%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL652+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n007.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 03:00:25 PM UTC 2026
% Result : Theorem 7.67s 7.99s
% Output : Proof 7.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL652+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.33 % Computer : n007.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 12:46:56 UTC 2026
% 0.08/0.34 % CPUTime :
% 7.67/7.99 % SZS status Theorem
% 7.67/7.99 % SZS output start Proof
% 7.67/7.99 tff(p3_type, type, (
% 7.67/7.99 p3: $i > $o)).
% 7.67/7.99 tff(tptp_fun_X_7_type, type, (
% 7.67/7.99 tptp_fun_X_7: $i > $i)).
% 7.67/7.99 tff(r1_type, type, (
% 7.67/7.99 r1: ( $i * $i ) > $o)).
% 7.67/7.99 tff(tptp_fun_Y_6_type, type, (
% 7.67/7.99 tptp_fun_Y_6: $i > $i)).
% 7.67/7.99 tff(p2_type, type, (
% 7.67/7.99 p2: $i > $o)).
% 7.67/7.99 tff(tptp_fun_Y_13_type, type, (
% 7.67/7.99 tptp_fun_Y_13: $i > $i)).
% 7.67/7.99 tff(tptp_fun_X_10_type, type, (
% 7.67/7.99 tptp_fun_X_10: $i > $i)).
% 7.67/7.99 tff(tptp_fun_Y_1_type, type, (
% 7.67/7.99 tptp_fun_Y_1: $i)).
% 7.67/7.99 tff(tptp_fun_Y_12_type, type, (
% 7.67/7.99 tptp_fun_Y_12: $i > $i)).
% 7.67/7.99 tff(tptp_fun_Y_11_type, type, (
% 7.67/7.99 tptp_fun_Y_11: $i > $i)).
% 7.67/7.99 tff(tptp_fun_X_9_type, type, (
% 7.67/7.99 tptp_fun_X_9: $i > $i)).
% 7.67/7.99 tff(tptp_fun_X_8_type, type, (
% 7.67/7.99 tptp_fun_X_8: $i > $i)).
% 7.67/7.99 tff(tptp_fun_X_0_type, type, (
% 7.67/7.99 tptp_fun_X_0: $i)).
% 7.67/7.99 tff(p1_type, type, (
% 7.67/7.99 p1: $i > $o)).
% 7.67/7.99 tff(tptp_fun_X_3_type, type, (
% 7.67/7.99 tptp_fun_X_3: $i > $i)).
% 7.67/7.99 tff(tptp_fun_X_16_type, type, (
% 7.67/7.99 tptp_fun_X_16: $i)).
% 7.67/7.99 tff(tptp_fun_Y_14_type, type, (
% 7.67/7.99 tptp_fun_Y_14: $i)).
% 7.67/7.99 tff(tptp_fun_X_15_type, type, (
% 7.67/7.99 tptp_fun_X_15: $i)).
% 7.67/7.99 tff(tptp_fun_X_5_type, type, (
% 7.67/7.99 tptp_fun_X_5: $i > $i)).
% 7.67/7.99 tff(tptp_fun_X_4_type, type, (
% 7.67/7.99 tptp_fun_X_4: $i > $i)).
% 7.67/7.99 tff(tptp_fun_Y_2_type, type, (
% 7.67/7.99 tptp_fun_Y_2: $i > $i)).
% 7.67/7.99 tff(p4_type, type, (
% 7.67/7.99 p4: $i > $o)).
% 7.67/7.99 tff(1,assumption,(~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))), introduced(assumption)).
% 7.67/7.99 tff(2,plain,
% 7.67/7.99 (((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X))))) | r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))),
% 7.67/7.99 inference(tautology,[status(thm)],[])).
% 7.67/7.99 tff(3,plain,
% 7.67/7.99 (r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))),
% 7.67/7.99 inference(unit_resolution,[status(thm)],[2, 1])).
% 7.67/7.99 tff(4,assumption,(~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))), introduced(assumption)).
% 7.67/7.99 tff(5,plain,
% 7.67/7.99 (((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y))))) | r1(Y!1, tptp_fun_X_9(Y!1))),
% 7.67/7.99 inference(tautology,[status(thm)],[])).
% 7.67/7.99 tff(6,plain,
% 7.67/7.99 (r1(Y!1, tptp_fun_X_9(Y!1))),
% 7.67/7.99 inference(unit_resolution,[status(thm)],[5, 4])).
% 7.67/7.99 tff(7,plain,
% 7.67/7.99 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))) <=> ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))))),
% 7.67/8.00 inference(bind,[status(th)],[])).
% 7.67/8.00 tff(8,plain,
% 7.67/8.00 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))),
% 7.67/8.00 inference(quant_intro,[status(thm)],[7])).
% 7.67/8.00 tff(9,plain,
% 7.67/8.00 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))))),
% 7.67/8.00 inference(bind,[status(th)],[])).
