/0.44 tff(93,plain,
% 0.15/0.44 (((~![X: $i] : ((~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(Y!10, 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)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))))) <=> ((~![X: $i] : ((~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(Y!10, 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)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(94,plain,
% 0.15/0.44 ((~![X: $i] : ((~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(Y!10, 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)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12))))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(95,plain,
% 0.15/0.44 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))) | p1(tptp_fun_X_2(X)) | (~r1(tptp_fun_Y_1(X), tptp_fun_X_2(X))))))) | (~r1(Y!10, X!12)) | (~((~p1(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.15/0.44 tff(96,plain,
% 0.15/0.44 ($false),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[95, 35, 92, 91])).
% 0.15/0.44 tff(97,plain,((~![X: $i] : ((~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(tptp_fun_Y_1(X!12))) | (~r1(X!12, tptp_fun_Y_1(X!12))) | p1(tptp_fun_X_2(X!12)) | (~r1(tptp_fun_Y_1(X!12), tptp_fun_X_2(X!12)))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.44 tff(98,plain,
% 0.15/0.44 (~![X: $i] : ((~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))))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[97, 90])).
% 0.15/0.44 tff(99,assumption,(![X: $i] : (p1(X) | (~r1(Y!10, X)))), introduced(assumption)).
% 0.15/0.44 tff(100,plain,
% 0.15/0.44 (~(p1(X!11) | (~r1(Y!10, X!11)))),
% 0.15/0.44 inference(and_elim,[status(thm)],[26])).
% 0.15/0.44 tff(101,plain,
% 0.15/0.44 (r1(Y!10, X!11)),
% 0.15/0.44 inference(or_elim,[status(thm)],[100])).
% 0.15/0.44 tff(102,plain,
% 0.15/0.44 (~p1(X!11)),
% 0.15/0.44 inference(or_elim,[status(thm)],[100])).
% 0.15/0.44 tff(103,plain,
% 0.15/0.44 (((~![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)))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(104,plain,
% 0.15/0.44 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | (p1(X!11) | (~r1(Y!10, X!11)))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(105,plain,
% 0.15/0.44 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | p1(X!11) | (~r1(Y!10, X!11))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.15/0.44 tff(106,plain,
% 0.15/0.44 ($false),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[105, 102, 101, 99])).
% 0.15/0.44 tff(107,plain,(~![X: $i] : (p1(X) | (~r1(Y!10, X)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.44 tff(108,plain,
% 0.15/0.44 (((~((~(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)) | (~((~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))) | (~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_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))) | (~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))))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(109,plain,
% 0.15/0.44 (![X: $i] : ((~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))) | (~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)))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[108, 61])).
% 0.15/0.44 tff(110,plain,
% 0.15/0.44 ((~(![X: $i] : ((~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))) | (~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)) | (~((~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))) | (~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)))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(111,plain,
% 0.15/0.44 (![X: $i] : ((~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))) | (~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)))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.15/0.44 tff(112,plain,
% 0.15/0.44 ((~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)))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[111, 107, 98])).
% 0.15/0.44 tff(113,plain,
% 0.15/0.44 (~((~![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))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[112, 67])).
% 0.15/0.44 tff(114,plain,
% 0.15/0.44 (((~![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))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(115,plain,
% 0.15/0.44 (r1(Y!10, tptp_fun_X_3(Y!10))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.15/0.44 tff(116,plain,
% 0.15/0.44 (((~((~(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)) | (~((~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))) | (~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))))))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(117,plain,
% 0.15/0.44 ((~(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)))))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[116, 61])).
% 0.15/0.44 tff(118,plain,
% 0.15/0.44 ((~((~(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)))))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(119,plain,
% 0.15/0.44 ((~(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)))))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.15/0.44 tff(120,plain,
% 0.15/0.44 (![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)))))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[119, 1])).
% 0.15/0.44 tff(121,plain,
% 0.15/0.44 (((~![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)))))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(122,plain,
% 0.15/0.44 ((~![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)))))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(123,plain,
% 0.15/0.44 ((~![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))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.15/0.44 tff(124,plain,
% 0.15/0.44 (![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))))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[123, 120, 115])).
