%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL650+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:24 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL650+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.33 % Computer : n002.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 5 20:02:37 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(p2_type, type, (
% 0.12/0.40 p2: $i > $o)).
% 0.12/0.40 tff(tptp_fun_X_11_type, type, (
% 0.12/0.40 tptp_fun_X_11: $i)).
% 0.12/0.40 tff(p1_type, type, (
% 0.12/0.40 p1: $i > $o)).
% 0.12/0.40 tff(r1_type, type, (
% 0.12/0.40 r1: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_Y_10_type, type, (
% 0.12/0.40 tptp_fun_Y_10: $i)).
% 0.12/0.40 tff(tptp_fun_X_9_type, type, (
% 0.12/0.40 tptp_fun_X_9: $i)).
% 0.12/0.40 tff(tptp_fun_Y_7_type, type, (
% 0.12/0.40 tptp_fun_Y_7: $i > $i)).
% 0.12/0.40 tff(p3_type, type, (
% 0.12/0.40 p3: $i > $o)).
% 0.12/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.12/0.40 tptp_fun_Y_8: $i)).
% 0.12/0.40 tff(tptp_fun_X_6_type, type, (
% 0.12/0.40 tptp_fun_X_6: $i > $i)).
% 0.12/0.40 tff(p4_type, type, (
% 0.12/0.40 p4: $i > $o)).
% 0.12/0.40 tff(tptp_fun_X_0_type, type, (
% 0.12/0.40 tptp_fun_X_0: $i)).
% 0.12/0.40 tff(tptp_fun_X_5_type, type, (
% 0.12/0.40 tptp_fun_X_5: $i)).
% 0.12/0.40 tff(p6_type, type, (
% 0.12/0.40 p6: $i > $o)).
% 0.12/0.40 tff(p8_type, type, (
% 0.12/0.40 p8: $i > $o)).
% 0.12/0.40 tff(tptp_fun_Y_4_type, type, (
% 0.12/0.40 tptp_fun_Y_4: $i)).
% 0.12/0.40 tff(tptp_fun_X_3_type, type, (
% 0.12/0.40 tptp_fun_X_3: $i)).
% 0.12/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.40 tptp_fun_Y_2: $i)).
% 0.12/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.40 tptp_fun_Y_1: $i)).
% 0.12/0.40 tff(p5_type, type, (
% 0.12/0.40 p5: $i > $o)).
% 0.12/0.40 tff(1,assumption,(~p1(X!11)), introduced(assumption)).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (((~(p5(Y!1) | (~r1(X!0, Y!1)))) & (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))) <=> ((~(p5(Y!1) | (~r1(X!0, Y!1)))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 ((r1(X!0, Y!8) & (r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))) <=> (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 ((r1(Y!8, X!9) & (r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))) <=> (r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 ((r1(X!0, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))))) <=> (r1(X!0, Y!8) & (r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[4])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 ((r1(X!0, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))))) <=> (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[5, 3])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 ((r1(Y!2, X!3) & (r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))) <=> (r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[8])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[9, 7])).
% 0.12/0.41 tff(11,plain,
% 0.12/0.41 ((~((~r1(X!0, Y!1)) | p5(Y!1))) <=> (~(p5(Y!1) | (~r1(X!0, Y!1))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(12,plain,
% 0.12/0.41 (((~((~r1(X!0, Y!1)) | p5(Y!1))) & (r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & (r1(X!0, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))))) <=> ((~(p5(Y!1) | (~r1(X!0, Y!1)))) & (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[11, 10, 6])).
% 0.12/0.41 tff(13,plain,
% 0.12/0.41 (((~((~r1(X!0, Y!1)) | p5(Y!1))) & (r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & (r1(X!0, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))))) <=> ((~(p5(Y!1) | (~r1(X!0, Y!1)))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[12, 2])).