% 7.67/8.00 tff(10,plain,
% 7.67/8.00 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))),
% 7.67/8.00 inference(quant_intro,[status(thm)],[9])).
% 7.67/8.00 tff(11,plain,
% 7.67/8.00 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))))),
% 7.67/8.00 inference(bind,[status(th)],[])).
% 7.67/8.00 tff(12,plain,
% 7.67/8.00 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))),
% 7.67/8.00 inference(quant_intro,[status(thm)],[11])).
% 7.67/8.00 tff(13,plain,
% 7.67/8.00 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))),
% 7.67/8.00 inference(transitivity,[status(thm)],[12, 10])).
% 7.67/8.00 tff(14,plain,
% 7.67/8.00 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))))),
% 7.67/8.00 inference(bind,[status(th)],[])).
% 7.67/8.00 tff(15,plain,
% 7.67/8.00 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))),
% 7.67/8.01 inference(quant_intro,[status(thm)],[14])).
% 7.67/8.01 tff(16,plain,
% 7.67/8.01 ((![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & (r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) & (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) <=> (![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) & r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))),
% 7.67/8.01 inference(rewrite,[status(thm)],[])).
% 7.67/8.01 tff(17,plain,
% 7.67/8.01 ((r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & (r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))) <=> (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))),
% 7.67/8.01 inference(rewrite,[status(thm)],[])).
% 7.67/8.01 tff(18,plain,
% 7.67/8.01 ((r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)))) <=> (r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))),
% 7.67/8.01 inference(rewrite,[status(thm)],[])).
% 7.67/8.01 tff(19,plain,
% 7.67/8.01 ((r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & (r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))) <=> (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & (r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)))))),
% 7.67/8.01 inference(monotonicity,[status(thm)],[18])).
% 7.67/8.01 tff(20,plain,
% 7.67/8.01 ((r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & (r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))) <=> (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))),
% 7.67/8.01 inference(transitivity,[status(thm)],[19, 17])).
% 7.67/8.01 tff(21,plain,
% 7.67/8.01 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))) & ![X: $i] : ((~r1(Y, X)) | ((r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~p2(X)))) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))),
% 7.67/8.01 inference(bind,[status(th)],[])).
% 7.67/8.01 tff(22,plain,
% 7.67/8.01 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))) & ![X: $i] : ((~r1(Y, X)) | ((r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~p2(X)))) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))),
% 7.67/8.01 inference(quant_intro,[status(thm)],[21])).
% 7.67/8.01 tff(23,plain,
% 7.67/8.01 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))))),
% 7.67/8.01 inference(bind,[status(th)],[])).
% 7.67/8.01 tff(24,plain,
% 7.67/8.01 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))),
% 7.67/8.01 inference(quant_intro,[status(thm)],[23])).
% 7.67/8.01 tff(25,plain,
% 7.67/8.01 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))) <=> (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))))), rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))))),
% 7.67/8.01 inference(bind,[status(th)],[])).
% 7.67/8.01 tff(26,plain,
% 7.67/8.01 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))),
% 7.67/8.01 inference(quant_intro,[status(thm)],[25])).
% 7.67/8.01 tff(27,plain,
% 7.67/8.01 ((r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) <=> (r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))))),
% 7.67/8.01 inference(rewrite,[status(thm)],[])).
% 7.67/8.01 tff(28,plain,
% 7.67/8.01 ((![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & (r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))) & ![X: $i] : ((~r1(Y, X)) | ((r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~p2(X)))) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))))) & (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & (r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) <=> (![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & (r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) & (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))),
% 7.67/8.01 inference(monotonicity,[status(thm)],[27, 26, 24, 22, 20])).
% 7.67/8.01 tff(29,plain,
% 7.67/8.01 ((![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & (r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))) & ![X: $i] : ((~r1(Y, X)) | ((r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~p2(X)))) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~r1(tptp_fun_X_9(Y), Y)) | (~p2(Y))))))) & (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & (r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) <=> (![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) & r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))),
% 7.67/8.02 inference(transitivity,[status(thm)],[28, 16])).
% 7.67/8.02 tff(30,plain,
% 7.67/8.02 (?[X: $i] : (~((~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![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] : (~((~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))),
% 7.67/8.02 inference(rewrite,[status(thm)],[])).
% 7.67/8.02 tff(31,plain,
% 7.67/8.02 ((~(~?[X: $i] : (~((~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![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] : (~((~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))),
% 7.67/8.02 inference(rewrite,[status(thm)],[])).
% 7.67/8.02 tff(32,plain,
% 7.67/8.02 ((~?[X: $i] : (~(((((((~![Y: $i] : ((~r1(X, Y)) | (~p4(Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) | (~p2(Y)))))) & p2(X)) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))))))))) | (![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))))))),
% 7.67/8.02 inference(rewrite,[status(thm)],[])).
