%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL642+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n002.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 03:00:20 PM UTC 2026
% Result : Theorem 0.27s 0.57s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL642+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.15/0.41 % Computer : n002.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 5 12:08:22 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.27/0.57 % SZS status Theorem
% 0.27/0.57 % SZS output start Proof
% 0.27/0.57 tff(p2_type, type, (
% 0.27/0.57 p2: $i > $o)).
% 0.27/0.57 tff(tptp_fun_X_6_type, type, (
% 0.27/0.57 tptp_fun_X_6: $i > $i)).
% 0.27/0.57 tff(tptp_fun_Y_15_type, type, (
% 0.27/0.57 tptp_fun_Y_15: $i)).
% 0.27/0.57 tff(tptp_fun_Y_7_type, type, (
% 0.27/0.57 tptp_fun_Y_7: $i > $i)).
% 0.27/0.57 tff(r1_type, type, (
% 0.27/0.57 r1: ( $i * $i ) > $o)).
% 0.27/0.57 tff(tptp_fun_X_10_type, type, (
% 0.27/0.57 tptp_fun_X_10: $i > $i)).
% 0.27/0.57 tff(tptp_fun_Y_9_type, type, (
% 0.27/0.57 tptp_fun_Y_9: $i > $i)).
% 0.27/0.57 tff(tptp_fun_Y_13_type, type, (
% 0.27/0.57 tptp_fun_Y_13: $i)).
% 0.27/0.57 tff(tptp_fun_X_14_type, type, (
% 0.27/0.57 tptp_fun_X_14: $i)).
% 0.27/0.57 tff(tptp_fun_X_18_type, type, (
% 0.27/0.57 tptp_fun_X_18: $i > $i)).
% 0.27/0.57 tff(tptp_fun_Y_17_type, type, (
% 0.27/0.57 tptp_fun_Y_17: $i > $i)).
% 0.27/0.57 tff(tptp_fun_X_16_type, type, (
% 0.27/0.57 tptp_fun_X_16: $i > $i)).
% 0.27/0.57 tff(tptp_fun_X_0_type, type, (
% 0.27/0.57 tptp_fun_X_0: $i)).
% 0.27/0.57 tff(tptp_fun_Y_8_type, type, (
% 0.27/0.57 tptp_fun_Y_8: $i)).
% 0.27/0.57 tff(tptp_fun_X_12_type, type, (
% 0.27/0.57 tptp_fun_X_12: $i)).
% 0.27/0.57 tff(tptp_fun_Y_11_type, type, (
% 0.27/0.57 tptp_fun_Y_11: $i)).
% 0.27/0.57 tff(tptp_fun_Y_1_type, type, (
% 0.27/0.57 tptp_fun_Y_1: $i)).
% 0.27/0.57 tff(p1_type, type, (
% 0.27/0.57 p1: $i > $o)).
% 0.27/0.58 tff(tptp_fun_Y_20_type, type, (
% 0.27/0.58 tptp_fun_Y_20: $i > $i)).
% 0.27/0.58 tff(tptp_fun_X_19_type, type, (
% 0.27/0.58 tptp_fun_X_19: $i > $i)).
% 0.27/0.58 tff(tptp_fun_Y_5_type, type, (
% 0.27/0.58 tptp_fun_Y_5: $i > $i)).
% 0.27/0.58 tff(tptp_fun_X_4_type, type, (
% 0.27/0.58 tptp_fun_X_4: $i > $i)).
% 0.27/0.58 tff(p3_type, type, (
% 0.27/0.58 p3: $i > $o)).
% 0.27/0.58 tff(tptp_fun_Y_3_type, type, (
% 0.27/0.58 tptp_fun_Y_3: $i)).
% 0.27/0.58 tff(tptp_fun_Y_2_type, type, (
% 0.27/0.58 tptp_fun_Y_2: $i)).
% 0.27/0.58 tff(1,assumption,(~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))), introduced(assumption)).
% 0.27/0.58 tff(2,plain,
% 0.27/0.58 (((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15)))) | p2(tptp_fun_X_6(Y!15))),
% 0.27/0.58 inference(tautology,[status(thm)],[])).
% 0.27/0.58 tff(3,plain,
% 0.27/0.58 (p2(tptp_fun_X_6(Y!15))),
% 0.27/0.58 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.27/0.58 tff(4,plain,
% 0.27/0.58 (((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15)))) | r1(Y!15, tptp_fun_X_6(Y!15))),
% 0.27/0.58 inference(tautology,[status(thm)],[])).
% 0.27/0.58 tff(5,plain,
% 0.27/0.58 (r1(Y!15, tptp_fun_X_6(Y!15))),
% 0.27/0.58 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.27/0.58 tff(6,assumption,(![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))), introduced(assumption)).
% 0.27/0.58 tff(7,assumption,(~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))))), introduced(assumption)).
% 0.27/0.58 tff(8,plain,
% 0.27/0.58 (((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1))))) | p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))),
% 0.27/0.58 inference(tautology,[status(thm)],[])).
% 0.27/0.58 tff(9,plain,
% 0.27/0.58 (p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))),
% 0.27/0.58 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.27/0.58 tff(10,plain,
% 0.27/0.58 (((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1))))) | r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))),
% 0.27/0.58 inference(tautology,[status(thm)],[])).
% 0.27/0.58 tff(11,plain,
% 0.27/0.58 (r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))),
% 0.27/0.58 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.27/0.58 tff(12,plain,
% 0.27/0.58 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))),
% 0.27/0.58 inference(bind,[status(th)],[])).
% 0.27/0.58 tff(13,plain,
% 0.27/0.58 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.27/0.58 inference(quant_intro,[status(thm)],[12])).
% 0.27/0.58 tff(14,plain,
% 0.27/0.58 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))))),
% 0.27/0.58 inference(bind,[status(th)],[])).
% 0.27/0.58 tff(15,plain,
% 0.27/0.58 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))),
% 0.27/0.58 inference(quant_intro,[status(thm)],[14])).
% 0.27/0.58 tff(16,plain,
% 0.27/0.58 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))))),
% 0.27/0.58 inference(bind,[status(th)],[])).
% 0.27/0.58 tff(17,plain,
% 0.27/0.58 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))),
% 0.27/0.58 inference(quant_intro,[status(thm)],[16])).
% 0.27/0.58 tff(18,plain,
% 0.27/0.58 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))),
% 0.27/0.58 inference(transitivity,[status(thm)],[17, 15])).
% 0.27/0.58 tff(19,plain,
% 0.27/0.58 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))))),
% 0.27/0.58 inference(bind,[status(th)],[])).
% 0.27/0.58 tff(20,plain,
% 0.27/0.58 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))),
% 0.27/0.58 inference(quant_intro,[status(thm)],[19])).
% 0.27/0.58 tff(21,plain,
% 0.27/0.58 (((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & (((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & ((r1(Y!13, X!14) & r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))) | (~r1(Y!13, X)))) | ((~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X))))) & ![X: $i] : ((~r1(Y!13, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_17(X)) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y))))))) <=> ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & ((r1(Y!13, X!14) & r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))) | (~r1(Y!13, X)))) | ((~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X))))) & ![X: $i] : ((~r1(Y!13, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_17(X)) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y)))))))),
% 0.27/0.59 inference(rewrite,[status(thm)],[])).
