%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL658+1.010 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:28 PM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL658+1.010 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.35 % Computer : n017.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 5 16:50:24 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44 % SZS output start Proof
% 0.13/0.44 tff(r1_type, type, (
% 0.13/0.44 r1: ( $i * $i ) > $o)).
% 0.13/0.44 tff(tptp_fun_Y_2_type, type, (
% 0.13/0.44 tptp_fun_Y_2: $i > $i)).
% 0.13/0.44 tff(tptp_fun_X_6_type, type, (
% 0.13/0.44 tptp_fun_X_6: $i > $i)).
% 0.13/0.44 tff(tptp_fun_X_15_type, type, (
% 0.13/0.44 tptp_fun_X_15: $i)).
% 0.13/0.44 tff(p1_type, type, (
% 0.13/0.44 p1: $i > $o)).
% 0.13/0.44 tff(tptp_fun_Y_5_type, type, (
% 0.13/0.44 tptp_fun_Y_5: $i > $i)).
% 0.13/0.44 tff(tptp_fun_Y_4_type, type, (
% 0.13/0.44 tptp_fun_Y_4: $i > $i)).
% 0.13/0.44 tff(tptp_fun_X_3_type, type, (
% 0.13/0.44 tptp_fun_X_3: $i > $i)).
% 0.13/0.44 tff(tptp_fun_Y_17_type, type, (
% 0.13/0.44 tptp_fun_Y_17: $i)).
% 0.13/0.44 tff(tptp_fun_X_1_type, type, (
% 0.13/0.44 tptp_fun_X_1: $i > $i)).
% 0.13/0.44 tff(tptp_fun_X_0_type, type, (
% 0.13/0.44 tptp_fun_X_0: $i)).
% 0.13/0.44 tff(tptp_fun_Y_16_type, type, (
% 0.13/0.44 tptp_fun_Y_16: $i)).
% 0.13/0.44 tff(tptp_fun_Y_14_type, type, (
% 0.13/0.44 tptp_fun_Y_14: $i)).
% 0.13/0.44 tff(tptp_fun_X_13_type, type, (
% 0.13/0.44 tptp_fun_X_13: $i)).
% 0.13/0.44 tff(tptp_fun_Y_12_type, type, (
% 0.13/0.44 tptp_fun_Y_12: $i)).
% 0.13/0.44 tff(tptp_fun_X_11_type, type, (
% 0.13/0.44 tptp_fun_X_11: $i)).
% 0.13/0.44 tff(tptp_fun_Y_10_type, type, (
% 0.13/0.44 tptp_fun_Y_10: $i)).
% 0.13/0.44 tff(tptp_fun_X_9_type, type, (
% 0.13/0.44 tptp_fun_X_9: $i > $i)).
% 0.13/0.44 tff(tptp_fun_Y_8_type, type, (
% 0.13/0.44 tptp_fun_Y_8: $i > $i)).
% 0.13/0.44 tff(tptp_fun_Y_7_type, type, (
% 0.13/0.44 tptp_fun_Y_7: $i > $i)).
% 0.13/0.44 tff(1,assumption,(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))), introduced(assumption)).
% 0.13/0.44 tff(2,assumption,(~(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))), introduced(assumption)).
% 0.13/0.44 tff(3,plain,
% 0.13/0.44 ((p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17)))) | r1(Y!17, tptp_fun_X_1(Y!17))),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(4,plain,
% 0.13/0.44 (r1(Y!17, tptp_fun_X_1(Y!17))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.13/0.44 tff(5,plain,
% 0.13/0.44 ((p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17)))) | (~p1(tptp_fun_X_1(Y!17)))),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(6,plain,
% 0.13/0.44 (~p1(tptp_fun_X_1(Y!17))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.13/0.44 tff(7,plain,
% 0.13/0.44 (^[X: $i] : refl((p1(X) | (~r1(Y!17, X))) <=> (p1(X) | (~r1(Y!17, X))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(8,plain,
% 0.13/0.44 (![X: $i] : (p1(X) | (~r1(Y!17, X))) <=> ![X: $i] : (p1(X) | (~r1(Y!17, X)))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[7])).
