%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL660+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:28 PM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL660+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.01 % Command : run_E %s %d THM
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sat Sep 5 11:05:29 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.08/0.37 % SZS status Theorem
% 0.08/0.37 % SZS output start Proof
% 0.08/0.37 tff(r1_type, type, (
% 0.08/0.37 r1: ( $i * $i ) > $o)).
% 0.08/0.37 tff(tptp_fun_X_4_type, type, (
% 0.08/0.37 tptp_fun_X_4: $i > $i)).
% 0.08/0.37 tff(tptp_fun_Y_11_type, type, (
% 0.08/0.37 tptp_fun_Y_11: $i)).
% 0.08/0.37 tff(p2_type, type, (
% 0.08/0.37 p2: $i > $o)).
% 0.08/0.37 tff(tptp_fun_Y_5_type, type, (
% 0.08/0.37 tptp_fun_Y_5: $i > $i)).
% 0.08/0.37 tff(tptp_fun_X_15_type, type, (
% 0.08/0.37 tptp_fun_X_15: $i > $i)).
% 0.08/0.37 tff(tptp_fun_Y_14_type, type, (
% 0.08/0.37 tptp_fun_Y_14: $i > $i)).
% 0.08/0.37 tff(tptp_fun_Y_13_type, type, (
% 0.08/0.37 tptp_fun_Y_13: $i)).
% 0.08/0.37 tff(tptp_fun_X_12_type, type, (
% 0.08/0.37 tptp_fun_X_12: $i)).
% 0.08/0.37 tff(tptp_fun_X_16_type, type, (
% 0.08/0.37 tptp_fun_X_16: $i > $i)).
% 0.08/0.37 tff(tptp_fun_X_18_type, type, (
% 0.08/0.37 tptp_fun_X_18: $i > $i)).
% 0.08/0.37 tff(tptp_fun_Y_17_type, type, (
% 0.08/0.37 tptp_fun_Y_17: $i > $i)).
% 0.08/0.37 tff(tptp_fun_X_0_type, type, (
% 0.08/0.37 tptp_fun_X_0: $i)).
% 0.08/0.37 tff(tptp_fun_Y_19_type, type, (
% 0.08/0.37 tptp_fun_Y_19: $i)).
% 0.08/0.37 tff(tptp_fun_X_21_type, type, (
% 0.08/0.37 tptp_fun_X_21: $i)).
% 0.08/0.37 tff(tptp_fun_Y_20_type, type, (
% 0.08/0.37 tptp_fun_Y_20: $i)).
% 0.08/0.37 tff(tptp_fun_Y_3_type, type, (
% 0.08/0.37 tptp_fun_Y_3: $i)).
% 0.08/0.37 tff(tptp_fun_X_6_type, type, (
% 0.08/0.37 tptp_fun_X_6: $i > $i)).
% 0.08/0.37 tff(p3_type, type, (
% 0.08/0.37 p3: $i > $o)).
% 0.08/0.37 tff(p1_type, type, (
% 0.08/0.37 p1: $i > $o)).
% 0.08/0.37 tff(tptp_fun_Y_10_type, type, (
% 0.08/0.37 tptp_fun_Y_10: $i > $i)).
% 0.08/0.37 tff(tptp_fun_X_9_type, type, (
% 0.08/0.37 tptp_fun_X_9: $i > $i)).
% 0.08/0.37 tff(p4_type, type, (
% 0.08/0.37 p4: $i > $o)).
% 0.08/0.37 tff(tptp_fun_Y_8_type, type, (
% 0.08/0.37 tptp_fun_Y_8: $i > $i)).
% 0.08/0.37 tff(tptp_fun_X_7_type, type, (
% 0.08/0.37 tptp_fun_X_7: $i > $i)).
% 0.08/0.37 tff(tptp_fun_Y_2_type, type, (
% 0.08/0.37 tptp_fun_Y_2: $i)).
% 0.08/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.08/0.37 tptp_fun_Y_1: $i)).
% 0.08/0.37 tff(1,assumption,(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))), introduced(assumption)).
% 0.08/0.37 tff(2,plain,
% 0.08/0.37 (((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.08/0.37 inference(rewrite,[status(thm)],[])).
% 0.08/0.37 tff(3,plain,
% 0.08/0.37 ((((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.08/0.37 inference(rewrite,[status(thm)],[])).
% 0.08/0.37 tff(4,plain,
% 0.08/0.37 (((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~(p1(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & ((((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X)))))))) <=> ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~(p1(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X)))))))),
% 0.08/0.37 inference(rewrite,[status(thm)],[])).
% 0.08/0.37 tff(5,plain,
% 0.08/0.37 ((((r1(X!0, Y!11) & (((r1(Y!11, X!12) & ((~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) | ((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21)))))))) & ![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] : (p2(X) | (~r1(Y, X))))))) <=> ((((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X)))))))),
% 0.08/0.38 inference(rewrite,[status(thm)],[])).
% 0.08/0.38 tff(6,plain,
% 0.08/0.38 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))) <=> (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))), ((r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))) <=> (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))), (((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))))), rewrite(((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))), (((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))))),
% 0.08/0.38 inference(bind,[status(th)],[])).
% 0.08/0.38 tff(7,plain,
% 0.08/0.38 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))),
% 0.08/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.08/0.38 tff(8,plain,
% 0.08/0.38 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))) <=> (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y))))), ((r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y))))) <=> (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y))))))), (((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))))), rewrite(((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) <=> (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y))))))), (((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) <=> (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y))))))))),
% 0.08/0.38 inference(bind,[status(th)],[])).
% 0.08/0.38 tff(9,plain,
% 0.08/0.38 (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) <=> ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y))))))),
% 0.08/0.38 inference(quant_intro,[status(thm)],[8])).