% 0.27/0.59 tff(22,plain,
% 0.27/0.59 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y)))) <=> (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y))))), ((r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y))))) <=> (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y))))))), (((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y)))))) <=> ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y)))))))), rewrite(((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y))))))), (((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y))))))))),
% 0.27/0.59 inference(bind,[status(th)],[])).
% 0.27/0.59 tff(23,plain,
% 0.27/0.59 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y))))))),
% 0.27/0.59 inference(quant_intro,[status(thm)],[22])).
% 0.27/0.59 tff(24,plain,
% 0.27/0.59 ((((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~r1(Y!8, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & (((r1(Y!13, X!14) & (r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!13, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | ((~p2(Y!13)) & ![X: $i] : ((~r1(Y!13, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_16(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & (r1(X, tptp_fun_Y_17(X)) & (r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~r1(tptp_fun_X_18(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_16(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & ((r1(Y!13, X!14) & r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))) | (~r1(Y!13, X)))) | ((~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X))))) & ![X: $i] : ((~r1(Y!13, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_17(X)) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))))),
% 0.27/0.59 inference(rewrite,[status(thm)],[])).
% 0.27/0.59 tff(25,plain,
% 0.27/0.59 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))) <=> (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))), ((r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))) <=> (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))), (((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))), rewrite(((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))), (((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.27/0.59 inference(bind,[status(th)],[])).
% 0.27/0.59 tff(26,plain,
% 0.27/0.59 (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))),
% 0.27/0.59 inference(quant_intro,[status(thm)],[25])).
% 0.27/0.59 tff(27,plain,
% 0.27/0.59 ((~((~r1(X!0, Y!3)) | p1(Y!3))) <=> (~(p1(Y!3) | (~r1(X!0, Y!3))))),
% 0.27/0.59 inference(rewrite,[status(thm)],[])).
% 0.27/0.59 tff(28,plain,
% 0.27/0.59 ((~((~r1(X!0, Y!1)) | p2(Y!1))) <=> (~((~r1(X!0, Y!1)) | p2(Y!1)))),
% 0.27/0.59 inference(rewrite,[status(thm)],[])).
% 0.27/0.59 tff(29,plain,
% 0.27/0.59 (((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & (((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~r1(Y!8, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & (((r1(Y!13, X!14) & (r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!13, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | ((~p2(Y!13)) & ![X: $i] : ((~r1(Y!13, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_16(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & (r1(X, tptp_fun_Y_17(X)) & (r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~r1(tptp_fun_X_18(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_16(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y))))))) <=> ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & (((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & ((r1(Y!13, X!14) & r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))) | (~r1(Y!13, X)))) | ((~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X))))) & ![X: $i] : ((~r1(Y!13, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_17(X)) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y)))))))),
% 0.27/0.60 inference(monotonicity,[status(thm)],[28, 27, 26, 24, 23])).
% 0.27/0.60 tff(30,plain,
% 0.27/0.60 (((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & (((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~r1(Y!8, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & (((r1(Y!13, X!14) & (r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!13, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | ((~p2(Y!13)) & ![X: $i] : ((~r1(Y!13, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_16(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & (r1(X, tptp_fun_Y_17(X)) & (r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~r1(tptp_fun_X_18(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_16(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y))))))) <=> ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & ((r1(Y!13, X!14) & r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))) | (~r1(Y!13, X)))) | ((~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X))))) & ![X: $i] : ((~r1(Y!13, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_17(X)) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y)))))))),
% 0.37/0.61 inference(transitivity,[status(thm)],[29, 21])).
% 0.37/0.61 tff(31,plain,
% 0.37/0.61 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(32,plain,
% 0.37/0.61 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(33,plain,
% 0.37/0.62 ((~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | 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)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(34,plain,
% 0.37/0.62 ((~(~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | 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)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))))),
% 0.37/0.63 inference(monotonicity,[status(thm)],[33])).
% 0.37/0.63 tff(35,plain,
% 0.37/0.63 ((~(~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | 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)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 0.37/0.63 inference(transitivity,[status(thm)],[34, 32])).
% 0.37/0.63 tff(36,axiom,(~(~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | 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)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.37/0.64 tff(37,plain,
% 0.37/0.64 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 0.37/0.64 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.37/0.64 tff(38,plain,
% 0.37/0.64 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 0.37/0.64 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.37/0.64 tff(39,plain,
% 0.37/0.64 ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & ((r1(Y!13, X!14) & r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))) | (~r1(Y!13, X)))) | ((~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X))))) & ![X: $i] : ((~r1(Y!13, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_17(X)) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_19(Y)) & p1(tptp_fun_X_19(Y)) & (~((~r1(tptp_fun_X_19(Y), tptp_fun_Y_20(Y))) | p1(tptp_fun_Y_20(Y))))))),
% 0.37/0.64 inference(modus_ponens,[status(thm)],[38, 30])).
% 0.37/0.64 tff(40,plain,
% 0.37/0.64 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))),
% 0.37/0.64 inference(and_elim,[status(thm)],[39])).
% 0.37/0.64 tff(41,plain,
% 0.37/0.64 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))),
% 0.37/0.64 inference(modus_ponens,[status(thm)],[40, 20])).
% 0.37/0.64 tff(42,plain,
% 0.37/0.64 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))),
% 0.37/0.64 inference(modus_ponens,[status(thm)],[41, 18])).
% 0.37/0.64 tff(43,plain,
% 0.37/0.64 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.37/0.65 inference(modus_ponens,[status(thm)],[42, 13])).
% 0.37/0.65 tff(44,plain,
% 0.37/0.65 (~((~r1(X!0, Y!1)) | p2(Y!1))),
% 0.37/0.65 inference(and_elim,[status(thm)],[39])).
% 0.37/0.65 tff(45,plain,
% 0.37/0.65 (~p2(Y!1)),
% 0.37/0.65 inference(or_elim,[status(thm)],[44])).
% 0.37/0.65 tff(46,plain,
% 0.37/0.65 (r1(X!0, Y!1)),
% 0.37/0.65 inference(or_elim,[status(thm)],[44])).
% 0.37/0.65 tff(47,plain,
% 0.37/0.65 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_16(Y!1)) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_16(Y!1)) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.37/0.65 inference(rewrite,[status(thm)],[])).
% 0.37/0.65 tff(48,plain,
% 0.37/0.65 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_16(Y!1)) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.37/0.65 inference(quant_inst,[status(thm)],[])).
% 0.37/0.65 tff(49,plain,
% 0.37/0.65 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_16(Y!1)) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.37/0.65 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.37/0.65 tff(50,plain,
% 0.37/0.65 (~(p2(tptp_fun_X_16(Y!1)) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))),
% 0.37/0.65 inference(unit_resolution,[status(thm)],[49, 46, 45, 43])).
% 0.37/0.65 tff(51,plain,
% 0.37/0.65 ((p2(tptp_fun_X_16(Y!1)) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.37/0.65 inference(tautology,[status(thm)],[])).