% 0.12/0.41 tff(14,plain,
% 0.12/0.41 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X)))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(15,plain,
% 0.12/0.41 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X)))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(16,plain,
% 0.12/0.41 ((~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((~p8(X)) & (~p6(X))) & (~p4(X))) & (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p1(X))) | (p1(X) & p3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p4(X) & p3(X)) & p2(X)) & p1(X))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X)))))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(17,plain,
% 0.12/0.41 ((~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((~p8(X)) & (~p6(X))) & (~p4(X))) & (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p1(X))) | (p1(X) & p3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p4(X) & p3(X)) & p2(X)) & p1(X)))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[16])).
% 0.12/0.41 tff(18,plain,
% 0.12/0.41 ((~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((~p8(X)) & (~p6(X))) & (~p4(X))) & (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p1(X))) | (p1(X) & p3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p4(X) & p3(X)) & p2(X)) & p1(X)))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.12/0.41 tff(19,axiom,(~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((~p8(X)) & (~p6(X))) & (~p4(X))) & (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p1(X))) | (p1(X) & p3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p4(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p2(X)) & (~p3(X))) | (p3(X) & p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(~![X: $i] : ((~r1(Y, X)) | (~(((~p1(X)) & (~p2(X))) | (p2(X) & p1(X)))))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p4(X) & p3(X)) & p2(X)) & p1(X)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.12/0.41 tff(20,plain,
% 0.12/0.41 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.41 tff(21,plain,
% 0.12/0.41 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p5(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p4(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p4(X) & p3(X) & p2(X) & p1(X))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.12/0.41 tff(22,plain,
% 0.12/0.41 ((~(p5(Y!1) | (~r1(X!0, Y!1)))) & r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & (~((~r1(Y!4, X!5)) | ((~p8(X!5)) & (~p6(X!5)) & (~p4(X!5)) & (~p2(X!5))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.12/0.42 tff(23,plain,
% 0.12/0.42 (r1(X!0, Y!8)),
% 0.12/0.42 inference(and_elim,[status(thm)],[22])).
% 0.12/0.42 tff(24,plain,
% 0.12/0.42 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(25,plain,
% 0.12/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.42 tff(26,plain,
% 0.12/0.42 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(27,plain,
% 0.12/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.42 tff(28,plain,
% 0.12/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.12/0.42 inference(transitivity,[status(thm)],[27, 25])).
% 0.12/0.42 tff(29,plain,
% 0.12/0.42 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) <=> ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(30,plain,
% 0.12/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.42 tff(31,plain,
% 0.12/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p3(X)) | ((~p3(X)) & (~p1(X)))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p3(X) & p2(X)) | ((~p2(X)) & (~p3(X))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))),
% 0.12/0.42 inference(and_elim,[status(thm)],[22])).
% 0.12/0.42 tff(32,plain,
% 0.12/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.42 tff(33,plain,
% 0.12/0.42 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.12/0.42 tff(34,plain,
% 0.12/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | ((~r1(X!0, Y!8)) | (~((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | (~r1(X!0, Y!8)) | (~((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(35,plain,
% 0.12/0.42 (((~r1(X!0, Y!8)) | (~((~r1(Y!8, tptp_fun_X_6(Y!8))) | p4(tptp_fun_X_6(Y!8)) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))) <=> ((~r1(X!0, Y!8)) | (~((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(36,plain,
% 0.12/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | ((~r1(X!0, Y!8)) | (~((~r1(Y!8, tptp_fun_X_6(Y!8))) | p4(tptp_fun_X_6(Y!8)) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | ((~r1(X!0, Y!8)) | (~((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8)))))))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[35])).
% 0.12/0.42 tff(37,plain,
% 0.12/0.42 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | ((~r1(X!0, Y!8)) | (~((~r1(Y!8, tptp_fun_X_6(Y!8))) | p4(tptp_fun_X_6(Y!8)) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | (~r1(X!0, Y!8)) | (~((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))))))),
% 0.12/0.42 inference(transitivity,[status(thm)],[36, 34])).
