%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL644+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 03:00:21 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL644+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 05:03:37 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 % SZS output start Proof
% 0.12/0.41 tff(p1_type, type, (
% 0.12/0.41 p1: $i > $o)).
% 0.12/0.41 tff(tptp_fun_Y_8_type, type, (
% 0.12/0.41 tptp_fun_Y_8: $i)).
% 0.12/0.41 tff(r1_type, type, (
% 0.12/0.41 r1: ( $i * $i ) > $o)).
% 0.12/0.41 tff(tptp_fun_X_0_type, type, (
% 0.12/0.41 tptp_fun_X_0: $i)).
% 0.12/0.41 tff(tptp_fun_X_7_type, type, (
% 0.12/0.41 tptp_fun_X_7: $i > $i)).
% 0.12/0.41 tff(p2_type, type, (
% 0.12/0.41 p2: $i > $o)).
% 0.12/0.41 tff(tptp_fun_Y_6_type, type, (
% 0.12/0.41 tptp_fun_Y_6: $i)).
% 0.12/0.41 tff(tptp_fun_X_5_type, type, (
% 0.12/0.41 tptp_fun_X_5: $i)).
% 0.12/0.41 tff(tptp_fun_Y_4_type, type, (
% 0.12/0.41 tptp_fun_Y_4: $i)).
% 0.12/0.41 tff(tptp_fun_X_3_type, type, (
% 0.12/0.41 tptp_fun_X_3: $i)).
% 0.12/0.41 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.41 tptp_fun_Y_2: $i)).
% 0.12/0.41 tff(tptp_fun_X_1_type, type, (
% 0.12/0.41 tptp_fun_X_1: $i > $i)).
% 0.12/0.41 tff(1,plain,
% 0.12/0.41 (((![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~p2(Y))) | ((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) | ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) & $false) <=> $false),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(2,plain,
% 0.12/0.41 (((~p1(Y!8)) & r1(X!0, Y!8) & (![X: $i] : (p1(X) | (~r1(Y!8, X))) & p1(Y!8))) <=> $false),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(3,plain,
% 0.12/0.41 ((![X: $i] : (p1(X) | (~r1(Y!8, X))) & p1(Y!8)) <=> (![X: $i] : (p1(X) | (~r1(Y!8, X))) & p1(Y!8))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(4,plain,
% 0.12/0.41 (((~p1(Y!8)) & r1(X!0, Y!8) & (![X: $i] : (p1(X) | (~r1(Y!8, X))) & p1(Y!8))) <=> ((~p1(Y!8)) & r1(X!0, Y!8) & (![X: $i] : (p1(X) | (~r1(Y!8, X))) & p1(Y!8)))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[3])).
% 0.12/0.41 tff(5,plain,
% 0.12/0.41 (((~p1(Y!8)) & r1(X!0, Y!8) & (![X: $i] : (p1(X) | (~r1(Y!8, X))) & p1(Y!8))) <=> $false),
% 0.12/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.41 tff(6,plain,
% 0.12/0.41 ((![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~p2(Y))) | (((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) | ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~p2(Y))) | ((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) | ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(7,plain,
% 0.12/0.41 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | ((~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(8,plain,
% 0.12/0.41 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[7])).
% 0.12/0.41 tff(9,plain,
% 0.12/0.41 ((((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) | ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) | $false) <=> (((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) | ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(10,plain,
% 0.12/0.41 (((~p2(Y!6)) & (~p1(Y!6)) & r1(X!0, Y!6) & (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) & (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))))) <=> $false),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(11,plain,
% 0.12/0.41 ((p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X)))) <=> (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(12,plain,
% 0.12/0.41 ((p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) <=> (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(13,plain,
% 0.12/0.41 (((~p2(Y!6)) & (~p1(Y!6)) & r1(X!0, Y!6) & (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) & (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))))) <=> ((~p2(Y!6)) & (~p1(Y!6)) & r1(X!0, Y!6) & (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) & (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X)))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[12, 11])).
% 0.12/0.41 tff(14,plain,
% 0.12/0.41 (((~p2(Y!6)) & (~p1(Y!6)) & r1(X!0, Y!6) & (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) & (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X))))) <=> $false),
% 0.12/0.41 inference(transitivity,[status(thm)],[13, 10])).
% 0.12/0.41 tff(15,plain,
% 0.12/0.41 (((~p1(Y!4)) & r1(X!0, Y!4) & (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) & ((~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))) <=> ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(16,plain,
% 0.12/0.41 (((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))) <=> ((~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(17,plain,
% 0.12/0.41 ((p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) <=> (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(18,plain,
% 0.12/0.41 (((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))) <=> ((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[17])).
% 0.12/0.41 tff(19,plain,
% 0.12/0.41 (((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))) <=> ((~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[18, 16])).
% 0.12/0.41 tff(20,plain,
% 0.12/0.41 ((p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) <=> (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(21,plain,
% 0.12/0.41 (((~p1(Y!4)) & r1(X!0, Y!4) & (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) & ((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))) <=> ((~p1(Y!4)) & r1(X!0, Y!4) & (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) & ((~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[20, 19])).
% 0.12/0.41 tff(22,plain,
% 0.12/0.41 (((~p1(Y!4)) & r1(X!0, Y!4) & (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) & ((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))) <=> ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[21, 15])).