% 7.67/8.02 tff(33,plain,
% 7.67/8.02 ((~(~?[X: $i] : (~(((((((~![Y: $i] : ((~r1(X, Y)) | (~p4(Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) | (~p2(Y)))))) & p2(X)) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))))))))) | (![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))))),
% 7.67/8.03 inference(monotonicity,[status(thm)],[32])).
% 7.67/8.03 tff(34,plain,
% 7.67/8.03 ((~(~?[X: $i] : (~(((((((~![Y: $i] : ((~r1(X, Y)) | (~p4(Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) | (~p2(Y)))))) & p2(X)) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))))))))) | (![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))),
% 7.67/8.03 inference(transitivity,[status(thm)],[33, 31])).
% 7.67/8.03 tff(35,axiom,(~(~?[X: $i] : (~(((((((~![Y: $i] : ((~r1(X, Y)) | (~p4(Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) | (~p2(Y)))))) & p2(X)) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))))))))) | (![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 7.80/8.03 tff(36,plain,
% 7.80/8.03 (?[X: $i] : (~((~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))),
% 7.80/8.03 inference(modus_ponens,[status(thm)],[35, 34])).
% 7.80/8.03 tff(37,plain,
% 7.80/8.03 (?[X: $i] : (~((~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))),
% 7.80/8.03 inference(modus_ponens,[status(thm)],[36, 30])).
% 7.80/8.03 tff(38,plain,
% 7.80/8.03 (![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_5(Y)) | (~r1(Y, tptp_fun_X_5(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) & r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))),
% 7.80/8.03 inference(modus_ponens,[status(thm)],[37, 29])).
% 7.80/8.03 tff(39,plain,
% 7.80/8.03 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_13(X)) & ![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (r1(X, tptp_fun_Y_6(X)) & p2(tptp_fun_Y_6(X)) & (~((~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X))))) & ((r1(Y, tptp_fun_X_10(Y)) & p2(tptp_fun_X_10(Y)) & (~((~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))) | (r1(Y, tptp_fun_X_9(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))),
% 7.80/8.03 inference(and_elim,[status(thm)],[38])).
% 7.80/8.03 tff(40,plain,
% 7.80/8.03 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))),
% 7.80/8.03 inference(modus_ponens,[status(thm)],[39, 15])).
% 7.80/8.03 tff(41,plain,
% 7.80/8.03 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))),
% 7.80/8.03 inference(modus_ponens,[status(thm)],[40, 13])).
% 7.80/8.03 tff(42,plain,
% 7.80/8.03 (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))),
% 7.80/8.04 inference(modus_ponens,[status(thm)],[41, 8])).
% 7.80/8.04 tff(43,plain,
% 7.80/8.04 (r1(X!0, Y!1)),
% 7.80/8.04 inference(and_elim,[status(thm)],[38])).
% 7.80/8.04 tff(44,plain,
% 7.80/8.04 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))) | ((~r1(X!0, Y!1)) | (~((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))) | (~r1(X!0, Y!1)) | (~((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))))),
% 7.80/8.04 inference(rewrite,[status(thm)],[])).
% 7.80/8.04 tff(45,plain,
% 7.80/8.04 (((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | p3(tptp_fun_Y_11(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y))))))))))) <=> ((~r1(X!0, Y!1)) | (~((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))))),
% 7.80/8.04 inference(rewrite,[status(thm)],[])).
% 7.80/8.04 tff(46,plain,
% 7.80/8.04 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))) | ((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | p3(tptp_fun_Y_11(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))) | ((~r1(X!0, Y!1)) | (~((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))))),
% 7.80/8.04 inference(monotonicity,[status(thm)],[45])).
% 7.80/8.04 tff(47,plain,
% 7.80/8.04 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))) | ((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | p3(tptp_fun_Y_11(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))) | (~r1(X!0, Y!1)) | (~((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))))),
% 7.80/8.04 inference(transitivity,[status(thm)],[46, 44])).
% 7.80/8.04 tff(48,plain,
% 7.80/8.04 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))) | ((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | p3(tptp_fun_Y_11(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))))))),
% 7.80/8.05 inference(quant_inst,[status(thm)],[])).
% 7.80/8.05 tff(49,plain,
% 7.80/8.05 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~((~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))) | (~r1(X!0, Y!1)) | (~((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))))),
% 7.80/8.05 inference(modus_ponens,[status(thm)],[48, 47])).
% 7.80/8.05 tff(50,plain,
% 7.80/8.05 (~((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[49, 43, 42])).
% 7.80/8.05 tff(51,plain,
% 7.80/8.05 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))) | ![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))),
% 7.80/8.05 inference(tautology,[status(thm)],[])).
% 7.80/8.05 tff(52,plain,
% 7.80/8.05 (![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[51, 50])).