% 0.37/0.65 tff(52,plain,
% 0.37/0.65 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.37/0.65 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.37/0.65 tff(53,plain,
% 0.37/0.65 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X))))),
% 0.37/0.65 inference(rewrite,[status(thm)],[])).
% 0.37/0.65 tff(54,plain,
% 0.37/0.65 (((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)) | p2(X))) <=> ((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X))))),
% 0.37/0.65 inference(rewrite,[status(thm)],[])).
% 0.37/0.65 tff(55,plain,
% 0.37/0.65 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)))))),
% 0.37/0.65 inference(monotonicity,[status(thm)],[54])).
% 0.37/0.65 tff(56,plain,
% 0.37/0.65 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X))))),
% 0.37/0.65 inference(transitivity,[status(thm)],[55, 53])).
% 0.37/0.65 tff(57,plain,
% 0.37/0.65 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)) | p2(X)))),
% 0.42/0.65 inference(quant_inst,[status(thm)],[])).
% 0.42/0.65 tff(58,plain,
% 0.42/0.65 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)))),
% 0.42/0.65 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.42/0.65 tff(59,plain,
% 0.42/0.65 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)))),
% 0.42/0.65 inference(unit_resolution,[status(thm)],[58, 52, 11, 9])).
% 0.42/0.65 tff(60,plain,
% 0.42/0.65 (((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1))))) | (~p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))))),
% 0.42/0.65 inference(tautology,[status(thm)],[])).
% 0.42/0.65 tff(61,plain,
% 0.42/0.65 (~p2(tptp_fun_X_10(tptp_fun_X_16(Y!1)))),
% 0.42/0.65 inference(unit_resolution,[status(thm)],[60, 7])).
% 0.42/0.65 tff(62,plain,
% 0.42/0.65 (((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1))))) | r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))),
% 0.42/0.65 inference(tautology,[status(thm)],[])).
% 0.42/0.65 tff(63,plain,
% 0.42/0.65 (r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))),
% 0.42/0.65 inference(unit_resolution,[status(thm)],[62, 7])).
% 0.42/0.65 tff(64,plain,
% 0.42/0.65 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)))) | (p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))))),
% 0.42/0.65 inference(rewrite,[status(thm)],[])).
% 0.42/0.65 tff(65,plain,
% 0.42/0.65 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)))) | (p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))))),
% 0.42/0.65 inference(quant_inst,[status(thm)],[])).
% 0.42/0.65 tff(66,plain,
% 0.42/0.65 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), X)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1))))),
% 0.42/0.65 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.42/0.65 tff(67,plain,
% 0.42/0.65 ($false),
% 0.42/0.65 inference(unit_resolution,[status(thm)],[66, 63, 61, 59])).
% 0.42/0.65 tff(68,plain,((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1))))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.65 tff(69,plain,
% 0.42/0.65 ((p2(tptp_fun_X_16(Y!1)) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | r1(Y!1, tptp_fun_X_16(Y!1))),
% 0.42/0.65 inference(tautology,[status(thm)],[])).
% 0.42/0.65 tff(70,plain,
% 0.42/0.65 (r1(Y!1, tptp_fun_X_16(Y!1))),
% 0.42/0.65 inference(unit_resolution,[status(thm)],[69, 50])).
% 0.42/0.65 tff(71,plain,
% 0.42/0.65 ((p2(tptp_fun_X_16(Y!1)) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(tptp_fun_X_16(Y!1)))),
% 0.42/0.65 inference(tautology,[status(thm)],[])).
% 0.42/0.65 tff(72,plain,
% 0.42/0.65 (~p2(tptp_fun_X_16(Y!1))),
% 0.42/0.65 inference(unit_resolution,[status(thm)],[71, 50])).
% 0.42/0.65 tff(73,plain,
% 0.42/0.65 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))) | ((~r1(Y!1, tptp_fun_X_16(Y!1))) | p2(tptp_fun_X_16(Y!1)) | (~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | p2(tptp_fun_X_16(Y!1)) | (~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))))))),
% 0.42/0.65 inference(rewrite,[status(thm)],[])).
% 0.42/0.65 tff(74,plain,
% 0.42/0.65 ((p2(tptp_fun_X_16(Y!1)) | (~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))))) | (~r1(Y!1, tptp_fun_X_16(Y!1)))) <=> ((~r1(Y!1, tptp_fun_X_16(Y!1))) | p2(tptp_fun_X_16(Y!1)) | (~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))))))),
% 0.42/0.65 inference(rewrite,[status(thm)],[])).
% 0.42/0.65 tff(75,plain,
% 0.42/0.65 ((~((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))))) <=> (~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1))))))),
% 0.42/0.65 inference(rewrite,[status(thm)],[])).
% 0.42/0.65 tff(76,plain,
% 0.42/0.65 ((p2(tptp_fun_X_16(Y!1)) | (~((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))))) | (~r1(Y!1, tptp_fun_X_16(Y!1)))) <=> (p2(tptp_fun_X_16(Y!1)) | (~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))))) | (~r1(Y!1, tptp_fun_X_16(Y!1))))),
% 0.42/0.65 inference(monotonicity,[status(thm)],[75])).
% 0.42/0.65 tff(77,plain,
% 0.42/0.65 ((p2(tptp_fun_X_16(Y!1)) | (~((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))))) | (~r1(Y!1, tptp_fun_X_16(Y!1)))) <=> ((~r1(Y!1, tptp_fun_X_16(Y!1))) | p2(tptp_fun_X_16(Y!1)) | (~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))))))),
% 0.42/0.65 inference(transitivity,[status(thm)],[76, 74])).
% 0.42/0.65 tff(78,plain,
% 0.42/0.65 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))) | (p2(tptp_fun_X_16(Y!1)) | (~((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))))) | (~r1(Y!1, tptp_fun_X_16(Y!1))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))) | ((~r1(Y!1, tptp_fun_X_16(Y!1))) | p2(tptp_fun_X_16(Y!1)) | (~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1))))))))),
% 0.42/0.66 inference(monotonicity,[status(thm)],[77])).
% 0.42/0.66 tff(79,plain,
% 0.42/0.66 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))) | (p2(tptp_fun_X_16(Y!1)) | (~((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))))) | (~r1(Y!1, tptp_fun_X_16(Y!1))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | p2(tptp_fun_X_16(Y!1)) | (~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))))))),
% 0.42/0.66 inference(transitivity,[status(thm)],[78, 73])).
% 0.42/0.66 tff(80,plain,
% 0.42/0.66 ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))) | (p2(tptp_fun_X_16(Y!1)) | (~((~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))))) | (~r1(Y!1, tptp_fun_X_16(Y!1))))),
% 0.42/0.66 inference(quant_inst,[status(thm)],[])).
% 0.42/0.66 tff(81,plain,
% 0.42/0.66 ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))) | (~r1(Y!1, tptp_fun_X_16(Y!1))) | p2(tptp_fun_X_16(Y!1)) | (~((~r1(tptp_fun_Y_9(tptp_fun_X_16(Y!1)), tptp_fun_X_10(tptp_fun_X_16(Y!1)))) | p2(tptp_fun_X_10(tptp_fun_X_16(Y!1))) | (~r1(tptp_fun_X_16(Y!1), tptp_fun_Y_9(tptp_fun_X_16(Y!1)))) | (~p2(tptp_fun_Y_9(tptp_fun_X_16(Y!1))))))),
% 0.42/0.66 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.42/0.66 tff(82,plain,
% 0.42/0.66 ($false),
% 0.42/0.66 inference(unit_resolution,[status(thm)],[81, 72, 70, 68, 6])).