% 0.08/0.38 tff(10,plain,
% 0.08/0.38 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.08/0.38 inference(rewrite,[status(thm)],[])).
% 0.08/0.38 tff(11,plain,
% 0.08/0.38 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))),
% 0.08/0.38 inference(rewrite,[status(thm)],[])).
% 0.08/0.38 tff(12,plain,
% 0.08/0.38 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.08/0.38 inference(monotonicity,[status(thm)],[11])).
% 0.08/0.38 tff(13,plain,
% 0.08/0.38 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.08/0.38 inference(transitivity,[status(thm)],[12, 10])).
% 0.08/0.38 tff(14,plain,
% 0.08/0.38 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.08/0.38 inference(rewrite,[status(thm)],[])).
% 0.08/0.38 tff(15,plain,
% 0.08/0.38 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.08/0.38 inference(monotonicity,[status(thm)],[11])).
% 0.08/0.38 tff(16,plain,
% 0.08/0.38 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.08/0.38 inference(transitivity,[status(thm)],[15, 14])).
% 0.08/0.38 tff(17,plain,
% 0.08/0.38 ((~((~r1(X!0, Y!2)) | p1(Y!2))) <=> (~(p1(Y!2) | (~r1(X!0, Y!2))))),
% 0.08/0.38 inference(rewrite,[status(thm)],[])).
% 0.08/0.38 tff(18,plain,
% 0.08/0.38 ((~((~r1(X!0, Y!1)) | p4(Y!1))) <=> (~((~r1(X!0, Y!1)) | p4(Y!1)))),
% 0.08/0.38 inference(rewrite,[status(thm)],[])).
% 0.08/0.38 tff(19,plain,
% 0.08/0.38 (((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((r1(X!0, Y!11) & (((r1(Y!11, X!12) & ((~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) | ((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21)))))))) & ![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] : (p2(X) | (~r1(Y, X)))))))) <=> ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~(p1(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & ((((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X))))))))),
% 0.08/0.38 inference(monotonicity,[status(thm)],[18, 17, 16, 13, 9, 7, 5])).
% 0.08/0.38 tff(20,plain,
% 0.08/0.38 (((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((r1(X!0, Y!11) & (((r1(Y!11, X!12) & ((~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) | ((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21)))))))) & ![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] : (p2(X) | (~r1(Y, X)))))))) <=> ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~(p1(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X)))))))),
% 0.08/0.38 inference(transitivity,[status(thm)],[19, 4])).
% 0.08/0.38 tff(21,plain,
% 0.08/0.38 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 0.08/0.38 inference(rewrite,[status(thm)],[])).
% 0.08/0.38 tff(22,plain,
% 0.08/0.38 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 0.08/0.38 inference(rewrite,[status(thm)],[])).
% 0.08/0.38 tff(23,plain,
% 0.08/0.38 ((~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p3(Y)))) & (![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)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~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)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))))),
% 0.08/0.38 inference(rewrite,[status(thm)],[])).
% 0.08/0.38 tff(24,plain,
% 0.08/0.38 ((~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p3(Y)))) & (![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)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~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)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))))),
% 0.08/0.38 inference(monotonicity,[status(thm)],[23])).
% 0.08/0.38 tff(25,plain,
% 0.08/0.38 ((~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p3(Y)))) & (![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)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~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)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 0.08/0.39 inference(transitivity,[status(thm)],[24, 22])).
% 0.08/0.39 tff(26,axiom,(~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p3(Y)))) & (![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)) | p4(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y))) | (~p4(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~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/sandbox/benchmark/theBenchmark.p','main')).
% 0.08/0.39 tff(27,plain,
% 0.08/0.39 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.08/0.39 tff(28,plain,
% 0.08/0.39 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p4(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p3(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p4(X)) | ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.08/0.39 tff(29,plain,
% 0.08/0.39 ((~((~r1(X!0, Y!1)) | p4(Y!1))) & (~(p1(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) & ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p4(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p4(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.08/0.39 tff(30,plain,
% 0.08/0.39 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.08/0.39 inference(and_elim,[status(thm)],[29])).
% 0.08/0.39 tff(31,plain,
% 0.08/0.39 ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[30, 3])).
% 0.08/0.39 tff(32,plain,
% 0.08/0.39 ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[31, 2])).
% 0.08/0.39 tff(33,plain,
% 0.08/0.39 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[32, 1])).
% 0.08/0.39 tff(34,plain,
% 0.08/0.39 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(35,plain,
% 0.08/0.39 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(36,plain,
% 0.08/0.39 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) <=> (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(37,plain,
% 0.08/0.39 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.08/0.39 inference(bind,[status(th)],[])).
% 0.08/0.39 tff(38,plain,
% 0.08/0.39 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(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_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.08/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.08/0.39 tff(39,plain,
% 0.08/0.39 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.08/0.39 inference(monotonicity,[status(thm)],[38])).
% 0.08/0.39 tff(40,plain,
% 0.08/0.39 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.08/0.39 inference(transitivity,[status(thm)],[39, 36])).
% 0.08/0.39 tff(41,plain,
% 0.08/0.39 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.08/0.39 inference(monotonicity,[status(thm)],[40])).
% 0.08/0.39 tff(42,plain,
% 0.08/0.39 ((![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.08/0.39 inference(transitivity,[status(thm)],[41, 35])).
% 0.08/0.39 tff(43,plain,
% 0.08/0.39 (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))),
% 0.08/0.39 inference(and_elim,[status(thm)],[29])).