% 7.80/8.05 tff(53,plain,
% 7.80/8.05 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | ((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_X_9(Y!1)))) | p3(tptp_fun_X_7(tptp_fun_X_9(Y!1))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_X_9(Y!1)))) | p3(tptp_fun_X_7(tptp_fun_X_9(Y!1))))))),
% 7.80/8.05 inference(rewrite,[status(thm)],[])).
% 7.80/8.05 tff(54,plain,
% 7.80/8.05 ((~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | ((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_X_9(Y!1)))) | p3(tptp_fun_X_7(tptp_fun_X_9(Y!1))))))),
% 7.80/8.05 inference(quant_inst,[status(thm)],[])).
% 7.80/8.05 tff(55,plain,
% 7.80/8.05 ((~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_X_9(Y!1)))) | p3(tptp_fun_X_7(tptp_fun_X_9(Y!1)))))),
% 7.80/8.05 inference(modus_ponens,[status(thm)],[54, 53])).
% 7.80/8.05 tff(56,plain,
% 7.80/8.05 (~((~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_X_9(Y!1)))) | p3(tptp_fun_X_7(tptp_fun_X_9(Y!1))))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[55, 52, 6])).
% 7.80/8.05 tff(57,plain,
% 7.80/8.05 (((~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_X_9(Y!1)))) | p3(tptp_fun_X_7(tptp_fun_X_9(Y!1)))) | r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))),
% 7.80/8.05 inference(tautology,[status(thm)],[])).
% 7.80/8.05 tff(58,plain,
% 7.80/8.05 (r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[57, 56])).
% 7.80/8.05 tff(59,plain,
% 7.80/8.05 (((~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_X_9(Y!1)))) | p3(tptp_fun_X_7(tptp_fun_X_9(Y!1)))) | p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))),
% 7.80/8.05 inference(tautology,[status(thm)],[])).
% 7.80/8.05 tff(60,plain,
% 7.80/8.05 (p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[59, 56])).
% 7.80/8.05 tff(61,plain,
% 7.80/8.05 (((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))),
% 7.80/8.05 inference(tautology,[status(thm)],[])).
% 7.80/8.05 tff(62,plain,
% 7.80/8.05 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[61, 4])).
% 7.80/8.05 tff(63,plain,
% 7.80/8.05 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))) | ((~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))))),
% 7.80/8.05 inference(rewrite,[status(thm)],[])).
% 7.80/8.05 tff(64,plain,
% 7.80/8.05 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))) | ((~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1)))))),
% 7.80/8.05 inference(quant_inst,[status(thm)],[])).
% 7.80/8.05 tff(65,plain,
% 7.80/8.05 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_6(tptp_fun_X_9(Y!1))))),
% 7.80/8.05 inference(modus_ponens,[status(thm)],[64, 63])).
% 7.80/8.05 tff(66,plain,
% 7.80/8.05 ($false),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[65, 62, 60, 58])).
% 7.80/8.05 tff(67,plain,((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y))))), inference(lemma,lemma(discharge,[]))).
% 7.80/8.05 tff(68,plain,
% 7.80/8.05 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))) | ((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))),
% 7.80/8.05 inference(tautology,[status(thm)],[])).
% 7.80/8.05 tff(69,plain,
% 7.80/8.05 ((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y))))))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[68, 50])).
% 7.80/8.05 tff(70,plain,
% 7.80/8.05 ((~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y))))))),
% 7.80/8.05 inference(tautology,[status(thm)],[])).
% 7.80/8.05 tff(71,plain,
% 7.80/8.05 ((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y))))))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[70, 69])).
% 7.80/8.05 tff(72,plain,
% 7.80/8.05 (~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[71, 67])).
% 7.80/8.05 tff(73,plain,
% 7.80/8.05 ((p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1)))) | r1(Y!1, tptp_fun_X_10(Y!1))),
% 7.80/8.05 inference(tautology,[status(thm)],[])).
% 7.80/8.05 tff(74,plain,
% 7.80/8.05 (r1(Y!1, tptp_fun_X_10(Y!1))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[73, 72])).
% 7.80/8.05 tff(75,plain,
% 7.80/8.05 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))) | ((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))),
% 7.80/8.05 inference(tautology,[status(thm)],[])).
% 7.80/8.05 tff(76,plain,
% 7.80/8.05 ((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))),
% 7.80/8.05 inference(unit_resolution,[status(thm)],[75, 50])).
% 7.80/8.05 tff(77,plain,
% 7.80/8.05 ((~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))),
% 7.80/8.05 inference(tautology,[status(thm)],[])).
% 7.80/8.05 tff(78,plain,
% 7.80/8.05 ((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[77, 76])).
% 7.80/8.06 tff(79,plain,
% 7.80/8.06 (![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[78, 67])).
% 7.80/8.06 tff(80,plain,
% 7.80/8.06 (((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))),
% 7.80/8.06 inference(rewrite,[status(thm)],[])).