% 0.12/0.42 tff(38,plain,
% 0.12/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | ((~r1(X!0, Y!8)) | (~((~r1(Y!8, tptp_fun_X_6(Y!8))) | p4(tptp_fun_X_6(Y!8)) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(39,plain,
% 0.12/0.42 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p4(tptp_fun_X_6(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))) | (~r1(X!0, Y!8)) | (~((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8)))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.42 tff(40,plain,
% 0.12/0.42 (~((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8))))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[39, 33, 23])).
% 0.12/0.42 tff(41,plain,
% 0.12/0.42 (((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8)))) | ![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(42,plain,
% 0.12/0.43 (![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.43 tff(43,plain,
% 0.12/0.43 (r1(Y!8, X!9)),
% 0.12/0.43 inference(and_elim,[status(thm)],[22])).
% 0.12/0.43 tff(44,plain,
% 0.12/0.43 (((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | ((~r1(Y!8, X!9)) | (~((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | p3(tptp_fun_Y_7(X!9)) | (~r1(X!9, tptp_fun_Y_7(X!9))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~r1(Y!8, X!9)) | (~((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | p3(tptp_fun_Y_7(X!9)) | (~r1(X!9, tptp_fun_Y_7(X!9))))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(45,plain,
% 0.12/0.43 (((~r1(Y!8, X!9)) | (~((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))) <=> ((~r1(Y!8, X!9)) | (~((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | p3(tptp_fun_Y_7(X!9)) | (~r1(X!9, tptp_fun_Y_7(X!9))))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(46,plain,
% 0.12/0.43 (((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | ((~r1(Y!8, X!9)) | (~((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | ((~r1(Y!8, X!9)) | (~((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | p3(tptp_fun_Y_7(X!9)) | (~r1(X!9, tptp_fun_Y_7(X!9)))))))),
% 0.12/0.43 inference(monotonicity,[status(thm)],[45])).
% 0.12/0.43 tff(47,plain,
% 0.12/0.43 (((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | ((~r1(Y!8, X!9)) | (~((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~r1(Y!8, X!9)) | (~((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | p3(tptp_fun_Y_7(X!9)) | (~r1(X!9, tptp_fun_Y_7(X!9))))))),
% 0.12/0.43 inference(transitivity,[status(thm)],[46, 44])).
% 0.12/0.43 tff(48,plain,
% 0.12/0.43 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | ((~r1(Y!8, X!9)) | (~((~r1(X!9, tptp_fun_Y_7(X!9))) | p3(tptp_fun_Y_7(X!9)) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(49,plain,
% 0.12/0.43 ((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~r1(Y!8, X!9)) | (~((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | p3(tptp_fun_Y_7(X!9)) | (~r1(X!9, tptp_fun_Y_7(X!9)))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.43 tff(50,plain,
% 0.12/0.43 (~((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | p3(tptp_fun_Y_7(X!9)) | (~r1(X!9, tptp_fun_Y_7(X!9))))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[49, 43, 42])).
% 0.12/0.43 tff(51,plain,
% 0.12/0.43 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | p3(tptp_fun_Y_7(X!9)) | (~r1(X!9, tptp_fun_Y_7(X!9)))) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(52,plain,
% 0.12/0.43 (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.12/0.43 tff(53,plain,
% 0.12/0.43 (r1(X!9, Y!10)),
% 0.12/0.43 inference(and_elim,[status(thm)],[22])).
% 0.12/0.43 tff(54,plain,
% 0.12/0.43 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(55,plain,
% 0.12/0.43 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(56,plain,
% 0.12/0.43 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.43 tff(57,plain,
% 0.12/0.43 (![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[56, 53, 52])).
% 0.12/0.43 tff(58,plain,
% 0.12/0.43 (~((~r1(Y!10, X!11)) | (p4(X!11) & p3(X!11) & p2(X!11) & p1(X!11)))),
% 0.12/0.43 inference(and_elim,[status(thm)],[22])).
% 0.12/0.43 tff(59,plain,
% 0.12/0.43 (r1(Y!10, X!11)),
% 0.12/0.43 inference(or_elim,[status(thm)],[58])).