% 0.13/0.44 tff(9,plain,
% 0.13/0.44 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))) & (r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))) & r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(10,plain,
% 0.13/0.45 (((r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y)))) <=> (r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(11,plain,
% 0.13/0.45 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(12,plain,
% 0.13/0.45 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.45 tff(13,plain,
% 0.13/0.45 ((r1(X!0, Y!10) & (r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))) <=> (r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(14,plain,
% 0.13/0.45 ((r1(Y!10, X!11) & (r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))) <=> (r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(15,plain,
% 0.13/0.45 ((r1(X!11, Y!12) & (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))) <=> (r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(16,plain,
% 0.13/0.45 ((r1(Y!12, X!13) & (r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))) <=> (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(17,plain,
% 0.13/0.45 ((r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))) <=> (r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(18,plain,
% 0.13/0.45 ((r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))) <=> (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(19,plain,
% 0.13/0.45 ((r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) <=> (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(20,plain,
% 0.13/0.45 ((r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))) <=> (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[19])).
% 0.13/0.45 tff(21,plain,
% 0.13/0.45 ((r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))) <=> (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[20, 18])).
% 0.13/0.45 tff(22,plain,
% 0.13/0.45 ((r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))) <=> (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[21])).
% 0.13/0.45 tff(23,plain,
% 0.13/0.45 ((r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))) <=> (r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[22, 17])).
% 0.13/0.45 tff(24,plain,
% 0.13/0.45 ((r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))))) <=> (r1(Y!12, X!13) & (r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[23])).
% 0.13/0.45 tff(25,plain,
% 0.13/0.45 ((r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))))) <=> (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[24, 16])).
% 0.13/0.45 tff(26,plain,
% 0.13/0.45 ((r1(X!11, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))))) <=> (r1(X!11, Y!12) & (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[25])).
% 0.13/0.45 tff(27,plain,
% 0.13/0.45 ((r1(X!11, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))))) <=> (r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[26, 15])).
% 0.13/0.45 tff(28,plain,
% 0.13/0.45 ((r1(Y!10, X!11) & (r1(X!11, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))))))) <=> (r1(Y!10, X!11) & (r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[27])).
% 0.13/0.45 tff(29,plain,
% 0.13/0.45 ((r1(Y!10, X!11) & (r1(X!11, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))))))) <=> (r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[28, 14])).
% 0.13/0.45 tff(30,plain,
% 0.13/0.45 ((r1(X!0, Y!10) & (r1(Y!10, X!11) & (r1(X!11, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))))))) <=> (r1(X!0, Y!10) & (r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[29])).
% 0.13/0.45 tff(31,plain,
% 0.13/0.45 ((r1(X!0, Y!10) & (r1(Y!10, X!11) & (r1(X!11, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))))))) <=> (r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[30, 13])).
% 0.13/0.45 tff(32,plain,
% 0.13/0.45 (((r1(X!0, Y!10) & (r1(Y!10, X!11) & (r1(X!11, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) <=> ((r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[31, 12])).
% 0.13/0.45 tff(33,plain,
% 0.13/0.45 (((r1(X!0, Y!10) & (r1(Y!10, X!11) & (r1(X!11, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) <=> (r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[32, 10])).
% 0.13/0.45 tff(34,plain,
% 0.13/0.45 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(35,plain,
% 0.13/0.45 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.46 tff(36,plain,
% 0.21/0.46 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))) & ((r1(X!0, Y!10) & (r1(Y!10, X!11) & (r1(X!11, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))) & (r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[35, 33])).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))) & ((r1(X!0, Y!10) & (r1(Y!10, X!11) & (r1(X!11, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & (r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))) & r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[36, 9])).