% 0.15/0.44 tff(125,plain,
% 0.15/0.44 (((~![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)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(126,plain,
% 0.15/0.44 (~p1(tptp_fun_Y_4(Y!10))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[125, 113])).
% 0.15/0.44 tff(127,plain,
% 0.15/0.44 (((~![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))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(128,plain,
% 0.15/0.44 (r1(tptp_fun_X_3(Y!10), tptp_fun_Y_4(Y!10))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[127, 113])).
% 0.15/0.44 tff(129,plain,
% 0.15/0.44 (((~![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)))))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(130,plain,
% 0.15/0.44 ((~![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)))))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(131,plain,
% 0.15/0.44 ((~![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))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.15/0.44 tff(132,plain,
% 0.15/0.44 (~((~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)))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[131, 128, 126, 124])).
% 0.15/0.44 tff(133,plain,
% 0.15/0.44 (((~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)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(134,plain,
% 0.15/0.44 (p1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.15/0.44 tff(135,plain,
% 0.15/0.44 (((~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)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(136,plain,
% 0.15/0.44 (r1(tptp_fun_Y_4(Y!10), tptp_fun_X_8(tptp_fun_Y_4(Y!10)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.15/0.44 tff(137,plain,
% 0.15/0.44 (((~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))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(138,plain,
% 0.15/0.44 ((~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))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[137, 126])).
% 0.15/0.44 tff(139,plain,
% 0.15/0.44 (((~![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)))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(140,plain,
% 0.15/0.44 (![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)))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[139, 113])).
% 0.15/0.44 tff(141,plain,
% 0.15/0.44 (((~![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)))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(142,plain,
% 0.15/0.44 ((~![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)))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(143,plain,
% 0.15/0.44 ((~![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))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.15/0.44 tff(144,plain,
% 0.15/0.44 (![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(Y!10), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[143, 140, 128, 138])).
% 0.15/0.44 tff(145,plain,
% 0.15/0.44 (((~![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))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(146,plain,
% 0.15/0.44 ((~![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))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(147,plain,
% 0.15/0.44 ((~![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)))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.15/0.44 tff(148,plain,
% 0.15/0.44 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[147, 144, 136, 134])).
% 0.15/0.44 tff(149,plain,
% 0.15/0.44 (((~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)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(150,plain,
% 0.15/0.44 (r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[149, 132])).
% 0.15/0.44 tff(151,plain,
% 0.15/0.44 (((~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))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(152,plain,
% 0.15/0.44 (~p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[151, 132])).
% 0.15/0.44 tff(153,plain,
% 0.15/0.44 (((~![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)))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(154,plain,
% 0.15/0.44 ((~![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)))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(155,plain,
% 0.15/0.44 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), Y)))) | p1(tptp_fun_Y_9(tptp_fun_Y_4(Y!10))) | (~r1(tptp_fun_X_8(tptp_fun_Y_4(Y!10)), tptp_fun_Y_9(tptp_fun_Y_4(Y!10))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.15/0.44 tff(156,plain,
% 0.15/0.44 ($false),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[155, 152, 150, 148])).
% 0.15/0.44 tff(157,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,[]))).
% 0.15/0.44 tff(158,plain,
% 0.15/0.44 ((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)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(159,plain,
% 0.15/0.44 (~p1(tptp_fun_X_7(Y!10))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.15/0.44 tff(160,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)).
% 0.15/0.44 tff(161,plain,
% 0.15/0.44 ((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))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(162,plain,
% 0.15/0.44 (r1(Y!10, tptp_fun_X_7(Y!10))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.15/0.44 tff(163,assumption,(~p1(tptp_fun_X_7(Y!10))), introduced(assumption)).
% 0.15/0.44 tff(164,plain,
% 0.15/0.44 (^[X: $i] : refl((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)) | (~((~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)))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(165,plain,
% 0.15/0.44 (![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)) | (~((~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))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[164])).