% 0.42/0.66 tff(83,plain,(~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.66 tff(84,assumption,(![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))), introduced(assumption)).
% 0.42/0.66 tff(85,plain,
% 0.42/0.66 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | (~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X))))),
% 0.42/0.66 inference(rewrite,[status(thm)],[])).
% 0.42/0.66 tff(86,plain,
% 0.42/0.66 (((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) <=> ((~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X))))),
% 0.42/0.66 inference(rewrite,[status(thm)],[])).
% 0.42/0.66 tff(87,plain,
% 0.42/0.66 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))))),
% 0.42/0.66 inference(monotonicity,[status(thm)],[86])).
% 0.42/0.66 tff(88,plain,
% 0.42/0.66 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | (~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X))))),
% 0.42/0.66 inference(transitivity,[status(thm)],[87, 85])).
% 0.42/0.66 tff(89,plain,
% 0.42/0.66 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))),
% 0.42/0.66 inference(quant_inst,[status(thm)],[])).
% 0.42/0.66 tff(90,plain,
% 0.42/0.66 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))) | (~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))) | (~r1(Y!1, X)))),
% 0.42/0.66 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.42/0.66 tff(91,plain,
% 0.42/0.66 ($false),
% 0.42/0.66 inference(unit_resolution,[status(thm)],[90, 46, 84, 83])).
% 0.42/0.66 tff(92,plain,(~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.66 tff(93,assumption,(~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))), introduced(assumption)).
% 0.42/0.66 tff(94,plain,
% 0.42/0.66 ((p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(X!0, Y!8)),
% 0.42/0.66 inference(tautology,[status(thm)],[])).
% 0.42/0.66 tff(95,plain,
% 0.42/0.66 (r1(X!0, Y!8)),
% 0.42/0.66 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.42/0.66 tff(96,plain,
% 0.42/0.66 ((p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!8))),
% 0.42/0.66 inference(tautology,[status(thm)],[])).
% 0.42/0.66 tff(97,plain,
% 0.42/0.66 (~p2(Y!8)),
% 0.42/0.66 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.42/0.66 tff(98,plain,
% 0.42/0.67 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))),
% 0.42/0.67 inference(bind,[status(th)],[])).
% 0.42/0.67 tff(99,plain,
% 0.42/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.42/0.67 inference(quant_intro,[status(thm)],[98])).
% 0.42/0.67 tff(100,plain,
% 0.42/0.67 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))),
% 0.42/0.67 inference(bind,[status(th)],[])).
% 0.42/0.67 tff(101,plain,
% 0.42/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.42/0.67 inference(quant_intro,[status(thm)],[100])).
% 0.42/0.67 tff(102,plain,
% 0.42/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))),
% 0.42/0.67 inference(and_elim,[status(thm)],[39])).
% 0.42/0.67 tff(103,plain,
% 0.42/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.42/0.67 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.42/0.67 tff(104,plain,
% 0.42/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.42/0.67 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.42/0.67 tff(105,plain,
% 0.42/0.67 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!8) | (~r1(X!0, Y!8)) | (~((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(Y!8) | (~r1(X!0, Y!8)) | (~((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8)))))),
% 0.42/0.67 inference(rewrite,[status(thm)],[])).
% 0.42/0.67 tff(106,plain,
% 0.42/0.67 ((p2(Y!8) | (~r1(X!0, Y!8)) | (~((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | p2(tptp_fun_Y_7(Y!8))))) <=> (p2(Y!8) | (~r1(X!0, Y!8)) | (~((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8)))))),
% 0.42/0.67 inference(rewrite,[status(thm)],[])).
% 0.42/0.67 tff(107,plain,
% 0.42/0.67 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!8) | (~r1(X!0, Y!8)) | (~((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | p2(tptp_fun_Y_7(Y!8)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!8) | (~r1(X!0, Y!8)) | (~((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8))))))),
% 0.42/0.67 inference(monotonicity,[status(thm)],[106])).
% 0.42/0.67 tff(108,plain,
% 0.42/0.67 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!8) | (~r1(X!0, Y!8)) | (~((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | p2(tptp_fun_Y_7(Y!8)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(Y!8) | (~r1(X!0, Y!8)) | (~((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8)))))),
% 0.42/0.67 inference(transitivity,[status(thm)],[107, 105])).
% 0.42/0.67 tff(109,plain,
% 0.42/0.67 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!8) | (~r1(X!0, Y!8)) | (~((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | p2(tptp_fun_Y_7(Y!8)))))),
% 0.42/0.67 inference(quant_inst,[status(thm)],[])).
% 0.42/0.67 tff(110,plain,
% 0.42/0.67 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(Y!8) | (~r1(X!0, Y!8)) | (~((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8))))),
% 0.42/0.67 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.42/0.67 tff(111,plain,
% 0.42/0.67 (~((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8)))),
% 0.42/0.67 inference(unit_resolution,[status(thm)],[110, 104, 97, 95])).
% 0.42/0.67 tff(112,plain,
% 0.42/0.67 (((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8))) | p2(tptp_fun_X_6(Y!8))),
% 0.42/0.67 inference(tautology,[status(thm)],[])).
% 0.42/0.67 tff(113,plain,
% 0.42/0.67 (p2(tptp_fun_X_6(Y!8))),
% 0.42/0.67 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.42/0.67 tff(114,plain,
% 0.42/0.67 (((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8))) | r1(Y!8, tptp_fun_X_6(Y!8))),
% 0.42/0.67 inference(tautology,[status(thm)],[])).
% 0.42/0.67 tff(115,plain,
% 0.42/0.67 (r1(Y!8, tptp_fun_X_6(Y!8))),
% 0.42/0.67 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.42/0.67 tff(116,plain,
% 0.42/0.67 ((p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.42/0.67 inference(tautology,[status(thm)],[])).
% 0.42/0.67 tff(117,plain,
% 0.42/0.67 (![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.42/0.67 inference(unit_resolution,[status(thm)],[116, 93])).
% 0.42/0.67 tff(118,plain,
% 0.42/0.67 (((~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y))))),
% 0.42/0.67 inference(rewrite,[status(thm)],[])).
% 0.42/0.67 tff(119,plain,
% 0.42/0.67 (((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!8), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y))))),
% 0.42/0.67 inference(rewrite,[status(thm)],[])).
% 0.42/0.67 tff(120,plain,
% 0.42/0.67 (((~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!8), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y)))))),
% 0.42/0.67 inference(monotonicity,[status(thm)],[119])).
% 0.42/0.67 tff(121,plain,
% 0.42/0.67 (((~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!8), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y))))),
% 0.42/0.67 inference(transitivity,[status(thm)],[120, 118])).