% 0.12/0.43 tff(60,plain,
% 0.12/0.43 (((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11))))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(61,plain,
% 0.12/0.43 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11))))))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(62,plain,
% 0.12/0.43 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11)))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.12/0.43 tff(63,plain,
% 0.12/0.43 (~((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11))))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[62, 59, 57])).
% 0.12/0.43 tff(64,plain,
% 0.12/0.43 (((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11)))) | (p1(X!11) | p2(X!11))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(65,plain,
% 0.12/0.43 (p1(X!11) | p2(X!11)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.12/0.43 tff(66,plain,
% 0.12/0.43 ((~(p1(X!11) | p2(X!11))) | p1(X!11) | p2(X!11)),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(67,plain,
% 0.12/0.43 (p1(X!11) | p2(X!11)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.12/0.43 tff(68,plain,
% 0.12/0.43 (p2(X!11)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[67, 1])).
% 0.12/0.43 tff(69,plain,
% 0.12/0.43 (((~![X: $i] : ((~r1(Y!8, X)) | (~((~r1(X, tptp_fun_Y_7(X))) | p3(tptp_fun_Y_7(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))) | (~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | p4(tptp_fun_X_6(Y!8)) | (~r1(Y!8, tptp_fun_X_6(Y!8)))) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(70,plain,
% 0.12/0.43 (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[69, 40])).
% 0.12/0.43 tff(71,plain,
% 0.12/0.43 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(72,plain,
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% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(73,plain,
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% 0.12/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.12/0.43 tff(74,plain,
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% 0.12/0.43 inference(unit_resolution,[status(thm)],[73, 43, 70])).
% 0.12/0.43 tff(75,plain,
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% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(76,plain,
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% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(77,plain,
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% 0.12/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.12/0.43 tff(78,plain,
% 0.12/0.43 (![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[77, 53, 74])).
% 0.12/0.43 tff(79,plain,
% 0.12/0.43 (((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11))))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(80,plain,
% 0.12/0.43 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11))))))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(81,plain,
% 0.12/0.43 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p1(X)) | (~p3(X)))) | (~(p3(X) | p1(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11)))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.12/0.43 tff(82,plain,
% 0.12/0.43 (~((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11))))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[81, 59, 78])).
% 0.12/0.43 tff(83,plain,
% 0.12/0.43 (((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11)))) | (p3(X!11) | p1(X!11))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(84,plain,
% 0.12/0.43 (p3(X!11) | p1(X!11)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.12/0.43 tff(85,plain,
% 0.12/0.43 ((~(p3(X!11) | p1(X!11))) | p3(X!11) | p1(X!11)),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(86,plain,
% 0.12/0.43 (p3(X!11) | p1(X!11)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.12/0.43 tff(87,plain,
% 0.12/0.43 (p3(X!11)),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[86, 1])).
% 0.12/0.44 tff(88,plain,
% 0.12/0.44 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | p3(tptp_fun_Y_7(X!9)) | (~r1(X!9, tptp_fun_Y_7(X!9)))) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 0.12/0.44 inference(tautology,[status(thm)],[])).
% 0.12/0.44 tff(89,plain,
% 0.12/0.44 (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[88, 50])).
% 0.12/0.44 tff(90,plain,
% 0.12/0.44 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(91,plain,
% 0.12/0.44 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 0.12/0.44 inference(quant_inst,[status(thm)],[])).
% 0.12/0.44 tff(92,plain,
% 0.12/0.44 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.12/0.44 tff(93,plain,
% 0.12/0.44 (![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[92, 53, 89])).
% 0.12/0.44 tff(94,plain,
% 0.12/0.44 (((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11))))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(95,plain,
% 0.12/0.44 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11))))))),
% 0.12/0.44 inference(quant_inst,[status(thm)],[])).