% 0.08/0.39 tff(44,plain,
% 0.08/0.39 (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.08/0.39 tff(45,plain,
% 0.08/0.39 (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.08/0.39 tff(46,plain,
% 0.08/0.39 (![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[45, 1])).
% 0.08/0.39 tff(47,assumption,(~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))), introduced(assumption)).
% 0.08/0.39 tff(48,plain,
% 0.08/0.39 (((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))) | r1(X!0, tptp_fun_X_6(X!0))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(49,plain,
% 0.08/0.39 (r1(X!0, tptp_fun_X_6(X!0))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.08/0.39 tff(50,plain,
% 0.08/0.39 (((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))) | p3(tptp_fun_X_6(X!0))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(51,plain,
% 0.08/0.39 (p3(tptp_fun_X_6(X!0))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.08/0.39 tff(52,assumption,(![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))), introduced(assumption)).
% 0.08/0.39 tff(53,plain,
% 0.08/0.39 (((~![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))) | ((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))) <=> ((~![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))) | (~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(54,plain,
% 0.08/0.39 ((~![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))) | ((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))),
% 0.08/0.39 inference(quant_inst,[status(thm)],[])).
% 0.08/0.39 tff(55,plain,
% 0.08/0.39 ((~![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y)))) | (~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.08/0.39 tff(56,plain,
% 0.08/0.39 ($false),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[55, 52, 51, 49])).
% 0.08/0.39 tff(57,plain,(((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))) | (~![Y: $i] : ((~p3(Y)) | (~r1(X!0, Y))))), inference(lemma,lemma(discharge,[]))).
% 0.08/0.39 tff(58,plain,
% 0.08/0.39 ((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[57, 46])).
% 0.08/0.39 tff(59,assumption,(~r1(X!0, X!0)), introduced(assumption)).
% 0.08/0.39 tff(60,plain,
% 0.08/0.39 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.08/0.39 inference(bind,[status(th)],[])).
% 0.08/0.39 tff(61,plain,
% 0.08/0.39 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.08/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.08/0.39 tff(62,plain,
% 0.08/0.39 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(63,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.08/0.39 tff(64,plain,
% 0.08/0.39 (![X: $i] : r1(X, X)),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.08/0.39 tff(65,plain,(
% 0.08/0.39 ![X: $i] : r1(X, X)),
% 0.08/0.39 inference(skolemize,[status(sab)],[64])).
% 0.08/0.39 tff(66,plain,
% 0.08/0.39 (![X: $i] : r1(X, X)),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.08/0.39 tff(67,plain,
% 0.08/0.39 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.08/0.39 inference(quant_inst,[status(thm)],[])).
% 0.08/0.39 tff(68,plain,
% 0.08/0.39 ($false),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[67, 66, 59])).
% 0.08/0.39 tff(69,plain,(r1(X!0, X!0)), inference(lemma,lemma(discharge,[]))).
% 0.08/0.39 tff(70,plain,
% 0.08/0.39 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | ((~r1(X!0, X!0)) | (~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~r1(X!0, X!0)) | (~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(71,plain,
% 0.08/0.39 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | ((~r1(X!0, X!0)) | (~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))))),
% 0.08/0.39 inference(quant_inst,[status(thm)],[])).
% 0.08/0.39 tff(72,plain,
% 0.08/0.39 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~r1(X!0, X!0)) | (~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.08/0.39 tff(73,plain,
% 0.08/0.39 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p3(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~p3(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.08/0.39 tff(74,plain,
% 0.08/0.39 ($false),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[73, 58, 33])).
% 0.08/0.39 tff(75,plain,(~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))), inference(lemma,lemma(discharge,[]))).
% 0.08/0.39 tff(76,plain,
% 0.08/0.39 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | (~p2(Y!3))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(77,plain,
% 0.08/0.39 (~p2(Y!3)),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.08/0.39 tff(78,assumption,((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))), introduced(assumption)).
% 0.08/0.39 tff(79,assumption,(~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))), introduced(assumption)).
% 0.08/0.39 tff(80,plain,
% 0.08/0.39 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(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_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(81,plain,
% 0.08/0.39 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.08/0.39 tff(82,assumption,(~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))), introduced(assumption)).
% 0.08/0.39 tff(83,plain,
% 0.08/0.39 ((p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | r1(X!0, Y!19)),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(84,plain,
% 0.08/0.39 (r1(X!0, Y!19)),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.08/0.39 tff(85,plain,
% 0.08/0.39 ((p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | (~p2(Y!19))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(86,plain,
% 0.08/0.39 (~p2(Y!19)),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.08/0.39 tff(87,assumption,(![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))), introduced(assumption)).
% 0.08/0.39 tff(88,plain,
% 0.08/0.39 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(89,plain,
% 0.08/0.39 ((p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19)))))) <=> (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(90,plain,
% 0.08/0.39 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19))))))),
% 0.08/0.39 inference(monotonicity,[status(thm)],[89])).
% 0.08/0.39 tff(91,plain,
% 0.08/0.39 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)))))),
% 0.08/0.39 inference(transitivity,[status(thm)],[90, 88])).
% 0.08/0.39 tff(92,plain,
% 0.08/0.39 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))))),
% 0.08/0.39 inference(quant_inst,[status(thm)],[])).
% 0.08/0.39 tff(93,plain,
% 0.08/0.39 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.08/0.39 tff(94,plain,
% 0.08/0.39 (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[93, 87, 86, 84])).
% 0.08/0.39 tff(95,plain,
% 0.08/0.39 (((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19))) | p2(tptp_fun_X_4(Y!19))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(96,plain,
% 0.08/0.39 (p2(tptp_fun_X_4(Y!19))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.08/0.39 tff(97,plain,
% 0.08/0.39 (((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19))) | r1(Y!19, tptp_fun_X_4(Y!19))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(98,plain,
% 0.08/0.39 (r1(Y!19, tptp_fun_X_4(Y!19))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.08/0.39 tff(99,plain,
% 0.08/0.39 ((p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(100,plain,
% 0.08/0.39 (![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[99, 82])).