% 7.80/8.06 tff(81,plain,
% 7.80/8.06 ((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))),
% 7.80/8.06 inference(quant_inst,[status(thm)],[])).
% 7.80/8.06 tff(82,plain,
% 7.80/8.06 ((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y))))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))),
% 7.80/8.06 inference(modus_ponens,[status(thm)],[81, 80])).
% 7.80/8.06 tff(83,plain,
% 7.80/8.06 (![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[82, 79, 74])).
% 7.80/8.06 tff(84,plain,
% 7.80/8.06 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))) | ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))), tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))), tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1)))))))),
% 7.80/8.06 inference(rewrite,[status(thm)],[])).
% 7.80/8.06 tff(85,plain,
% 7.80/8.06 ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))) | ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))), tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1)))))))),
% 7.80/8.06 inference(quant_inst,[status(thm)],[])).
% 7.80/8.06 tff(86,plain,
% 7.80/8.06 ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))), tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))))),
% 7.80/8.06 inference(modus_ponens,[status(thm)],[85, 84])).
% 7.80/8.06 tff(87,plain,
% 7.80/8.06 (~((~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))), tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1)))))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[86, 83, 3])).
% 7.80/8.06 tff(88,plain,
% 7.80/8.06 (((~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))), tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))),
% 7.80/8.06 inference(tautology,[status(thm)],[])).
% 7.80/8.06 tff(89,plain,
% 7.80/8.06 (r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[88, 87])).
% 7.80/8.06 tff(90,plain,
% 7.80/8.06 (((~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))), tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_Y_11(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))),
% 7.80/8.06 inference(tautology,[status(thm)],[])).
% 7.80/8.06 tff(91,plain,
% 7.80/8.06 (p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[90, 87])).
% 7.80/8.06 tff(92,plain,
% 7.80/8.06 (((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X))))) | ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))),
% 7.80/8.06 inference(tautology,[status(thm)],[])).
% 7.80/8.06 tff(93,plain,
% 7.80/8.06 (![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[92, 1])).
% 7.80/8.06 tff(94,plain,
% 7.80/8.06 (((~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))) | ((~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))) | (~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))))),
% 7.80/8.06 inference(rewrite,[status(thm)],[])).
% 7.80/8.06 tff(95,plain,
% 7.80/8.06 ((~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))) | ((~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))))),
% 7.80/8.06 inference(quant_inst,[status(thm)],[])).
% 7.80/8.06 tff(96,plain,
% 7.80/8.06 ((~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))) | (~p2(tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), tptp_fun_X_10(tptp_fun_Y_12(tptp_fun_X_10(Y!1)))))),
% 7.80/8.06 inference(modus_ponens,[status(thm)],[95, 94])).
% 7.80/8.06 tff(97,plain,
% 7.80/8.06 ($false),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[96, 93, 91, 89])).
% 7.80/8.06 tff(98,plain,((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X))))), inference(lemma,lemma(discharge,[]))).
% 7.80/8.06 tff(99,plain,
% 7.80/8.06 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))) | ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))),
% 7.80/8.06 inference(tautology,[status(thm)],[])).
% 7.80/8.06 tff(100,plain,
% 7.80/8.06 (![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[99, 50])).
% 7.80/8.06 tff(101,plain,
% 7.80/8.06 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))))),
% 7.80/8.06 inference(rewrite,[status(thm)],[])).
% 7.80/8.06 tff(102,plain,
% 7.80/8.06 (((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X))))))) <=> ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))))),
% 7.80/8.06 inference(rewrite,[status(thm)],[])).
% 7.80/8.06 tff(103,plain,
% 7.80/8.06 ((~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))) <=> (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X))))),
% 7.80/8.06 inference(rewrite,[status(thm)],[])).
% 7.80/8.06 tff(104,plain,
% 7.80/8.06 (((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X))))) <=> ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))),
% 7.80/8.06 inference(monotonicity,[status(thm)],[103])).
% 7.80/8.06 tff(105,plain,
% 7.80/8.06 ((~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))) <=> (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X))))))),
% 7.80/8.06 inference(monotonicity,[status(thm)],[104])).
% 7.80/8.06 tff(106,plain,
% 7.80/8.06 ((~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) <=> (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))),
% 7.80/8.06 inference(rewrite,[status(thm)],[])).
% 7.80/8.06 tff(107,plain,
% 7.80/8.06 (((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) <=> ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))),
% 7.80/8.06 inference(monotonicity,[status(thm)],[106])).
% 7.80/8.06 tff(108,plain,
% 7.80/8.06 ((~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) <=> (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))))),
% 7.80/8.06 inference(monotonicity,[status(thm)],[107])).
% 7.80/8.06 tff(109,plain,
% 7.80/8.06 (((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X))))))) <=> ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))))),
% 7.80/8.06 inference(monotonicity,[status(thm)],[108, 105])).