% 0.15/0.44 tff(166,plain,
% 0.15/0.44 (^[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)) | (~((~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)))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(167,plain,
% 0.15/0.44 (![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)) | (~((~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))))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[166])).
% 0.15/0.44 tff(168,plain,
% 0.15/0.44 (![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)))))))),
% 0.15/0.44 inference(and_elim,[status(thm)],[26])).
% 0.15/0.44 tff(169,plain,
% 0.15/0.44 (![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))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.15/0.44 tff(170,plain,
% 0.15/0.44 (![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))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.15/0.44 tff(171,plain,
% 0.15/0.44 (((~![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))))))) | (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)))) | 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)))) | (~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)) | (~((~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_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | 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)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(172,plain,
% 0.15/0.44 ((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_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))) | (~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_7(Y!10)) | (~r1(Y!10, tptp_fun_X_7(Y!10))) | (~((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | 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)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(173,plain,
% 0.15/0.44 (((~![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))))))) | (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_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))) | (~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(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(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)))) | 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)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10))))))))),
% 0.15/0.44 inference(monotonicity,[status(thm)],[172])).
% 0.15/0.44 tff(174,plain,
% 0.15/0.44 (((~![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))))))) | (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_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))) | (~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(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(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)))) | 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)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))))),
% 0.15/0.44 inference(transitivity,[status(thm)],[173, 171])).
% 0.15/0.44 tff(175,plain,
% 0.15/0.44 ((~![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))))))) | (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_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))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(176,plain,
% 0.15/0.44 ((~![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))))))) | 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)))) | 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)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.15/0.44 tff(177,plain,
% 0.15/0.44 (~((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | 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)))) | (~r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[176, 170, 163, 162])).
% 0.15/0.44 tff(178,plain,
% 0.15/0.44 (((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | 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)))) | (~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)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(179,plain,
% 0.15/0.44 (r1(tptp_fun_X_7(Y!10), tptp_fun_Y_1(tptp_fun_X_7(Y!10)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.15/0.44 tff(180,plain,
% 0.15/0.44 (((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | 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)))) | (~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)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(181,plain,
% 0.15/0.44 (p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[180, 177])).
% 0.15/0.44 tff(182,plain,
% 0.15/0.44 ((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))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(183,plain,
% 0.15/0.44 (![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y!10), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[182, 160])).
% 0.15/0.44 tff(184,plain,
% 0.15/0.44 (((~![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))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(185,plain,
% 0.15/0.44 ((~![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))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(186,plain,
% 0.15/0.44 ((~![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)))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.15/0.45 tff(187,plain,
% 0.15/0.45 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[186, 183, 181, 179])).
% 0.15/0.45 tff(188,plain,
% 0.15/0.45 (((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | 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)))) | (~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)))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(189,plain,
% 0.15/0.45 (r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10)))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[188, 177])).
% 0.15/0.45 tff(190,plain,
% 0.15/0.45 (((~p1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)))) | 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)))) | (~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))))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(191,plain,
% 0.15/0.45 (~p1(tptp_fun_X_2(tptp_fun_X_7(Y!10)))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[190, 177])).
% 0.15/0.45 tff(192,plain,
% 0.15/0.45 (((~![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)))))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(193,plain,
% 0.15/0.45 ((~![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)))))),
% 0.15/0.45 inference(quant_inst,[status(thm)],[])).
% 0.15/0.45 tff(194,plain,
% 0.15/0.45 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), X)))) | p1(tptp_fun_X_2(tptp_fun_X_7(Y!10))) | (~r1(tptp_fun_Y_1(tptp_fun_X_7(Y!10)), tptp_fun_X_2(tptp_fun_X_7(Y!10))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.15/0.45 tff(195,plain,
% 0.15/0.45 ($false),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[194, 191, 189, 187])).
% 0.15/0.45 tff(196,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: $i] : (p1(X) | (~r1(Y, X)))))) | p1(tptp_fun_X_7(Y!10))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.45 tff(197,plain,
% 0.15/0.45 ($false),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[196, 159, 157])).
% 0.15/0.45 % SZS output end Proof
% 0.15/0.45 % E exiting
%------------------------------------------------------------------------------