% 0.08/0.39 tff(101,plain,
% 0.08/0.39 (((~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!19))) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(102,plain,
% 0.08/0.39 ((~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!19))) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y))))),
% 0.08/0.39 inference(quant_inst,[status(thm)],[])).
% 0.08/0.39 tff(103,plain,
% 0.08/0.39 ((~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.08/0.39 tff(104,plain,
% 0.08/0.39 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[103, 100, 98, 96])).
% 0.08/0.39 tff(105,plain,
% 0.08/0.39 (((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_Y_5(Y!19)))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(106,plain,
% 0.08/0.39 (~p2(tptp_fun_Y_5(Y!19))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[105, 94])).
% 0.08/0.39 tff(107,plain,
% 0.08/0.39 (((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19))) | r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(108,plain,
% 0.08/0.39 (r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[107, 94])).
% 0.08/0.39 tff(109,plain,
% 0.08/0.39 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))) | (p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(110,plain,
% 0.08/0.39 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))) | (p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))),
% 0.08/0.39 inference(quant_inst,[status(thm)],[])).
% 0.08/0.39 tff(111,plain,
% 0.08/0.39 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19)))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.08/0.39 tff(112,plain,
% 0.08/0.39 ($false),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[111, 108, 106, 104])).
% 0.08/0.39 tff(113,plain,((p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))), inference(lemma,lemma(discharge,[]))).
% 0.08/0.39 tff(114,plain,
% 0.08/0.39 (p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[113, 81])).
% 0.08/0.39 tff(115,plain,
% 0.08/0.39 ((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(116,plain,
% 0.08/0.39 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[115, 114, 78])).
% 0.08/0.39 tff(117,plain,
% 0.08/0.39 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | r1(X!0, Y!3)),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(118,plain,
% 0.08/0.39 (r1(X!0, Y!3)),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[117, 79])).
% 0.08/0.39 tff(119,plain,
% 0.08/0.39 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | (~r1(X!0, Y!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(120,plain,
% 0.08/0.39 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))),
% 0.08/0.39 inference(quant_inst,[status(thm)],[])).
% 0.08/0.39 tff(121,plain,
% 0.08/0.39 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | (~r1(X!0, Y!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.08/0.39 tff(122,plain,
% 0.08/0.39 (![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[121, 118, 116])).
% 0.08/0.39 tff(123,plain,
% 0.08/0.39 (^[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)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> (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] : (p2(X) | (~r1(Y, X)))))))))),
% 0.08/0.39 inference(bind,[status(th)],[])).
% 0.08/0.39 tff(124,plain,
% 0.08/0.39 (![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] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X))))))))),
% 0.08/0.39 inference(quant_intro,[status(thm)],[123])).
% 0.08/0.39 tff(125,plain,
% 0.08/0.39 (^[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)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> (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] : (p2(X) | (~r1(Y, X)))))))))),
% 0.08/0.39 inference(bind,[status(th)],[])).
% 0.08/0.39 tff(126,plain,
% 0.08/0.39 (![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] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X))))))))),
% 0.08/0.39 inference(quant_intro,[status(thm)],[125])).
% 0.08/0.39 tff(127,plain,
% 0.08/0.39 (![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] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X))))))))),
% 0.08/0.39 inference(transitivity,[status(thm)],[126, 124])).
% 0.08/0.39 tff(128,plain,
% 0.08/0.39 (^[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)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) <=> (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] : (p2(X) | (~r1(Y, X)))))))))),
% 0.08/0.39 inference(bind,[status(th)],[])).
% 0.08/0.39 tff(129,plain,
% 0.08/0.39 (![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] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X))))))))),
% 0.08/0.39 inference(quant_intro,[status(thm)],[128])).
% 0.08/0.39 tff(130,plain,
% 0.08/0.39 (![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] : (p2(X) | (~r1(Y, X))))))),
% 0.08/0.39 inference(and_elim,[status(thm)],[29])).
% 0.08/0.39 tff(131,plain,
% 0.08/0.39 (![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] : (p2(X) | (~r1(Y, X))))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.08/0.39 tff(132,plain,
% 0.08/0.39 (![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] : (p2(X) | (~r1(Y, X))))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.08/0.39 tff(133,assumption,(~p2(Y!3)), introduced(assumption)).
% 0.08/0.39 tff(134,plain,
% 0.08/0.39 (((~![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] : (p2(X) | (~r1(Y, X))))))))) | (p2(Y!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, 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] : (p2(X) | (~r1(Y, X))))))))) | p2(Y!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(135,plain,
% 0.08/0.39 ((~![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] : (p2(X) | (~r1(Y, X))))))))) | (p2(Y!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.08/0.39 inference(quant_inst,[status(thm)],[])).
% 0.08/0.39 tff(136,plain,
% 0.08/0.39 ((~![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] : (p2(X) | (~r1(Y, X))))))))) | p2(Y!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 0.08/0.39 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.08/0.39 tff(137,plain,
% 0.08/0.39 (~(p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[136, 133, 118, 132])).
% 0.08/0.39 tff(138,plain,
% 0.08/0.39 ((p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(139,plain,
% 0.08/0.39 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.08/0.39 tff(140,assumption,(~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))), introduced(assumption)).
% 0.08/0.39 tff(141,plain,
% 0.08/0.39 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))) | p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(142,plain,
% 0.08/0.39 (p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.08/0.39 tff(143,plain,
% 0.08/0.39 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))) | r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.08/0.39 inference(tautology,[status(thm)],[])).