% 0.21/0.46 tff(38,plain,
% 0.21/0.46 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | (~![Y: $i] : 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% 0.21/0.46 inference(rewrite,[status(thm)],[])).
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((~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] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (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] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~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] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(40,plain,
% 0.21/0.46 ((~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))))))))))) | (~((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (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] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~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] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 ((~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))))))))))) | (~((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (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] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~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] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[40])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 ((~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))))))))))) | (~((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (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] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~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] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[41, 39])).
% 0.21/0.47 tff(43,axiom,(~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))))))))))) | (~((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (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] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~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] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.47 tff(45,plain,
% 0.21/0.47 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (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] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~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] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[44, 38])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))) & r1(X!0, Y!10) & r1(Y!10, X!11) & r1(X!11, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & (~(p1(Y!16) | (~r1(X!15, Y!16)))) & r1(X!15, Y!17) & ![X: $i] : (p1(X) | (~r1(Y!17, X))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~r1(X!0, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[45, 37])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 (![X: $i] : (p1(X) | (~r1(Y!17, X)))),
% 0.21/0.47 inference(and_elim,[status(thm)],[46])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (![X: $i] : (p1(X) | (~r1(Y!17, X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[47, 8])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (((~![X: $i] : (p1(X) | (~r1(Y!17, X)))) | (p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!17, X)))) | p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 ((~![X: $i] : (p1(X) | (~r1(Y!17, X)))) | (p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 ((~![X: $i] : (p1(X) | (~r1(Y!17, X)))) | p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[51, 48, 6, 4])).
% 0.21/0.47 tff(53,plain,(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 (r1(X!0, Y!10)),
% 0.21/0.47 inference(and_elim,[status(thm)],[46])).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(56,plain,
% 0.21/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(60,plain,
% 0.21/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.47 tff(61,plain,
% 0.21/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[60, 58])).
% 0.21/0.47 tff(62,plain,
% 0.21/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))))))))),
% 0.21/0.48 inference(and_elim,[status(thm)],[46])).
% 0.21/0.48 tff(63,plain,
% 0.21/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.21/0.48 tff(65,plain,
% 0.21/0.48 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))) | ((~r1(X!0, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))) | (~r1(X!0, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(66,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))) | ((~r1(X!0, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(67,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))) | (~r1(X!0, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[67, 64, 54])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 (r1(Y!10, X!11)),
% 0.21/0.48 inference(and_elim,[status(thm)],[46])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(71,plain,
% 0.21/0.48 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(72,plain,
% 0.21/0.48 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.48 tff(73,plain,
% 0.21/0.48 (![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[72, 69, 68])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 (r1(X!11, Y!12)),
% 0.21/0.48 inference(and_elim,[status(thm)],[46])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 (((~![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ((~![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(77,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.48 tff(78,plain,
% 0.21/0.48 (![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[77, 74, 73])).
% 0.21/0.48 tff(79,plain,
% 0.21/0.48 (r1(Y!12, X!13)),
% 0.21/0.48 inference(and_elim,[status(thm)],[46])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 (((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | ((~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) <=> ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(81,plain,
% 0.21/0.48 ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | ((~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(82,plain,
% 0.21/0.48 ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.48 tff(83,plain,
% 0.21/0.48 (![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[82, 79, 78])).
% 0.21/0.48 tff(84,plain,
% 0.21/0.48 (r1(X!13, Y!14)),
% 0.21/0.48 inference(and_elim,[status(thm)],[46])).
% 0.21/0.48 tff(85,plain,
% 0.21/0.48 (((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | ((~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(86,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | ((~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(87,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 (![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[87, 84, 83])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 (r1(Y!14, X!15)),
% 0.21/0.48 inference(and_elim,[status(thm)],[46])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 (((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ((~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 ((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ((~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(92,plain,
% 0.21/0.48 ((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.48 tff(93,plain,
% 0.21/0.48 (![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[92, 89, 88])).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 (r1(X!15, Y!17)),
% 0.21/0.48 inference(and_elim,[status(thm)],[46])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 (((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!15, Y!17)) | (~(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!15, Y!17)) | (~(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!15, Y!17)) | (~(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!15, Y!17)) | (~(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.48 tff(98,plain,
% 0.21/0.48 ((~(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[97, 94, 93])).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 (![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[98, 53])).