% 0.42/0.67 tff(122,plain,
% 0.42/0.67 ((~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!8), Y)) | p2(Y)))),
% 0.42/0.67 inference(quant_inst,[status(thm)],[])).
% 0.42/0.67 tff(123,plain,
% 0.42/0.67 ((~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y)))),
% 0.42/0.67 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.42/0.67 tff(124,plain,
% 0.42/0.67 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y)))),
% 0.42/0.67 inference(unit_resolution,[status(thm)],[123, 117, 115, 113])).
% 0.42/0.67 tff(125,plain,
% 0.42/0.67 (((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8))) | (~p2(tptp_fun_Y_7(Y!8)))),
% 0.42/0.67 inference(tautology,[status(thm)],[])).
% 0.42/0.67 tff(126,plain,
% 0.42/0.67 (~p2(tptp_fun_Y_7(Y!8))),
% 0.42/0.67 inference(unit_resolution,[status(thm)],[125, 111])).
% 0.42/0.67 tff(127,plain,
% 0.42/0.67 (((~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))) | (~r1(Y!8, tptp_fun_X_6(Y!8))) | (~p2(tptp_fun_X_6(Y!8))) | p2(tptp_fun_Y_7(Y!8))) | r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))),
% 0.42/0.67 inference(tautology,[status(thm)],[])).
% 0.42/0.67 tff(128,plain,
% 0.42/0.67 (r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))),
% 0.42/0.67 inference(unit_resolution,[status(thm)],[127, 111])).
% 0.42/0.67 tff(129,plain,
% 0.42/0.67 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y)))) | (p2(tptp_fun_Y_7(Y!8)) | (~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y)))) | p2(tptp_fun_Y_7(Y!8)) | (~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))))),
% 0.42/0.67 inference(rewrite,[status(thm)],[])).
% 0.42/0.67 tff(130,plain,
% 0.42/0.67 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y)))) | (p2(tptp_fun_Y_7(Y!8)) | (~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8))))),
% 0.42/0.68 inference(quant_inst,[status(thm)],[])).
% 0.42/0.68 tff(131,plain,
% 0.42/0.68 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!8), Y)))) | p2(tptp_fun_Y_7(Y!8)) | (~r1(tptp_fun_X_6(Y!8), tptp_fun_Y_7(Y!8)))),
% 0.42/0.68 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.42/0.68 tff(132,plain,
% 0.42/0.68 ($false),
% 0.42/0.68 inference(unit_resolution,[status(thm)],[131, 128, 126, 124])).
% 0.42/0.68 tff(133,plain,(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.68 tff(134,plain,
% 0.42/0.68 ((~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))),
% 0.42/0.68 inference(tautology,[status(thm)],[])).
% 0.42/0.68 tff(135,plain,
% 0.42/0.68 (~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))),
% 0.42/0.68 inference(unit_resolution,[status(thm)],[134, 133, 92])).
% 0.42/0.68 tff(136,plain,
% 0.42/0.68 (((~(p2(X!0) | (~((~p2(Y!11)) | (~r1(X!0, Y!11)) | (~r1(Y!11, X!12)) | p2(X!12))))) | (~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))))) | ((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))),
% 0.42/0.68 inference(tautology,[status(thm)],[])).
% 0.42/0.68 tff(137,plain,
% 0.42/0.68 ((~(p2(X!0) | (~((~p2(Y!11)) | (~r1(X!0, Y!11)) | (~r1(Y!11, X!12)) | p2(X!12))))) | (~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))))))),
% 0.42/0.68 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.42/0.68 tff(138,plain,
% 0.42/0.68 (((~((~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(X!0) | (~((~p2(Y!11)) | (~r1(X!0, Y!11)) | (~r1(Y!11, X!12)) | p2(X!12))))))) | (~((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))))))) <=> ((~((~(p2(X!0) | (~((~p2(Y!11)) | (~r1(X!0, Y!11)) | (~r1(Y!11, X!12)) | p2(X!12))))) | (~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))))) | (~((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.42/0.69 inference(rewrite,[status(thm)],[])).
% 0.42/0.69 tff(139,plain,
% 0.42/0.69 (((~((~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(X!0) | (~((~p2(Y!11)) | (~r1(X!0, Y!11)) | (~r1(Y!11, X!12)) | p2(X!12))))))) | (~((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))))))) <=> ((~((~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(X!0) | (~((~p2(Y!11)) | (~r1(X!0, Y!11)) | (~r1(Y!11, X!12)) | p2(X!12))))))) | (~((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y)))))))))))),
% 0.42/0.69 inference(rewrite,[status(thm)],[])).
% 0.42/0.69 tff(140,plain,
% 0.42/0.69 (((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & ((r1(Y!13, X!14) & r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))) | (~r1(Y!13, X)))) | ((~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X))))) & ![X: $i] : ((~r1(Y!13, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_17(X)) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))) <=> ((~((~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(X!0) | (~((~p2(Y!11)) | (~r1(X!0, Y!11)) | (~r1(Y!11, X!12)) | p2(X!12))))))) | (~((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y)))))))))))),
% 0.42/0.69 inference(rewrite,[status(thm)],[])).
% 0.42/0.69 tff(141,plain,
% 0.42/0.69 ((((r1(X!0, Y!8) & (~p2(Y!8)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) & (p2(X!0) | (r1(X!0, Y!11) & p2(Y!11) & (~((~r1(Y!11, X!12)) | p2(X!12)))))) | (r1(X!0, Y!13) & ((r1(Y!13, X!14) & r1(X!14, Y!15) & (~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_9(X)) & p2(tptp_fun_Y_9(X)) & (~((~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X))))) | (~r1(Y!13, X)))) | ((~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X))))) & ![X: $i] : ((~r1(Y!13, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_16(Y)) & (~p2(tptp_fun_X_16(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & r1(X, tptp_fun_Y_17(X)) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & (~p2(tptp_fun_X_18(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))),
% 0.42/0.69 inference(and_elim,[status(thm)],[39])).
% 0.42/0.69 tff(142,plain,
% 0.42/0.69 ((~((~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(X!0) | (~((~p2(Y!11)) | (~r1(X!0, Y!11)) | (~r1(Y!11, X!12)) | p2(X!12))))))) | (~((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))))))),
% 0.42/0.69 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.42/0.69 tff(143,plain,
% 0.42/0.69 ((~((~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!8, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(X!0) | (~((~p2(Y!11)) | (~r1(X!0, Y!11)) | (~r1(Y!11, X!12)) | p2(X!12))))))) | (~((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_16(Y), Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(X), Y))))))))))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[142, 139])).
% 0.46/0.70 tff(144,plain,
% 0.46/0.70 ((~((~(p2(X!0) | (~((~p2(Y!11)) | (~r1(X!0, Y!11)) | (~r1(Y!11, X!12)) | p2(X!12))))) | (~((~(p2(Y!8) | (~r1(X!0, Y!8)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))))))) | (~((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[143, 138])).
% 0.46/0.70 tff(145,plain,
% 0.46/0.70 (~((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[144, 137])).
% 0.46/0.70 tff(146,plain,
% 0.46/0.70 (((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | ((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(147,plain,
% 0.46/0.70 ((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.46/0.70 tff(148,plain,
% 0.46/0.70 (((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | r1(X!0, Y!13)),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(149,plain,
% 0.46/0.70 (r1(X!0, Y!13)),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[148, 145])).