% 0.08/0.39 tff(144,plain,
% 0.08/0.39 (r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.08/0.39 inference(unit_resolution,[status(thm)],[143, 140])).
% 0.08/0.39 tff(145,assumption,(![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))), introduced(assumption)).
% 0.08/0.39 tff(146,plain,
% 0.08/0.39 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X))))),
% 0.08/0.39 inference(rewrite,[status(thm)],[])).
% 0.08/0.39 tff(147,plain,
% 0.08/0.40 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X))))),
% 0.08/0.40 inference(quant_inst,[status(thm)],[])).
% 0.08/0.40 tff(148,plain,
% 0.08/0.40 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))),
% 0.08/0.40 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.08/0.40 tff(149,plain,
% 0.08/0.40 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[148, 145, 144, 142])).
% 0.08/0.40 tff(150,plain,
% 0.08/0.40 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))) | r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(151,plain,
% 0.08/0.40 (r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[150, 140])).
% 0.08/0.40 tff(152,plain,
% 0.08/0.40 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))) | (~p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(153,plain,
% 0.08/0.40 (~p2(tptp_fun_X_15(tptp_fun_X_16(Y!3)))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[152, 140])).
% 0.08/0.40 tff(154,plain,
% 0.08/0.40 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))) | (p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))),
% 0.08/0.40 inference(rewrite,[status(thm)],[])).
% 0.08/0.40 tff(155,plain,
% 0.08/0.40 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))) | (p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))),
% 0.08/0.40 inference(quant_inst,[status(thm)],[])).
% 0.08/0.40 tff(156,plain,
% 0.08/0.40 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))),
% 0.08/0.40 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.08/0.40 tff(157,plain,
% 0.08/0.40 ($false),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[156, 153, 151, 149])).
% 0.08/0.40 tff(158,plain,(((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.08/0.40 tff(159,plain,
% 0.08/0.40 ((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[158, 139])).
% 0.08/0.40 tff(160,plain,
% 0.08/0.40 ((p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | r1(Y!3, tptp_fun_X_16(Y!3))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(161,plain,
% 0.08/0.40 (r1(Y!3, tptp_fun_X_16(Y!3))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[160, 137])).
% 0.08/0.40 tff(162,plain,
% 0.08/0.40 ((p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(tptp_fun_X_16(Y!3)))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(163,plain,
% 0.08/0.40 (~p2(tptp_fun_X_16(Y!3))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[162, 137])).
% 0.08/0.40 tff(164,plain,
% 0.08/0.40 (((~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | (p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))))),
% 0.08/0.40 inference(rewrite,[status(thm)],[])).
% 0.08/0.40 tff(165,plain,
% 0.08/0.40 ((~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | (p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))))),
% 0.08/0.40 inference(quant_inst,[status(thm)],[])).
% 0.08/0.40 tff(166,plain,
% 0.08/0.40 ((~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))))),
% 0.08/0.40 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.08/0.40 tff(167,plain,
% 0.08/0.40 ($false),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[166, 163, 161, 159, 122])).
% 0.08/0.40 tff(168,plain,((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | p2(Y!3)), inference(lemma,lemma(discharge,[]))).
% 0.08/0.40 tff(169,plain,
% 0.08/0.40 (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[168, 77, 75])).
% 0.08/0.40 tff(170,plain,
% 0.08/0.40 (((~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))) | (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))))) | ((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(171,plain,
% 0.08/0.40 ((~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))) | (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.08/0.40 tff(172,plain,
% 0.08/0.40 (((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, 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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) <=> ((~((~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))) | (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))))),
% 0.08/0.40 inference(rewrite,[status(thm)],[])).
% 0.08/0.40 tff(173,plain,
% 0.08/0.40 (((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, 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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) <=> ((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, 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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.08/0.40 inference(rewrite,[status(thm)],[])).
% 0.08/0.40 tff(174,plain,
% 0.08/0.40 ((((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, 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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.08/0.40 inference(rewrite,[status(thm)],[])).
% 0.08/0.40 tff(175,plain,
% 0.08/0.40 (((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 0.08/0.40 inference(and_elim,[status(thm)],[29])).
% 0.08/0.40 tff(176,plain,
% 0.08/0.40 ((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, 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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.08/0.40 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.08/0.40 tff(177,plain,
% 0.08/0.40 ((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, 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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.08/0.40 inference(modus_ponens,[status(thm)],[176, 173])).
% 0.08/0.40 tff(178,plain,
% 0.08/0.40 ((~((~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))) | (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))))),
% 0.08/0.40 inference(modus_ponens,[status(thm)],[177, 172])).
% 0.08/0.40 tff(179,plain,
% 0.08/0.40 (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[178, 171])).
% 0.08/0.40 tff(180,plain,
% 0.08/0.40 (((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) | ((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(181,plain,
% 0.08/0.40 ((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.08/0.40 tff(182,plain,
% 0.08/0.40 (((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) | ![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(183,plain,
% 0.08/0.40 (![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[182, 179])).
% 0.08/0.40 tff(184,assumption,(~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))), introduced(assumption)).
% 0.08/0.40 tff(185,plain,
% 0.08/0.40 (((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(186,plain,
% 0.08/0.40 (![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.08/0.40 tff(187,assumption,(~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))), introduced(assumption)).
% 0.08/0.40 tff(188,plain,
% 0.08/0.40 (((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))) | r1(Y!13, tptp_fun_X_4(Y!13))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(189,plain,
% 0.08/0.40 (r1(Y!13, tptp_fun_X_4(Y!13))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.08/0.40 tff(190,plain,
% 0.08/0.40 (((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))) | p2(tptp_fun_X_4(Y!13))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(191,plain,
% 0.08/0.40 (p2(tptp_fun_X_4(Y!13))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[190, 187])).