% 0.21/0.48 tff(100,assumption,(~((~r1(Y!17, tptp_fun_X_3(Y!17))) | (~p1(tptp_fun_X_3(Y!17))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17))))), introduced(assumption)).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 (((~r1(Y!17, tptp_fun_X_3(Y!17))) | (~p1(tptp_fun_X_3(Y!17))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17)))) | r1(Y!17, tptp_fun_X_3(Y!17))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 (r1(Y!17, tptp_fun_X_3(Y!17))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 (((~![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!17, tptp_fun_X_3(Y!17))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!17), Y))))) <=> ((~![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!17, tptp_fun_X_3(Y!17))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!17), Y))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 ((~![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!17, tptp_fun_X_3(Y!17))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!17), Y))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 ((~![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!17, tptp_fun_X_3(Y!17))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!17), Y)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!17), Y)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[105, 102, 99])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 (((~r1(Y!17, tptp_fun_X_3(Y!17))) | (~p1(tptp_fun_X_3(Y!17))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17)))) | r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 (r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[107, 100])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 (((~r1(Y!17, tptp_fun_X_3(Y!17))) | (~p1(tptp_fun_X_3(Y!17))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17)))) | (~p1(tptp_fun_Y_4(Y!17)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 (~p1(tptp_fun_Y_4(Y!17))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[109, 100])).
% 0.21/0.48 tff(111,plain,
% 0.21/0.48 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!17), Y)))) | (p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!17), Y)))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!17), Y)))) | (p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!17), Y)))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[113, 110, 108, 106])).
% 0.21/0.48 tff(115,plain,((~r1(Y!17, tptp_fun_X_3(Y!17))) | (~p1(tptp_fun_X_3(Y!17))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (((~![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | ((~r1(X!15, Y!17)) | (~((~r1(Y!17, tptp_fun_X_3(Y!17))) | (~p1(tptp_fun_X_3(Y!17))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (~r1(X!15, Y!17)) | (~((~r1(Y!17, tptp_fun_X_3(Y!17))) | (~p1(tptp_fun_X_3(Y!17))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | ((~r1(X!15, Y!17)) | (~((~r1(Y!17, tptp_fun_X_3(Y!17))) | (~p1(tptp_fun_X_3(Y!17))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (~r1(X!15, Y!17)) | (~((~r1(Y!17, tptp_fun_X_3(Y!17))) | (~p1(tptp_fun_X_3(Y!17))) | p1(tptp_fun_Y_4(Y!17)) | (~r1(tptp_fun_X_3(Y!17), tptp_fun_Y_4(Y!17)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[118, 94, 115, 1])).
% 0.21/0.48 tff(120,plain,(~![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(121,assumption,(~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))), introduced(assumption)).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 ((p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | r1(X!15, tptp_fun_Y_7(X!15))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 (r1(X!15, tptp_fun_Y_7(X!15))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 ((p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~p1(tptp_fun_Y_7(X!15)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 (~p1(tptp_fun_Y_7(X!15))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[124, 121])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 (^[Y: $i] : refl((p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) <=> (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 (![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (^[Y: $i] : rewrite((p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) <=> (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 (![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 (![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))))),
% 0.21/0.48 inference(and_elim,[status(thm)],[46])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 (![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 (![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.21/0.48 tff(133,plain,
% 0.21/0.48 (((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 ((p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15))))))) <=> (p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(135,plain,
% 0.21/0.48 (((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15))))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[134])).
% 0.21/0.48 tff(136,plain,
% 0.21/0.48 (((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[135, 133])).