% 7.80/8.06 tff(110,plain,
% 7.80/8.06 (((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X))))))) <=> ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))))),
% 7.80/8.06 inference(transitivity,[status(thm)],[109, 102])).
% 7.80/8.06 tff(111,plain,
% 7.80/8.06 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))))))),
% 7.80/8.06 inference(monotonicity,[status(thm)],[110])).
% 7.80/8.06 tff(112,plain,
% 7.80/8.06 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))))),
% 7.80/8.06 inference(transitivity,[status(thm)],[111, 101])).
% 7.80/8.06 tff(113,plain,
% 7.80/8.06 ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))))),
% 7.80/8.06 inference(quant_inst,[status(thm)],[])).
% 7.80/8.06 tff(114,plain,
% 7.80/8.06 ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))))),
% 7.80/8.06 inference(modus_ponens,[status(thm)],[113, 112])).
% 7.80/8.06 tff(115,plain,
% 7.80/8.06 ((~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_12(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(tptp_fun_X_10(Y!1)), X)))))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[114, 100, 74])).
% 7.80/8.06 tff(116,plain,
% 7.80/8.06 (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[115, 98])).
% 7.80/8.06 tff(117,plain,
% 7.80/8.06 (((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | ![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))),
% 7.80/8.06 inference(tautology,[status(thm)],[])).
% 7.80/8.06 tff(118,plain,
% 7.80/8.06 (![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))),
% 7.80/8.06 inference(unit_resolution,[status(thm)],[117, 116])).
% 7.80/8.06 tff(119,plain,
% 7.80/8.06 (^[X: $i] : refl(((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))) <=> ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))))),
% 7.80/8.06 inference(bind,[status(th)],[])).
% 7.80/8.06 tff(120,plain,
% 7.80/8.06 (![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))) <=> ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))),
% 7.80/8.06 inference(quant_intro,[status(thm)],[119])).
% 7.80/8.06 tff(121,plain,
% 7.80/8.06 (![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))),
% 7.80/8.06 inference(and_elim,[status(thm)],[38])).
% 7.80/8.06 tff(122,plain,
% 7.80/8.06 (![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))),
% 7.80/8.06 inference(modus_ponens,[status(thm)],[121, 120])).
% 7.80/8.06 tff(123,plain,
% 7.80/8.06 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~(p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~(p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))))),
% 7.80/8.07 inference(rewrite,[status(thm)],[])).
% 7.80/8.07 tff(124,plain,
% 7.80/8.07 (((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))) <=> ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~(p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))))),
% 7.80/8.07 inference(rewrite,[status(thm)],[])).
% 7.80/8.07 tff(125,plain,
% 7.80/8.07 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~(p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1))))))))),
% 7.80/8.07 inference(monotonicity,[status(thm)],[124])).
% 7.80/8.07 tff(126,plain,
% 7.80/8.07 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~(p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))))),
% 7.80/8.07 inference(transitivity,[status(thm)],[125, 123])).
% 7.80/8.07 tff(127,plain,
% 7.80/8.07 ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))))),
% 7.80/8.07 inference(quant_inst,[status(thm)],[])).
% 7.80/8.07 tff(128,plain,
% 7.80/8.07 ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~(p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1))))))),
% 7.80/8.07 inference(modus_ponens,[status(thm)],[127, 126])).
% 7.80/8.07 tff(129,plain,
% 7.80/8.07 (~(p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[128, 122, 74])).
% 7.80/8.07 tff(130,plain,
% 7.80/8.07 ((p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1))))) | (~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))),
% 7.80/8.07 inference(tautology,[status(thm)],[])).
% 7.80/8.07 tff(131,plain,
% 7.80/8.07 (~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[130, 129])).
% 7.80/8.07 tff(132,plain,
% 7.80/8.07 (((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))) | p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))),
% 7.80/8.07 inference(tautology,[status(thm)],[])).
% 7.80/8.07 tff(133,plain,
% 7.80/8.07 ((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[132, 131])).
% 7.80/8.07 tff(134,plain,
% 7.80/8.07 ((p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1))))) | r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))),
% 7.80/8.07 inference(tautology,[status(thm)],[])).
% 7.80/8.07 tff(135,plain,
% 7.80/8.07 (r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[134, 129])).
% 7.80/8.07 tff(136,assumption,(![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))), introduced(assumption)).
% 7.80/8.07 tff(137,plain,
% 7.80/8.07 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))))))),
% 7.80/8.07 inference(rewrite,[status(thm)],[])).
% 7.80/8.07 tff(138,plain,
% 7.80/8.07 (((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))))) <=> ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))))))),
% 7.80/8.07 inference(rewrite,[status(thm)],[])).
% 7.80/8.07 tff(139,plain,
% 7.80/8.07 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))))))),
% 7.80/8.07 inference(monotonicity,[status(thm)],[138])).