% 0.46/0.70 tff(150,assumption,(~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))), introduced(assumption)).
% 0.46/0.70 tff(151,plain,
% 0.46/0.70 ((p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!13))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(152,plain,
% 0.46/0.71 (~p2(Y!13)),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.46/0.71 tff(153,assumption,(r1(X!0, Y!13)), introduced(assumption)).
% 0.46/0.71 tff(154,plain,
% 0.46/0.71 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!13) | (~r1(X!0, Y!13)) | (~((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))) | p2(tptp_fun_Y_7(Y!13)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(Y!13) | (~r1(X!0, Y!13)) | (~((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))) | p2(tptp_fun_Y_7(Y!13)))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(155,plain,
% 0.46/0.71 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!13) | (~r1(X!0, Y!13)) | (~((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))) | p2(tptp_fun_Y_7(Y!13)))))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(156,plain,
% 0.46/0.71 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(Y!13) | (~r1(X!0, Y!13)) | (~((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))) | p2(tptp_fun_Y_7(Y!13))))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.46/0.71 tff(157,plain,
% 0.46/0.71 (p2(Y!13) | (~((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))) | p2(tptp_fun_Y_7(Y!13))))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[156, 104, 153])).
% 0.46/0.71 tff(158,plain,
% 0.46/0.71 (~((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))) | p2(tptp_fun_Y_7(Y!13)))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[157, 152])).
% 0.46/0.71 tff(159,plain,
% 0.46/0.71 (((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))) | p2(tptp_fun_Y_7(Y!13))) | r1(Y!13, tptp_fun_X_6(Y!13))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(160,plain,
% 0.46/0.71 (r1(Y!13, tptp_fun_X_6(Y!13))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.46/0.71 tff(161,plain,
% 0.46/0.71 (((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))) | p2(tptp_fun_Y_7(Y!13))) | p2(tptp_fun_X_6(Y!13))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(162,plain,
% 0.46/0.71 (p2(tptp_fun_X_6(Y!13))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[161, 158])).
% 0.46/0.71 tff(163,plain,
% 0.46/0.71 ((p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(164,plain,
% 0.46/0.71 (![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[163, 150])).
% 0.46/0.71 tff(165,plain,
% 0.46/0.71 (((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(166,plain,
% 0.46/0.71 (((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!13), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(167,plain,
% 0.46/0.71 (((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!13), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y)))))),
% 0.46/0.71 inference(monotonicity,[status(thm)],[166])).
% 0.46/0.71 tff(168,plain,
% 0.46/0.71 (((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!13), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y))))),
% 0.46/0.71 inference(transitivity,[status(thm)],[167, 165])).
% 0.46/0.71 tff(169,plain,
% 0.46/0.71 ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!13), Y)) | p2(Y)))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(170,plain,
% 0.46/0.71 ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.46/0.71 tff(171,plain,
% 0.46/0.71 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y)))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[170, 164, 162, 160])).
% 0.46/0.71 tff(172,plain,
% 0.46/0.71 (((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))) | p2(tptp_fun_Y_7(Y!13))) | (~p2(tptp_fun_Y_7(Y!13)))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(173,plain,
% 0.46/0.71 (~p2(tptp_fun_Y_7(Y!13))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[172, 158])).
% 0.46/0.71 tff(174,plain,
% 0.46/0.71 (((~p2(tptp_fun_X_6(Y!13))) | (~r1(Y!13, tptp_fun_X_6(Y!13))) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))) | p2(tptp_fun_Y_7(Y!13))) | r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(175,plain,
% 0.46/0.71 (r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[174, 158])).
% 0.46/0.71 tff(176,plain,
% 0.46/0.71 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y)))) | (p2(tptp_fun_Y_7(Y!13)) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y)))) | p2(tptp_fun_Y_7(Y!13)) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(177,plain,
% 0.46/0.71 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y)))) | (p2(tptp_fun_Y_7(Y!13)) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13))))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(178,plain,
% 0.46/0.71 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!13), Y)))) | p2(tptp_fun_Y_7(Y!13)) | (~r1(tptp_fun_X_6(Y!13), tptp_fun_Y_7(Y!13)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.46/0.71 tff(179,plain,
% 0.46/0.71 ($false),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[178, 175, 173, 171])).
% 0.46/0.71 tff(180,plain,((p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~r1(X!0, Y!13))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.71 tff(181,plain,
% 0.46/0.71 (p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[180, 149])).
% 0.46/0.71 tff(182,plain,
% 0.46/0.71 ((~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))),
% 0.46/0.72 inference(tautology,[status(thm)],[])).
% 0.46/0.72 tff(183,plain,
% 0.46/0.72 (~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[182, 181, 147])).
% 0.46/0.72 tff(184,plain,
% 0.46/0.72 (((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.46/0.72 inference(tautology,[status(thm)],[])).
% 0.46/0.72 tff(185,plain,
% 0.46/0.72 (![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.46/0.72 tff(186,plain,
% 0.46/0.72 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(187,plain,
% 0.46/0.72 (((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(188,plain,
% 0.46/0.72 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))))),
% 0.46/0.72 inference(monotonicity,[status(thm)],[187])).
% 0.46/0.72 tff(189,plain,
% 0.46/0.72 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))),
% 0.46/0.72 inference(transitivity,[status(thm)],[188, 186])).
% 0.46/0.72 tff(190,plain,
% 0.46/0.72 ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y)))),
% 0.46/0.72 inference(quant_inst,[status(thm)],[])).
% 0.46/0.72 tff(191,plain,
% 0.46/0.72 ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))),
% 0.46/0.72 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.46/0.72 tff(192,plain,
% 0.46/0.72 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[191, 185, 5, 3])).
% 0.46/0.72 tff(193,plain,
% 0.46/0.72 (((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15)))) | (~p2(tptp_fun_Y_7(Y!15)))),
% 0.46/0.72 inference(tautology,[status(thm)],[])).
% 0.46/0.72 tff(194,plain,
% 0.46/0.72 (~p2(tptp_fun_Y_7(Y!15))),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[193, 1])).
% 0.46/0.72 tff(195,plain,
% 0.46/0.72 (((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15)))) | r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))),
% 0.46/0.72 inference(tautology,[status(thm)],[])).
% 0.46/0.72 tff(196,plain,
% 0.46/0.72 (r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[195, 1])).
% 0.46/0.72 tff(197,plain,
% 0.46/0.72 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | (p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(198,plain,
% 0.46/0.72 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | (p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))),
% 0.46/0.72 inference(quant_inst,[status(thm)],[])).
% 0.46/0.72 tff(199,plain,
% 0.46/0.72 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15)))),
% 0.46/0.72 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.46/0.72 tff(200,plain,
% 0.46/0.72 ($false),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[199, 196, 194, 192])).
% 0.46/0.72 tff(201,plain,((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15)))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.72 tff(202,assumption,(~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))), introduced(assumption)).
% 0.46/0.72 tff(203,plain,
% 0.46/0.72 ((p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(X!14))),
% 0.46/0.72 inference(tautology,[status(thm)],[])).