% 0.21/0.48 tff(137,plain,
% 0.21/0.48 ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(138,plain,
% 0.21/0.48 ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 (~((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[138, 132, 125, 123])).
% 0.21/0.48 tff(140,plain,
% 0.21/0.48 (((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15))))) | p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(141,plain,
% 0.21/0.48 (p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 (((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15))))) | r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 (r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[142, 139])).
% 0.21/0.48 tff(144,plain,
% 0.21/0.48 ((p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(145,plain,
% 0.21/0.48 (![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[144, 121])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 (((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), Y))))) <=> ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), Y))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), Y))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), Y)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), Y)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[148, 145, 143, 141])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 (((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15))))) | r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 (r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[150, 139])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 (((~r1(tptp_fun_Y_7(X!15), tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~p1(tptp_fun_X_3(tptp_fun_Y_7(X!15)))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15))))) | (~p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (~p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[152, 139])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), Y)))) | (p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), Y)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), Y)))) | (p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), Y)))) | p1(tptp_fun_Y_4(tptp_fun_Y_7(X!15))) | (~r1(tptp_fun_X_3(tptp_fun_Y_7(X!15)), tptp_fun_Y_4(tptp_fun_Y_7(X!15))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[156, 153, 151, 149])).
% 0.21/0.48 tff(158,plain,(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(159,assumption,(![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))), introduced(assumption)).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 (((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ((~r1(X!15, Y!17)) | (~(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~r1(X!15, Y!17)) | (~(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ((~r1(X!15, Y!17)) | (~(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 ((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~r1(X!15, Y!17)) | (~(p1(tptp_fun_X_1(Y!17)) | (~r1(Y!17, tptp_fun_X_1(Y!17)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[162, 94, 159, 53])).
% 0.21/0.48 tff(164,plain,(~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(166,plain,
% 0.21/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[165])).
% 0.21/0.49 tff(167,plain,
% 0.21/0.49 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(168,plain,
% 0.21/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[167])).
% 0.21/0.49 tff(169,plain,
% 0.21/0.49 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(170,plain,
% 0.21/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[169])).
% 0.21/0.49 tff(171,plain,
% 0.21/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[170, 168])).
% 0.21/0.49 tff(172,plain,
% 0.21/0.49 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(173,plain,
% 0.21/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[172])).
% 0.21/0.49 tff(174,plain,
% 0.21/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (p1(tptp_fun_X_3(Y)) & r1(Y, tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))))) | (p1(tptp_fun_Y_5(X)) & r1(X, tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))) & ![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) & (((~p1(tptp_fun_Y_7(X))) & r1(X, tptp_fun_Y_7(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (p1(tptp_fun_Y_8(X)) & r1(X, tptp_fun_Y_8(X)) & (~(p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))))))))))),
% 0.21/0.49 inference(and_elim,[status(thm)],[46])).
% 0.21/0.49 tff(175,plain,
% 0.21/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.21/0.49 tff(176,plain,
% 0.21/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : (![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), 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)))) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.21/0.49 tff(177,plain,
% 0.21/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[176, 166])).
% 0.21/0.49 tff(178,plain,
% 0.21/0.49 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | ((~r1(X!0, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~r1(X!0, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(179,plain,
% 0.21/0.49 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | ((~r1(X!0, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(180,plain,
% 0.21/0.49 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~r1(X!0, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.21/0.49 tff(181,plain,
% 0.21/0.49 (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[180, 177, 54])).
% 0.21/0.49 tff(182,plain,
% 0.21/0.49 (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(183,plain,
% 0.21/0.50 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(184,plain,
% 0.21/0.50 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.21/0.50 tff(185,plain,
% 0.21/0.50 (![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[184, 69, 181])).
% 0.21/0.50 tff(186,plain,
% 0.21/0.50 (((~![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))) | ((~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(187,plain,
% 0.21/0.50 ((~![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))) | ((~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(188,plain,
% 0.21/0.50 ((~![Y: $i] : ((~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.21/0.50 tff(189,plain,
% 0.21/0.50 (![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[188, 74, 185])).