% 7.80/8.07 tff(140,plain,
% 7.80/8.07 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))))))),
% 7.80/8.07 inference(transitivity,[status(thm)],[139, 137])).
% 7.80/8.07 tff(141,plain,
% 7.80/8.07 ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1))))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))))),
% 7.80/8.07 inference(quant_inst,[status(thm)],[])).
% 7.80/8.07 tff(142,plain,
% 7.80/8.07 ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | p3(tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_10(Y!1)), tptp_fun_X_8(tptp_fun_Y_2(tptp_fun_X_10(Y!1)))))))),
% 7.80/8.07 inference(modus_ponens,[status(thm)],[141, 140])).
% 7.80/8.07 tff(143,plain,
% 7.80/8.07 ($false),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[142, 136, 135, 133])).
% 7.80/8.07 tff(144,plain,(~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))), inference(lemma,lemma(discharge,[]))).
% 7.80/8.07 tff(145,plain,
% 7.80/8.07 (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_13(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(X), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_12(X), X)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(tptp_fun_X_10(Y))) | (~r1(Y, tptp_fun_X_10(Y))) | (~r1(tptp_fun_X_10(Y), tptp_fun_Y_11(Y))) | p3(tptp_fun_Y_11(Y)))))))) | (~((~(p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))),
% 7.80/8.07 inference(tautology,[status(thm)],[])).
% 7.80/8.07 tff(146,plain,
% 7.80/8.07 (![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[145, 50])).
% 7.80/8.07 tff(147,plain,
% 7.80/8.07 ((p3(tptp_fun_Y_11(Y!1)) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_11(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1)))) | p2(tptp_fun_X_10(Y!1))),
% 7.80/8.07 inference(tautology,[status(thm)],[])).
% 7.80/8.07 tff(148,plain,
% 7.80/8.07 (p2(tptp_fun_X_10(Y!1))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[147, 72])).
% 7.80/8.07 tff(149,plain,
% 7.80/8.07 (((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))))),
% 7.80/8.07 inference(rewrite,[status(thm)],[])).
% 7.80/8.07 tff(150,plain,
% 7.80/8.07 (((~p2(tptp_fun_X_10(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))) <=> ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))))),
% 7.80/8.07 inference(rewrite,[status(thm)],[])).
% 7.80/8.07 tff(151,plain,
% 7.80/8.07 (((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | ((~p2(tptp_fun_X_10(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | ((~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))))),
% 7.80/8.07 inference(monotonicity,[status(thm)],[150])).
% 7.80/8.07 tff(152,plain,
% 7.80/8.07 (((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | ((~p2(tptp_fun_X_10(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))))),
% 7.80/8.07 inference(transitivity,[status(thm)],[151, 149])).
% 7.80/8.07 tff(153,plain,
% 7.80/8.07 ((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | ((~p2(tptp_fun_X_10(Y!1))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))),
% 7.80/8.07 inference(quant_inst,[status(thm)],[])).
% 7.80/8.07 tff(154,plain,
% 7.80/8.07 ((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))))) | (~r1(Y!1, tptp_fun_X_10(Y!1))) | (~p2(tptp_fun_X_10(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))),
% 7.80/8.07 inference(modus_ponens,[status(thm)],[153, 152])).
% 7.80/8.07 tff(155,plain,
% 7.80/8.07 (![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y))))))) | ![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | p3(tptp_fun_X_8(Y)))))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[154, 74, 148, 146])).
% 7.80/8.07 tff(156,plain,
% 7.80/8.07 (![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[155, 144])).
% 7.80/8.07 tff(157,plain,
% 7.80/8.07 (((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))) | r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))),
% 7.80/8.07 inference(tautology,[status(thm)],[])).
% 7.80/8.07 tff(158,plain,
% 7.80/8.07 (r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[157, 116])).
% 7.80/8.07 tff(159,assumption,((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y))))), introduced(assumption)).
% 7.80/8.07 tff(160,assumption,(r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), introduced(assumption)).
% 7.80/8.07 tff(161,assumption,(![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))), introduced(assumption)).
% 7.80/8.07 tff(162,plain,
% 7.80/8.07 (((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))) | ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))))))),
% 7.80/8.07 inference(rewrite,[status(thm)],[])).
% 7.80/8.07 tff(163,plain,
% 7.80/8.07 ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))) | ((~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))))))),
% 7.80/8.07 inference(quant_inst,[status(thm)],[])).
% 7.80/8.07 tff(164,plain,
% 7.80/8.07 ((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y))))))),
% 7.80/8.07 inference(modus_ponens,[status(thm)],[163, 162])).
% 7.80/8.07 tff(165,plain,
% 7.80/8.07 ($false),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[164, 161, 160, 159])).