% 0.08/0.40 tff(192,assumption,(![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))), introduced(assumption)).
% 0.08/0.40 tff(193,plain,
% 0.08/0.40 (((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y))))),
% 0.08/0.40 inference(rewrite,[status(thm)],[])).
% 0.08/0.40 tff(194,plain,
% 0.08/0.40 ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y))))),
% 0.08/0.40 inference(quant_inst,[status(thm)],[])).
% 0.08/0.40 tff(195,plain,
% 0.08/0.40 ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))),
% 0.08/0.40 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.08/0.40 tff(196,plain,
% 0.08/0.40 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[195, 192, 191, 189])).
% 0.08/0.40 tff(197,plain,
% 0.08/0.40 (((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))) | (~p2(tptp_fun_Y_5(Y!13)))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(198,plain,
% 0.08/0.40 (~p2(tptp_fun_Y_5(Y!13))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[197, 187])).
% 0.08/0.40 tff(199,plain,
% 0.08/0.40 (((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))) | r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(200,plain,
% 0.08/0.40 (r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[199, 187])).
% 0.08/0.40 tff(201,plain,
% 0.08/0.40 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))) | (p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))),
% 0.08/0.40 inference(rewrite,[status(thm)],[])).
% 0.08/0.40 tff(202,plain,
% 0.08/0.40 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))) | (p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))),
% 0.08/0.40 inference(quant_inst,[status(thm)],[])).
% 0.08/0.40 tff(203,plain,
% 0.08/0.40 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))),
% 0.08/0.40 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.08/0.40 tff(204,plain,
% 0.08/0.40 ($false),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[203, 200, 198, 196])).
% 0.08/0.40 tff(205,plain,(((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.08/0.40 tff(206,plain,
% 0.08/0.40 ((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[205, 186])).
% 0.08/0.40 tff(207,plain,
% 0.08/0.40 (((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | (~p2(Y!13))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(208,plain,
% 0.08/0.40 (~p2(Y!13)),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[207, 184])).
% 0.08/0.40 tff(209,plain,
% 0.08/0.40 (((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | r1(X!12, Y!13)),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(210,plain,
% 0.08/0.40 (r1(X!12, Y!13)),
% 0.08/0.40 inference(unit_resolution,[status(thm)],[209, 184])).
% 0.08/0.40 tff(211,assumption,((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))), introduced(assumption)).
% 0.08/0.40 tff(212,assumption,(~p2(Y!13)), introduced(assumption)).
% 0.08/0.40 tff(213,plain,
% 0.08/0.40 ((~(p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))) | p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))))),
% 0.08/0.40 inference(tautology,[status(thm)],[])).
% 0.08/0.40 tff(214,plain,
% 0.08/0.40 (~(p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[213, 212, 211])).
% 0.08/0.41 tff(215,plain,
% 0.08/0.41 (((~(p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) | (p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(216,plain,
% 0.08/0.41 ((~(p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.08/0.41 tff(217,assumption,(![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))), introduced(assumption)).
% 0.08/0.41 tff(218,assumption,(r1(X!12, Y!13)), introduced(assumption)).
% 0.08/0.41 tff(219,plain,
% 0.08/0.41 (((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.08/0.41 inference(rewrite,[status(thm)],[])).
% 0.08/0.41 tff(220,plain,
% 0.08/0.41 (((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))) <=> ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.08/0.41 inference(rewrite,[status(thm)],[])).
% 0.08/0.41 tff(221,plain,
% 0.08/0.41 (((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.08/0.41 inference(monotonicity,[status(thm)],[220])).
% 0.08/0.41 tff(222,plain,
% 0.08/0.41 (((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.08/0.41 inference(transitivity,[status(thm)],[221, 219])).
% 0.08/0.41 tff(223,plain,
% 0.08/0.41 ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.08/0.41 inference(quant_inst,[status(thm)],[])).
% 0.08/0.41 tff(224,plain,
% 0.08/0.41 ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))),
% 0.08/0.41 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.08/0.41 tff(225,plain,
% 0.08/0.41 ($false),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[224, 218, 217, 216])).
% 0.08/0.41 tff(226,plain,((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!12, Y!13)) | p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))))), inference(lemma,lemma(discharge,[]))).
% 0.08/0.41 tff(227,plain,
% 0.08/0.41 (~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[226, 210, 208, 206])).
% 0.08/0.41 tff(228,assumption,(![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))), introduced(assumption)).
% 0.08/0.41 tff(229,plain,
% 0.08/0.41 (((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))),
% 0.08/0.41 inference(rewrite,[status(thm)],[])).
% 0.08/0.41 tff(230,plain,
% 0.08/0.41 ((p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))))) <=> (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))),
% 0.08/0.41 inference(rewrite,[status(thm)],[])).
% 0.08/0.41 tff(231,plain,
% 0.08/0.41 (((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))))))),
% 0.08/0.41 inference(monotonicity,[status(thm)],[230])).
% 0.08/0.41 tff(232,plain,
% 0.08/0.41 (((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))))))),
% 0.08/0.41 inference(transitivity,[status(thm)],[231, 229])).
% 0.08/0.41 tff(233,plain,
% 0.08/0.41 ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.08/0.41 inference(quant_inst,[status(thm)],[])).
% 0.08/0.41 tff(234,plain,
% 0.08/0.41 ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))))),
% 0.08/0.41 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.08/0.41 tff(235,plain,
% 0.08/0.41 ($false),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[234, 218, 212, 228, 211])).