% 0.46/0.72 tff(204,plain,
% 0.46/0.72 (~p2(X!14)),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.46/0.72 tff(205,plain,
% 0.46/0.72 (((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))),
% 0.46/0.72 inference(tautology,[status(thm)],[])).
% 0.46/0.72 tff(206,plain,
% 0.46/0.72 (![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[205, 183])).
% 0.46/0.72 tff(207,plain,
% 0.46/0.72 (((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(Y!13, X!14)),
% 0.46/0.72 inference(tautology,[status(thm)],[])).
% 0.46/0.72 tff(208,plain,
% 0.46/0.72 (r1(Y!13, X!14)),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[207, 183])).
% 0.46/0.72 tff(209,plain,
% 0.46/0.72 (((~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (p2(X!14) | (~r1(Y!13, X!14)) | (~((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))) | p2(tptp_fun_X_10(X!14)))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | p2(X!14) | (~r1(Y!13, X!14)) | (~((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))) | p2(tptp_fun_X_10(X!14)))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(210,plain,
% 0.46/0.72 ((~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (p2(X!14) | (~r1(Y!13, X!14)) | (~((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))) | p2(tptp_fun_X_10(X!14)))))),
% 0.46/0.72 inference(quant_inst,[status(thm)],[])).
% 0.46/0.72 tff(211,plain,
% 0.46/0.72 ((~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | p2(X!14) | (~r1(Y!13, X!14)) | (~((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))) | p2(tptp_fun_X_10(X!14))))),
% 0.46/0.73 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.46/0.73 tff(212,plain,
% 0.46/0.73 (p2(X!14) | (~((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))) | p2(tptp_fun_X_10(X!14))))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[211, 208, 206])).
% 0.46/0.73 tff(213,plain,
% 0.46/0.73 (~((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))) | p2(tptp_fun_X_10(X!14)))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[212, 204])).
% 0.46/0.73 tff(214,plain,
% 0.46/0.73 (((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))) | p2(tptp_fun_X_10(X!14))) | r1(X!14, tptp_fun_Y_9(X!14))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(215,plain,
% 0.46/0.73 (r1(X!14, tptp_fun_Y_9(X!14))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.46/0.73 tff(216,plain,
% 0.46/0.73 (((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))) | p2(tptp_fun_X_10(X!14))) | p2(tptp_fun_Y_9(X!14))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(217,plain,
% 0.46/0.73 (p2(tptp_fun_Y_9(X!14))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[216, 213])).
% 0.46/0.73 tff(218,plain,
% 0.46/0.73 ((p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(219,plain,
% 0.46/0.73 (![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[218, 202])).
% 0.46/0.73 tff(220,plain,
% 0.46/0.73 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X))))),
% 0.46/0.73 inference(rewrite,[status(thm)],[])).
% 0.46/0.73 tff(221,plain,
% 0.46/0.73 (((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!14), X)) | p2(X))) <=> ((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X))))),
% 0.46/0.73 inference(rewrite,[status(thm)],[])).
% 0.46/0.73 tff(222,plain,
% 0.46/0.73 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!14), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X)))))),
% 0.46/0.73 inference(monotonicity,[status(thm)],[221])).
% 0.46/0.73 tff(223,plain,
% 0.46/0.73 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!14), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X))))),
% 0.46/0.73 inference(transitivity,[status(thm)],[222, 220])).
% 0.46/0.73 tff(224,plain,
% 0.46/0.73 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | ![X: $i] : ((~r1(tptp_fun_Y_9(X!14), X)) | p2(X)))),
% 0.46/0.73 inference(quant_inst,[status(thm)],[])).
% 0.46/0.73 tff(225,plain,
% 0.46/0.73 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X)))),
% 0.46/0.73 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.46/0.73 tff(226,plain,
% 0.46/0.73 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X)))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[225, 219, 217, 215])).
% 0.46/0.73 tff(227,plain,
% 0.46/0.73 (((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))) | p2(tptp_fun_X_10(X!14))) | (~p2(tptp_fun_X_10(X!14)))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(228,plain,
% 0.46/0.73 (~p2(tptp_fun_X_10(X!14))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[227, 213])).
% 0.46/0.73 tff(229,plain,
% 0.46/0.73 (((~p2(tptp_fun_Y_9(X!14))) | (~r1(X!14, tptp_fun_Y_9(X!14))) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))) | p2(tptp_fun_X_10(X!14))) | r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(230,plain,
% 0.46/0.73 (r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[229, 213])).
% 0.46/0.73 tff(231,plain,
% 0.46/0.73 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X)))) | (p2(tptp_fun_X_10(X!14)) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X)))) | p2(tptp_fun_X_10(X!14)) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))))),
% 0.46/0.73 inference(rewrite,[status(thm)],[])).
% 0.46/0.73 tff(232,plain,
% 0.46/0.73 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X)))) | (p2(tptp_fun_X_10(X!14)) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14))))),
% 0.46/0.73 inference(quant_inst,[status(thm)],[])).
% 0.46/0.73 tff(233,plain,
% 0.46/0.73 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_9(X!14), X)))) | p2(tptp_fun_X_10(X!14)) | (~r1(tptp_fun_Y_9(X!14), tptp_fun_X_10(X!14)))),
% 0.46/0.73 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.46/0.73 tff(234,plain,
% 0.46/0.73 ($false),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[233, 230, 228, 226])).
% 0.46/0.73 tff(235,plain,(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.73 tff(236,assumption,((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15)))), introduced(assumption)).
% 0.46/0.73 tff(237,plain,
% 0.46/0.73 (((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!15))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(238,plain,
% 0.46/0.73 (~p2(Y!15)),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[237, 183])).
% 0.46/0.73 tff(239,plain,
% 0.46/0.73 ((~(p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))) | p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15)))))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(240,plain,
% 0.46/0.73 (~(p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[239, 238, 236])).
% 0.46/0.73 tff(241,plain,
% 0.46/0.73 (((~(p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))) | (~((~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))) | (p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(242,plain,
% 0.46/0.73 ((~(p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))) | (~((~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.46/0.73 tff(243,assumption,(![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))), introduced(assumption)).
% 0.46/0.73 tff(244,plain,
% 0.46/0.73 (((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(X!14, Y!15)),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(245,plain,
% 0.46/0.73 (r1(X!14, Y!15)),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[244, 183])).
% 0.46/0.73 tff(246,plain,
% 0.46/0.73 (((~![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | ((~r1(X!14, Y!15)) | (~((~(p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))) | (~((~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))))) <=> ((~![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | (~r1(X!14, Y!15)) | (~((~(p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))) | (~((~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))))),
% 0.46/0.73 inference(rewrite,[status(thm)],[])).
% 0.46/0.73 tff(247,plain,
% 0.46/0.73 (((~r1(X!14, Y!15)) | (~((~(p2(Y!15) | (~((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)))))) | (~(![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) <=> ((~r1(X!14, Y!15)) | (~((~(p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))) | (~((~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))))),
% 0.46/0.74 inference(rewrite,[status(thm)],[])).