% 0.21/0.50 tff(190,plain,
% 0.21/0.50 (((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))) | ((~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))) <=> ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))) | (~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(191,plain,
% 0.21/0.50 ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))) | ((~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(192,plain,
% 0.21/0.50 ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))) | (~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.21/0.50 tff(193,plain,
% 0.21/0.50 (![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[192, 79, 189])).
% 0.21/0.50 tff(194,plain,
% 0.21/0.50 (((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) | ((~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) <=> ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) | (~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(195,plain,
% 0.21/0.50 ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) | ((~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(196,plain,
% 0.21/0.50 ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) | (~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.21/0.50 tff(197,plain,
% 0.21/0.50 (![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[196, 84, 193])).
% 0.21/0.50 tff(198,plain,
% 0.21/0.50 (((~![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | (~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15))))))))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | (~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15))))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(199,plain,
% 0.21/0.51 (((~r1(Y!14, X!15)) | (~((~(p1(X!15) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X!15)) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | ![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) <=> ((~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | (~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15))))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(200,plain,
% 0.21/0.51 (((~![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(Y!14, X!15)) | (~((~(p1(X!15) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X!15)) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | ![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | (~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))))))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[199])).
% 0.21/0.51 tff(201,plain,
% 0.21/0.51 (((~![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(Y!14, X!15)) | (~((~(p1(X!15) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X!15)) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | ![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | (~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15))))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[200, 198])).
% 0.21/0.51 tff(202,plain,
% 0.21/0.51 ((~![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(Y!14, X!15)) | (~((~(p1(X!15) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X!15)) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | ![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(203,plain,
% 0.21/0.51 ((~![X: $i] : ((~r1(Y!14, X)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_5(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | (~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.21/0.51 tff(204,plain,
% 0.21/0.51 (~((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | (~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15))))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[203, 89, 197])).
% 0.21/0.51 tff(205,plain,
% 0.21/0.51 (((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | (~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))))))) | (p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(206,plain,
% 0.21/0.51 (p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.21/0.51 tff(207,plain,
% 0.21/0.51 ((~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(208,plain,
% 0.21/0.51 (p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.21/0.51 tff(209,plain,
% 0.21/0.51 (p1(X!15)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[208, 164, 158])).
% 0.21/0.51 tff(210,assumption,(![Y: $i] : (p1(Y) | (~r1(X!15, Y)))), introduced(assumption)).
% 0.21/0.51 tff(211,plain,
% 0.21/0.51 (~(p1(Y!16) | (~r1(X!15, Y!16)))),
% 0.21/0.51 inference(and_elim,[status(thm)],[46])).
% 0.21/0.51 tff(212,plain,
% 0.21/0.51 (r1(X!15, Y!16)),
% 0.21/0.51 inference(or_elim,[status(thm)],[211])).
% 0.21/0.51 tff(213,plain,
% 0.21/0.51 (~p1(Y!16)),
% 0.21/0.51 inference(or_elim,[status(thm)],[211])).
% 0.21/0.51 tff(214,plain,
% 0.21/0.51 (((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) | (p1(Y!16) | (~r1(X!15, Y!16)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) | p1(Y!16) | (~r1(X!15, Y!16)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(215,plain,
% 0.21/0.51 ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) | (p1(Y!16) | (~r1(X!15, Y!16)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(216,plain,
% 0.21/0.51 ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) | p1(Y!16) | (~r1(X!15, Y!16))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.21/0.51 tff(217,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[216, 213, 212, 210])).
% 0.21/0.51 tff(218,plain,(~![Y: $i] : (p1(Y) | (~r1(X!15, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(219,plain,
% 0.21/0.51 (((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | (~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))))))) | (![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15))))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(220,plain,
% 0.21/0.51 (![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[219, 204])).
% 0.21/0.51 tff(221,plain,
% 0.21/0.51 ((~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(222,plain,
% 0.21/0.51 (![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.21/0.51 tff(223,plain,
% 0.21/0.51 (![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[222, 218])).