% 0.08/0.41 tff(236,plain,((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~r1(X!12, Y!13)) | p2(Y!13) | (~((~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13)))))), inference(lemma,lemma(discharge,[]))).
% 0.08/0.41 tff(237,plain,
% 0.08/0.41 (~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[236, 210, 208, 206])).
% 0.08/0.41 tff(238,plain,
% 0.08/0.41 (((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12)))) | ![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(239,plain,
% 0.08/0.41 ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12)))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.08/0.41 tff(240,assumption,(![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))), introduced(assumption)).
% 0.08/0.41 tff(241,plain,
% 0.08/0.41 (((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | r1(Y!11, X!12)),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(242,plain,
% 0.08/0.41 (r1(Y!11, X!12)),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[241, 184])).
% 0.08/0.41 tff(243,plain,
% 0.08/0.41 (((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | (~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.08/0.41 inference(rewrite,[status(thm)],[])).
% 0.08/0.41 tff(244,plain,
% 0.08/0.41 (((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!12, tptp_fun_Y_17(X!12))) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | p2(tptp_fun_X_18(X!12)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.08/0.41 inference(rewrite,[status(thm)],[])).
% 0.08/0.41 tff(245,plain,
% 0.08/0.41 (((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!12, tptp_fun_Y_17(X!12))) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | p2(tptp_fun_X_18(X!12)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.08/0.41 inference(monotonicity,[status(thm)],[244])).
% 0.08/0.41 tff(246,plain,
% 0.08/0.41 (((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!12, tptp_fun_Y_17(X!12))) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | p2(tptp_fun_X_18(X!12)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | (~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.08/0.41 inference(transitivity,[status(thm)],[245, 243])).
% 0.08/0.41 tff(247,plain,
% 0.08/0.41 ((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!12, tptp_fun_Y_17(X!12))) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | p2(tptp_fun_X_18(X!12)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.08/0.41 inference(quant_inst,[status(thm)],[])).
% 0.08/0.41 tff(248,plain,
% 0.08/0.41 ((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | (~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.08/0.41 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.08/0.41 tff(249,plain,
% 0.08/0.41 ((~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[248, 242, 240])).
% 0.08/0.41 tff(250,plain,
% 0.08/0.41 (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[249, 239, 227])).
% 0.08/0.41 tff(251,plain,
% 0.08/0.41 ((p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(X!12))),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(252,plain,
% 0.08/0.41 (~p2(X!12)),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.08/0.41 tff(253,plain,
% 0.08/0.41 (((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(254,plain,
% 0.08/0.41 (![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[253, 184])).
% 0.08/0.41 tff(255,plain,
% 0.08/0.41 (((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | (p2(X!12) | (~r1(Y!11, X!12)) | (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(X!12) | (~r1(Y!11, X!12)) | (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))))),
% 0.08/0.41 inference(rewrite,[status(thm)],[])).
% 0.08/0.41 tff(256,plain,
% 0.08/0.41 ((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | (p2(X!12) | (~r1(Y!11, X!12)) | (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))))),
% 0.08/0.41 inference(quant_inst,[status(thm)],[])).
% 0.08/0.41 tff(257,plain,
% 0.08/0.41 ((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(X!12) | (~r1(Y!11, X!12)) | (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))))),
% 0.08/0.41 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.08/0.41 tff(258,plain,
% 0.08/0.41 (p2(X!12) | (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[257, 242, 254])).
% 0.08/0.41 tff(259,plain,
% 0.08/0.41 (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[258, 252])).
% 0.08/0.41 tff(260,plain,
% 0.08/0.41 (((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))) | p2(tptp_fun_Y_14(X!12))),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(261,plain,
% 0.08/0.41 (p2(tptp_fun_Y_14(X!12))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.08/0.41 tff(262,plain,
% 0.08/0.41 (((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))) | r1(X!12, tptp_fun_Y_14(X!12))),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(263,plain,
% 0.08/0.41 (r1(X!12, tptp_fun_Y_14(X!12))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[262, 259])).
% 0.08/0.41 tff(264,plain,
% 0.08/0.41 ((p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(265,plain,
% 0.08/0.41 (![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[264, 250])).
% 0.08/0.41 tff(266,plain,
% 0.08/0.41 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_14(X!12))) | (~r1(X!12, tptp_fun_Y_14(X!12))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_14(X!12))) | (~r1(X!12, tptp_fun_Y_14(X!12))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X))))),
% 0.08/0.41 inference(rewrite,[status(thm)],[])).
% 0.08/0.41 tff(267,plain,
% 0.08/0.41 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_14(X!12))) | (~r1(X!12, tptp_fun_Y_14(X!12))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X))))),
% 0.08/0.41 inference(quant_inst,[status(thm)],[])).
% 0.08/0.41 tff(268,plain,
% 0.08/0.41 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_14(X!12))) | (~r1(X!12, tptp_fun_Y_14(X!12))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))),
% 0.08/0.41 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.08/0.41 tff(269,plain,
% 0.08/0.41 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[268, 265, 263, 261])).
% 0.08/0.41 tff(270,plain,
% 0.08/0.41 (((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))) | r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(271,plain,
% 0.08/0.41 (r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[270, 259])).
% 0.08/0.41 tff(272,plain,
% 0.08/0.41 (((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))) | (~p2(tptp_fun_X_15(X!12)))),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(273,plain,
% 0.08/0.41 (~p2(tptp_fun_X_15(X!12))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[272, 259])).
% 0.08/0.41 tff(274,plain,
% 0.08/0.41 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))) | (p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))),
% 0.08/0.41 inference(rewrite,[status(thm)],[])).
% 0.08/0.41 tff(275,plain,
% 0.08/0.41 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))) | (p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))),
% 0.08/0.41 inference(quant_inst,[status(thm)],[])).