% 0.12/0.44 tff(96,plain,
% 0.12/0.44 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | (~r1(Y!10, X!11)) | (~((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11)))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.12/0.44 tff(97,plain,
% 0.12/0.44 (~((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11))))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[96, 59, 93])).
% 0.12/0.44 tff(98,plain,
% 0.12/0.44 (((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11)))) | ((~p2(X!11)) | (~p3(X!11)))),
% 0.12/0.44 inference(tautology,[status(thm)],[])).
% 0.12/0.44 tff(99,plain,
% 0.12/0.44 ((~p2(X!11)) | (~p3(X!11))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.12/0.44 tff(100,plain,
% 0.12/0.44 ((~((~p2(X!11)) | (~p3(X!11)))) | (~p2(X!11)) | (~p3(X!11))),
% 0.12/0.44 inference(tautology,[status(thm)],[])).
% 0.12/0.44 tff(101,plain,
% 0.12/0.44 ((~p2(X!11)) | (~p3(X!11))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.12/0.44 tff(102,plain,
% 0.12/0.44 ($false),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[101, 87, 68])).
% 0.12/0.44 tff(103,plain,(p1(X!11)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.44 tff(104,plain,
% 0.12/0.44 (((~((~p2(X!11)) | (~p1(X!11)))) | (~(p1(X!11) | p2(X!11)))) | ((~p2(X!11)) | (~p1(X!11)))),
% 0.12/0.44 inference(tautology,[status(thm)],[])).
% 0.12/0.44 tff(105,plain,
% 0.12/0.44 ((~p2(X!11)) | (~p1(X!11))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[104, 63])).
% 0.12/0.44 tff(106,plain,
% 0.12/0.44 ((~((~p2(X!11)) | (~p1(X!11)))) | (~p2(X!11)) | (~p1(X!11))),
% 0.12/0.44 inference(tautology,[status(thm)],[])).
% 0.12/0.44 tff(107,plain,
% 0.12/0.44 ((~p2(X!11)) | (~p1(X!11))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.12/0.44 tff(108,plain,
% 0.12/0.44 (~p2(X!11)),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[107, 103])).
% 0.12/0.44 tff(109,plain,
% 0.12/0.44 (((~((~p1(X!11)) | (~p3(X!11)))) | (~(p3(X!11) | p1(X!11)))) | ((~p1(X!11)) | (~p3(X!11)))),
% 0.12/0.44 inference(tautology,[status(thm)],[])).
% 0.12/0.44 tff(110,plain,
% 0.12/0.44 ((~p1(X!11)) | (~p3(X!11))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[109, 82])).
% 0.12/0.44 tff(111,plain,
% 0.12/0.44 ((~((~p1(X!11)) | (~p3(X!11)))) | (~p1(X!11)) | (~p3(X!11))),
% 0.12/0.44 inference(tautology,[status(thm)],[])).
% 0.12/0.44 tff(112,plain,
% 0.12/0.44 ((~p1(X!11)) | (~p3(X!11))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.12/0.44 tff(113,plain,
% 0.12/0.44 (~p3(X!11)),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[112, 103])).
% 0.12/0.44 tff(114,plain,
% 0.12/0.44 (((~((~p2(X!11)) | (~p3(X!11)))) | (~(p2(X!11) | p3(X!11)))) | (p2(X!11) | p3(X!11))),
% 0.12/0.44 inference(tautology,[status(thm)],[])).
% 0.12/0.44 tff(115,plain,
% 0.12/0.44 (p2(X!11) | p3(X!11)),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[114, 97])).
% 0.12/0.44 tff(116,plain,
% 0.12/0.44 ((~(p2(X!11) | p3(X!11))) | p2(X!11) | p3(X!11)),
% 0.12/0.44 inference(tautology,[status(thm)],[])).
% 0.12/0.44 tff(117,plain,
% 0.12/0.44 (p2(X!11) | p3(X!11)),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.12/0.44 tff(118,plain,
% 0.12/0.44 ($false),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[117, 113, 108])).
% 0.12/0.44 % SZS output end Proof
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------