% 0.46/0.74 tff(248,plain,
% 0.46/0.74 (((~![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | ((~r1(X!14, Y!15)) | (~((~(p2(Y!15) | (~((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)))))) | (~(![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | ((~r1(X!14, Y!15)) | (~((~(p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))) | (~((~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))))))),
% 0.46/0.74 inference(monotonicity,[status(thm)],[247])).
% 0.46/0.74 tff(249,plain,
% 0.46/0.74 (((~![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | ((~r1(X!14, Y!15)) | (~((~(p2(Y!15) | (~((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)))))) | (~(![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | (~r1(X!14, Y!15)) | (~((~(p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))) | (~((~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))))),
% 0.46/0.74 inference(transitivity,[status(thm)],[248, 246])).
% 0.46/0.74 tff(250,plain,
% 0.46/0.74 ((~![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | ((~r1(X!14, Y!15)) | (~((~(p2(Y!15) | (~((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)))))) | (~(![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.46/0.74 inference(quant_inst,[status(thm)],[])).
% 0.46/0.74 tff(251,plain,
% 0.46/0.74 ((~![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | (~r1(X!14, Y!15)) | (~((~(p2(Y!15) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))) | (~((~(p2(tptp_fun_X_16(Y!15)) | (~r1(Y!15, tptp_fun_X_16(Y!15))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!15), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))))),
% 0.46/0.74 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.46/0.74 tff(252,plain,
% 0.46/0.74 ($false),
% 0.46/0.74 inference(unit_resolution,[status(thm)],[251, 245, 243, 242])).
% 0.46/0.74 tff(253,plain,((~![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15)))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.74 tff(254,plain,
% 0.46/0.74 (~![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[253, 201])).
% 0.46/0.75 tff(255,plain,
% 0.46/0.75 (((~r1(X!0, Y!13)) | (~((~((~r1(Y!13, X!14)) | p2(Y!15) | (~r1(X!14, Y!15)) | (~![X: $i] : (p2(X) | (~r1(Y!13, X)) | (~((~p2(tptp_fun_Y_9(X))) | (~r1(X, tptp_fun_Y_9(X))) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))) | p2(tptp_fun_X_10(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | ![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(256,plain,
% 0.46/0.75 (![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[255, 145])).
% 0.46/0.75 tff(257,plain,
% 0.46/0.75 (((~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) <=> ((~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(258,plain,
% 0.46/0.75 (((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14)))))) <=> ((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(259,plain,
% 0.46/0.75 ((~((~r1(X!14, tptp_fun_Y_17(X!14))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~![Y: $i] : ((~r1(X!14, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14)))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(260,plain,
% 0.46/0.75 ((~(p2(X!14) | (~![Y: $i] : ((~r1(X!14, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(261,plain,
% 0.46/0.75 (((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~r1(X!14, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X!14, tptp_fun_Y_17(X!14))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~![Y: $i] : ((~r1(X!14, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14))))))),
% 0.46/0.76 inference(monotonicity,[status(thm)],[260, 259])).
% 0.46/0.76 tff(262,plain,
% 0.46/0.76 (((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~r1(X!14, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X!14, tptp_fun_Y_17(X!14))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~![Y: $i] : ((~r1(X!14, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.46/0.76 inference(transitivity,[status(thm)],[261, 258])).
% 0.46/0.76 tff(263,plain,
% 0.46/0.76 (((~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~r1(X!14, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X!14, tptp_fun_Y_17(X!14))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~![Y: $i] : ((~r1(X!14, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))))),
% 0.46/0.76 inference(monotonicity,[status(thm)],[262])).
% 0.46/0.76 tff(264,plain,
% 0.46/0.76 (((~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~r1(X!14, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X!14, tptp_fun_Y_17(X!14))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~![Y: $i] : ((~r1(X!14, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.46/0.77 inference(transitivity,[status(thm)],[263, 257])).
% 0.46/0.77 tff(265,plain,
% 0.46/0.77 ((~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~r1(X!14, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X!14, tptp_fun_Y_17(X!14))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~![Y: $i] : ((~r1(X!14, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.46/0.77 inference(quant_inst,[status(thm)],[])).
% 0.46/0.77 tff(266,plain,
% 0.46/0.77 ((~![X: $i] : ((~r1(Y!13, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | p2(tptp_fun_X_18(X)) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (~r1(Y!13, X!14)) | (~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.46/0.77 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.46/0.77 tff(267,plain,
% 0.46/0.77 ((~(p2(X!14) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14))))) | ![Y: $i] : ((~r1(X!14, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.46/0.77 inference(unit_resolution,[status(thm)],[266, 208, 256])).
% 0.46/0.77 tff(268,plain,
% 0.46/0.77 (~((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14))))),
% 0.46/0.77 inference(unit_resolution,[status(thm)],[267, 254, 235])).
% 0.46/0.77 tff(269,plain,
% 0.46/0.77 (((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!14), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p2(tptp_fun_X_18(X!14)) | (~r1(tptp_fun_Y_17(X!14), tptp_fun_X_18(X!14))) | (~r1(X!14, tptp_fun_Y_17(X!14)))) | ![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.46/0.77 inference(tautology,[status(thm)],[])).
% 0.46/0.77 tff(270,plain,
% 0.46/0.77 (![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.46/0.77 inference(unit_resolution,[status(thm)],[269, 268])).
% 0.46/0.77 tff(271,plain,
% 0.46/0.77 (((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!15) | (~r1(X!14, Y!15)) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(Y!15) | (~r1(X!14, Y!15)) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))),
% 0.46/0.77 inference(rewrite,[status(thm)],[])).
% 0.46/0.77 tff(272,plain,
% 0.46/0.77 ((p2(Y!15) | (~r1(X!14, Y!15)) | (~((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15))))) <=> (p2(Y!15) | (~r1(X!14, Y!15)) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))),
% 0.46/0.77 inference(rewrite,[status(thm)],[])).
% 0.46/0.77 tff(273,plain,
% 0.46/0.77 (((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!15) | (~r1(X!14, Y!15)) | (~((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!15) | (~r1(X!14, Y!15)) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15)))))))),
% 0.46/0.77 inference(monotonicity,[status(thm)],[272])).
% 0.46/0.77 tff(274,plain,
% 0.46/0.77 (((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!15) | (~r1(X!14, Y!15)) | (~((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(Y!15) | (~r1(X!14, Y!15)) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15))))))),
% 0.46/0.77 inference(transitivity,[status(thm)],[273, 271])).
% 0.46/0.77 tff(275,plain,
% 0.46/0.77 ((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(Y!15) | (~r1(X!14, Y!15)) | (~((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)))))),
% 0.46/0.77 inference(quant_inst,[status(thm)],[])).
% 0.46/0.77 tff(276,plain,
% 0.46/0.77 ((~![Y: $i] : (p2(Y) | (~r1(X!14, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(Y!15) | (~r1(X!14, Y!15)) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~p2(tptp_fun_X_6(Y!15)))))),
% 0.46/0.78 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.46/0.78 tff(277,plain,
% 0.46/0.78 ($false),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[276, 238, 245, 270, 201])).
% 0.46/0.78 % SZS output end Proof
% 0.46/0.78 % E exiting
%------------------------------------------------------------------------------