% 0.08/0.41 tff(276,plain,
% 0.08/0.41 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))),
% 0.08/0.41 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.08/0.41 tff(277,plain,
% 0.08/0.41 ($false),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[276, 273, 271, 269])).
% 0.08/0.41 tff(278,plain,(((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.08/0.41 tff(279,plain,
% 0.08/0.41 ((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))),
% 0.08/0.41 inference(unit_resolution,[status(thm)],[278, 183])).
% 0.08/0.41 tff(280,plain,
% 0.08/0.41 ((~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))))),
% 0.08/0.41 inference(tautology,[status(thm)],[])).
% 0.08/0.41 tff(281,plain,
% 0.08/0.41 (~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[280, 279, 181])).
% 0.08/0.42 tff(282,plain,
% 0.08/0.42 ((p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.08/0.42 inference(tautology,[status(thm)],[])).
% 0.08/0.42 tff(283,plain,
% 0.08/0.42 (![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.08/0.42 tff(284,assumption,(~((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))), introduced(assumption)).
% 0.08/0.42 tff(285,plain,
% 0.08/0.42 (((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | r1(Y!11, tptp_fun_X_4(Y!11))),
% 0.08/0.42 inference(tautology,[status(thm)],[])).
% 0.08/0.42 tff(286,plain,
% 0.08/0.42 (r1(Y!11, tptp_fun_X_4(Y!11))),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[285, 284])).
% 0.08/0.42 tff(287,plain,
% 0.08/0.42 (((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | p2(tptp_fun_X_4(Y!11))),
% 0.08/0.42 inference(tautology,[status(thm)],[])).
% 0.08/0.42 tff(288,plain,
% 0.08/0.42 (p2(tptp_fun_X_4(Y!11))),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[287, 284])).
% 0.08/0.42 tff(289,assumption,(![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))), introduced(assumption)).
% 0.08/0.42 tff(290,plain,
% 0.08/0.42 (((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y))))),
% 0.08/0.42 inference(rewrite,[status(thm)],[])).
% 0.08/0.42 tff(291,plain,
% 0.08/0.42 ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y))))),
% 0.08/0.42 inference(quant_inst,[status(thm)],[])).
% 0.08/0.42 tff(292,plain,
% 0.08/0.42 ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.08/0.42 tff(293,plain,
% 0.08/0.42 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[292, 289, 288, 286])).
% 0.08/0.42 tff(294,plain,
% 0.08/0.42 (((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | (~p2(tptp_fun_Y_5(Y!11)))),
% 0.08/0.42 inference(tautology,[status(thm)],[])).
% 0.08/0.42 tff(295,plain,
% 0.08/0.42 (~p2(tptp_fun_Y_5(Y!11))),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[294, 284])).
% 0.08/0.42 tff(296,plain,
% 0.08/0.42 (((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))),
% 0.08/0.42 inference(tautology,[status(thm)],[])).
% 0.08/0.42 tff(297,plain,
% 0.08/0.42 (r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[296, 284])).
% 0.08/0.42 tff(298,plain,
% 0.08/0.42 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | (p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))),
% 0.08/0.42 inference(rewrite,[status(thm)],[])).
% 0.08/0.42 tff(299,plain,
% 0.08/0.42 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | (p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))),
% 0.08/0.42 inference(quant_inst,[status(thm)],[])).
% 0.08/0.42 tff(300,plain,
% 0.08/0.42 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.08/0.42 tff(301,plain,
% 0.08/0.42 ($false),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[300, 297, 295, 293])).
% 0.08/0.42 tff(302,plain,(((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.08/0.42 tff(303,plain,
% 0.08/0.42 ((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[302, 283])).
% 0.08/0.42 tff(304,plain,
% 0.08/0.42 ((p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | (~p2(Y!11))),
% 0.08/0.42 inference(tautology,[status(thm)],[])).
% 0.08/0.42 tff(305,plain,
% 0.08/0.42 (~p2(Y!11)),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[304, 281])).
% 0.08/0.42 tff(306,plain,
% 0.08/0.42 (((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~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)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) | r1(X!0, Y!11)),
% 0.08/0.42 inference(tautology,[status(thm)],[])).
% 0.08/0.42 tff(307,plain,
% 0.08/0.42 (r1(X!0, Y!11)),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[306, 179])).
% 0.08/0.42 tff(308,plain,
% 0.08/0.42 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.08/0.42 tff(309,plain,
% 0.08/0.42 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))),
% 0.08/0.42 inference(rewrite,[status(thm)],[])).
% 0.08/0.42 tff(310,plain,
% 0.08/0.42 ((p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))))) <=> (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))),
% 0.08/0.42 inference(rewrite,[status(thm)],[])).
% 0.08/0.42 tff(311,plain,
% 0.08/0.42 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))))))),
% 0.08/0.42 inference(monotonicity,[status(thm)],[310])).
% 0.08/0.42 tff(312,plain,
% 0.08/0.42 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))),
% 0.08/0.42 inference(transitivity,[status(thm)],[311, 309])).
% 0.08/0.42 tff(313,plain,
% 0.08/0.42 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))),
% 0.08/0.42 inference(quant_inst,[status(thm)],[])).
% 0.08/0.42 tff(314,plain,
% 0.08/0.42 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))))),
% 0.08/0.42 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.08/0.42 tff(315,plain,
% 0.08/0.42 ($false),
% 0.08/0.42 inference(unit_resolution,[status(thm)],[314, 308, 307, 305, 303])).
% 0.08/0.42 % SZS output end Proof
% 0.08/0.42 % E exiting
%------------------------------------------------------------------------------