% 0.21/0.51 tff(224,plain,
% 0.21/0.51 (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[223, 209, 120])).
% 0.21/0.51 tff(225,plain,
% 0.21/0.51 (((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))) | (~p1(tptp_fun_X_6(X!15)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(226,plain,
% 0.21/0.51 (~p1(tptp_fun_X_6(X!15))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.21/0.51 tff(227,plain,
% 0.21/0.51 (((~p1(tptp_fun_X_6(X!15))) | p1(tptp_fun_Y_2(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_X_6(X!15), tptp_fun_Y_2(tptp_fun_X_6(X!15))))) | p1(tptp_fun_X_6(X!15))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(228,plain,
% 0.21/0.51 ((~p1(tptp_fun_X_6(X!15))) | p1(tptp_fun_Y_2(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_X_6(X!15), tptp_fun_Y_2(tptp_fun_X_6(X!15))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.21/0.51 tff(229,plain,
% 0.21/0.51 (((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))) | r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(230,plain,
% 0.21/0.51 (r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[229, 224])).
% 0.21/0.51 tff(231,plain,
% 0.21/0.51 (((~![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(X!15) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | (~(p1(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))) | (~(![Y: $i] : ((~r1(X!15, Y)) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) | (~p1(X!15)) | (~((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))))))) | ((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(232,plain,
% 0.21/0.51 ((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[231, 204])).
% 0.21/0.51 tff(233,plain,
% 0.21/0.51 ((~((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))))) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(234,plain,
% 0.21/0.51 ((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_7(X!15), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.21/0.51 tff(235,plain,
% 0.21/0.51 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[234, 158])).
% 0.21/0.51 tff(236,plain,
% 0.21/0.51 (((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))) | r1(X!15, tptp_fun_Y_5(X!15))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(237,plain,
% 0.21/0.51 (r1(X!15, tptp_fun_Y_5(X!15))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[236, 224])).
% 0.21/0.51 tff(238,assumption,(~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))), introduced(assumption)).
% 0.21/0.51 tff(239,assumption,(r1(X!15, tptp_fun_Y_5(X!15))), introduced(assumption)).
% 0.21/0.51 tff(240,assumption,(![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))), introduced(assumption)).
% 0.21/0.51 tff(241,plain,
% 0.21/0.51 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))) | ((~r1(X!15, tptp_fun_Y_5(X!15))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))) | (~r1(X!15, tptp_fun_Y_5(X!15))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(242,plain,
% 0.21/0.51 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))) | ((~r1(X!15, tptp_fun_Y_5(X!15))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(243,plain,
% 0.21/0.51 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))) | (~r1(X!15, tptp_fun_Y_5(X!15))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.21/0.52 tff(244,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[243, 240, 239, 238])).
% 0.21/0.52 tff(245,plain,((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X)))))))) | (~r1(X!15, tptp_fun_Y_5(X!15))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(246,plain,
% 0.21/0.52 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[245, 237, 235])).
% 0.21/0.52 tff(247,assumption,(![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))), introduced(assumption)).
% 0.21/0.52 tff(248,assumption,((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15))))), introduced(assumption)).
% 0.21/0.52 tff(249,assumption,(~p1(tptp_fun_X_6(X!15))), introduced(assumption)).
% 0.21/0.52 tff(250,assumption,(r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))), introduced(assumption)).
% 0.21/0.52 tff(251,plain,
% 0.21/0.52 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))) | (p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15)))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(252,plain,
% 0.21/0.52 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))) | (p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15)))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(253,plain,
% 0.21/0.52 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.21/0.52 tff(254,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[253, 250, 249, 248, 247])).
% 0.21/0.52 tff(255,plain,((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)) | (~((~r1(X, tptp_fun_Y_8(X))) | (~p1(tptp_fun_Y_8(X))) | p1(tptp_fun_X_9(X)) | (~r1(tptp_fun_Y_8(X), tptp_fun_X_9(X))))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(256,plain,
% 0.21/0.52 (~((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15)))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[255, 246, 226, 230])).