% 7.80/8.07 tff(166,plain,((~![Y: $i] : ((~r1(tptp_fun_X_10(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(Y), Y)))))))) | (~r1(tptp_fun_X_10(Y!1), tptp_fun_Y_13(tptp_fun_X_10(Y!1)))) | (~((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y))))))), inference(lemma,lemma(discharge,[]))).
% 7.80/8.07 tff(167,plain,
% 7.80/8.07 (~((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[166, 158, 156])).
% 7.80/8.07 tff(168,assumption,(~((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))))), introduced(assumption)).
% 7.80/8.07 tff(169,plain,
% 7.80/8.07 (((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))),
% 7.80/8.07 inference(tautology,[status(thm)],[])).
% 7.80/8.07 tff(170,plain,
% 7.80/8.07 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))),
% 7.80/8.07 inference(unit_resolution,[status(thm)],[169, 168])).
% 7.80/8.07 tff(171,assumption,(![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))), introduced(assumption)).
% 7.80/8.08 tff(172,plain,
% 7.80/8.08 (((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y))))) | r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))),
% 7.80/8.08 inference(tautology,[status(thm)],[])).
% 7.80/8.08 tff(173,plain,
% 7.80/8.08 (r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))),
% 7.80/8.08 inference(unit_resolution,[status(thm)],[172, 168])).
% 7.80/8.08 tff(174,plain,
% 7.80/8.08 (((~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))))))),
% 7.80/8.08 inference(rewrite,[status(thm)],[])).
% 7.80/8.08 tff(175,plain,
% 7.80/8.08 (((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~((~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))))) <=> ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))))))),
% 7.80/8.08 inference(rewrite,[status(thm)],[])).
% 7.80/8.08 tff(176,plain,
% 7.80/8.08 (((~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~((~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))))))),
% 7.80/8.08 inference(monotonicity,[status(thm)],[175])).
% 7.80/8.08 tff(177,plain,
% 7.80/8.08 (((~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~((~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))))))),
% 7.80/8.08 inference(transitivity,[status(thm)],[176, 174])).
% 7.80/8.08 tff(178,plain,
% 7.80/8.08 ((~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~((~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))))))),
% 7.80/8.08 inference(quant_inst,[status(thm)],[])).
% 7.80/8.08 tff(179,plain,
% 7.80/8.08 ((~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X)))))) | (~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~((~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))))),
% 7.80/8.08 inference(modus_ponens,[status(thm)],[178, 177])).
% 7.80/8.08 tff(180,plain,
% 7.80/8.08 (~((~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))))),
% 7.80/8.08 inference(unit_resolution,[status(thm)],[179, 173, 171])).
% 7.80/8.08 tff(181,plain,
% 7.80/8.08 (((~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))),
% 7.80/8.09 inference(tautology,[status(thm)],[])).
% 7.80/8.09 tff(182,plain,
% 7.80/8.09 (p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))),
% 7.80/8.09 inference(unit_resolution,[status(thm)],[181, 180])).
% 7.80/8.09 tff(183,plain,
% 7.80/8.09 (((~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))), tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | p3(tptp_fun_X_7(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))),
% 7.80/8.09 inference(tautology,[status(thm)],[])).
% 7.80/8.09 tff(184,plain,
% 7.80/8.09 (r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))),
% 7.80/8.09 inference(unit_resolution,[status(thm)],[183, 180])).
% 7.80/8.09 tff(185,plain,
% 7.80/8.09 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))) | ((~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))))),
% 7.80/8.09 inference(rewrite,[status(thm)],[])).
% 7.80/8.09 tff(186,plain,
% 7.80/8.09 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))) | ((~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))))),
% 7.80/8.09 inference(quant_inst,[status(thm)],[])).
% 7.80/8.09 tff(187,plain,
% 7.80/8.09 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y)))) | (~p2(tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1)))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), tptp_fun_Y_6(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))))),
% 7.80/8.09 inference(modus_ponens,[status(thm)],[186, 185])).
% 7.80/8.09 tff(188,plain,
% 7.80/8.09 ($false),
% 7.80/8.09 inference(unit_resolution,[status(thm)],[187, 184, 182, 170])).
% 7.80/8.09 tff(189,plain,(((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_9(tptp_fun_Y_13(tptp_fun_X_10(Y!1))), Y))))) | (~![X: $i] : ((~r1(tptp_fun_Y_13(tptp_fun_X_10(Y!1)), X)) | (~((~p2(tptp_fun_Y_6(X))) | (~r1(X, tptp_fun_Y_6(X))) | (~r1(tptp_fun_Y_6(X), tptp_fun_X_7(X))) | p3(tptp_fun_X_7(X))))))), inference(lemma,lemma(discharge,[]))).
% 7.80/8.09 tff(190,plain,
% 7.80/8.09 ($false),
% 7.80/8.09 inference(unit_resolution,[status(thm)],[189, 167, 118])).
% 7.80/8.09 % SZS output end Proof
% 7.80/8.10 % E exiting
%------------------------------------------------------------------------------