% 0.21/0.52 tff(257,assumption,(~((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15)))))), introduced(assumption)).
% 0.21/0.52 tff(258,plain,
% 0.21/0.52 (((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15))))) | p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(259,plain,
% 0.21/0.52 (p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.21/0.52 tff(260,plain,
% 0.21/0.52 (((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15))))) | r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(261,plain,
% 0.21/0.52 (r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[260, 257])).
% 0.21/0.52 tff(262,assumption,(![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))), introduced(assumption)).
% 0.21/0.52 tff(263,plain,
% 0.21/0.52 (((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), X))))) <=> ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), X))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(264,plain,
% 0.21/0.52 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), X))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(265,plain,
% 0.21/0.52 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), X)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.21/0.52 tff(266,plain,
% 0.21/0.52 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), X)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[265, 262, 261, 259])).
% 0.21/0.52 tff(267,plain,
% 0.21/0.52 (((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15))))) | r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(268,plain,
% 0.21/0.52 (r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[267, 257])).
% 0.21/0.52 tff(269,plain,
% 0.21/0.52 (((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15))))) | (~p1(tptp_fun_X_9(tptp_fun_X_6(X!15))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(270,plain,
% 0.21/0.52 (~p1(tptp_fun_X_9(tptp_fun_X_6(X!15)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[269, 257])).
% 0.21/0.52 tff(271,plain,
% 0.21/0.52 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), X)))) | (p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), X)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15)))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(272,plain,
% 0.21/0.52 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), X)))) | (p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15)))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(273,plain,
% 0.21/0.52 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), X)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.21/0.52 tff(274,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[273, 270, 268, 266])).
% 0.21/0.52 tff(275,plain,(((~r1(tptp_fun_X_6(X!15), tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_Y_8(tptp_fun_X_6(X!15)))) | p1(tptp_fun_X_9(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_Y_8(tptp_fun_X_6(X!15)), tptp_fun_X_9(tptp_fun_X_6(X!15))))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(276,plain,
% 0.21/0.52 (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[275, 256])).
% 0.21/0.52 tff(277,plain,
% 0.21/0.52 (((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | p1(tptp_fun_X_6(X!15)) | (~p1(tptp_fun_Y_5(X!15))) | (~r1(X!15, tptp_fun_Y_5(X!15)))) | ![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(278,plain,
% 0.21/0.52 (![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[277, 224])).
% 0.21/0.52 tff(279,plain,
% 0.21/0.52 (((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~((~p1(tptp_fun_X_6(X!15))) | p1(tptp_fun_Y_2(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_X_6(X!15), tptp_fun_Y_2(tptp_fun_X_6(X!15)))))) | ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~((~p1(tptp_fun_X_6(X!15))) | p1(tptp_fun_Y_2(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_X_6(X!15), tptp_fun_Y_2(tptp_fun_X_6(X!15)))))) | ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(280,plain,
% 0.21/0.52 ((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~((~p1(tptp_fun_X_6(X!15))) | p1(tptp_fun_Y_2(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_X_6(X!15), tptp_fun_Y_2(tptp_fun_X_6(X!15)))))) | ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(281,plain,
% 0.21/0.52 ((~![X: $i] : ((~r1(tptp_fun_Y_5(X!15), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))) | (~((~p1(tptp_fun_X_6(X!15))) | p1(tptp_fun_Y_2(tptp_fun_X_6(X!15))) | (~r1(tptp_fun_X_6(X!15), tptp_fun_Y_2(tptp_fun_X_6(X!15)))))) | ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_6(X!15), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.21/0.52 tff(282,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[281, 278, 230, 276, 228])).
% 0.21/0.52 % SZS output end Proof
% 0.21/0.52 % E exiting
%------------------------------------------------------------------------------