% 0.12/0.41 tff(23,plain,
% 0.12/0.41 (((~p2(Y!2)) & r1(X!0, Y!2) & (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) & ((~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y))))) <=> ((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(24,plain,
% 0.12/0.41 (((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y))))) <=> ((~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(25,plain,
% 0.12/0.41 ((p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) <=> (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(26,plain,
% 0.12/0.42 (((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y))))) <=> ((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[25])).
% 0.12/0.42 tff(27,plain,
% 0.12/0.42 (((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y))))) <=> ((~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y))))),
% 0.12/0.42 inference(transitivity,[status(thm)],[26, 24])).
% 0.12/0.42 tff(28,plain,
% 0.12/0.42 ((p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) <=> (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(29,plain,
% 0.12/0.42 (((~p2(Y!2)) & r1(X!0, Y!2) & (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) & ((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))))) <=> ((~p2(Y!2)) & r1(X!0, Y!2) & (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) & ((~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[28, 27])).
% 0.12/0.42 tff(30,plain,
% 0.12/0.42 (((~p2(Y!2)) & r1(X!0, Y!2) & (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) & ((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))))) <=> ((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y))))),
% 0.12/0.42 inference(transitivity,[status(thm)],[29, 23])).
% 0.12/0.42 tff(31,plain,
% 0.12/0.42 ((((~p2(Y!2)) & r1(X!0, Y!2) & (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) & ((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))))) | ((~p1(Y!4)) & r1(X!0, Y!4) & (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) & ((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))) | ((~p2(Y!6)) & (~p1(Y!6)) & r1(X!0, Y!6) & (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) & (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X)))))) <=> (((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) | ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) | $false)),
% 0.12/0.42 inference(monotonicity,[status(thm)],[30, 22, 14])).
% 0.12/0.42 tff(32,plain,
% 0.12/0.42 ((((~p2(Y!2)) & r1(X!0, Y!2) & (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) & ((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))))) | ((~p1(Y!4)) & r1(X!0, Y!4) & (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) & ((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))) | ((~p2(Y!6)) & (~p1(Y!6)) & r1(X!0, Y!6) & (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) & (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X)))))) <=> (((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) | ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))),
% 0.12/0.42 inference(transitivity,[status(thm)],[31, 9])).
% 0.12/0.42 tff(33,plain,
% 0.12/0.42 (^[Y: $i] : rewrite((p1(Y) | (~r1(X!0, Y)) | ((~p2(Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) <=> (p1(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~p2(Y))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(34,plain,
% 0.12/0.42 (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ((~p2(Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~p2(Y)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.12/0.42 tff(35,plain,
% 0.12/0.42 ((![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ((~p2(Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (((~p2(Y!2)) & r1(X!0, Y!2) & (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) & ((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))))) | ((~p1(Y!4)) & r1(X!0, Y!4) & (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) & ((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))) | ((~p2(Y!6)) & (~p1(Y!6)) & r1(X!0, Y!6) & (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) & (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X)))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) <=> (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~p2(Y))) | (((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) | ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[34, 32, 8])).
% 0.12/0.42 tff(36,plain,
% 0.12/0.42 ((![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ((~p2(Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (((~p2(Y!2)) & r1(X!0, Y!2) & (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) & ((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))))) | ((~p1(Y!4)) & r1(X!0, Y!4) & (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) & ((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))) | ((~p2(Y!6)) & (~p1(Y!6)) & r1(X!0, Y!6) & (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) & (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X)))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) <=> (![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~p2(Y))) | ((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) | ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.12/0.42 inference(transitivity,[status(thm)],[35, 6])).
% 0.12/0.42 tff(37,plain,
% 0.12/0.42 (((![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ((~p2(Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (((~p2(Y!2)) & r1(X!0, Y!2) & (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) & ((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))))) | ((~p1(Y!4)) & r1(X!0, Y!4) & (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) & ((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))) | ((~p2(Y!6)) & (~p1(Y!6)) & r1(X!0, Y!6) & (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) & (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X)))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ((~p1(Y!8)) & r1(X!0, Y!8) & (![X: $i] : (p1(X) | (~r1(Y!8, X))) & p1(Y!8)))) <=> ((![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))) | (~p2(Y))) | ((~p2(Y!2)) & r1(X!0, Y!2) & p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X))) & (~p1(X!3)) & r1(Y!2, X!3) & p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))) | ((~p1(Y!4)) & r1(X!0, Y!4) & p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X))) & (~p2(X!5)) & r1(Y!4, X!5) & p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) & $false)),
% 0.12/0.42 inference(monotonicity,[status(thm)],[36, 5])).
% 0.12/0.42 tff(38,plain,
% 0.12/0.42 (((![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | ((~p2(Y)) | (~(p2(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | (((~p2(Y!2)) & r1(X!0, Y!2) & (p1(Y!2) & ![X: $i] : (p1(X) | (~r1(Y!2, X)))) & ((~p1(X!3)) & r1(Y!2, X!3) & (p2(X!3) & ![Y: $i] : (p2(Y) | (~r1(X!3, Y)))))) | ((~p1(Y!4)) & r1(X!0, Y!4) & (p2(Y!4) & ![X: $i] : (p2(X) | (~r1(Y!4, X)))) & ((~p2(X!5)) & r1(Y!4, X!5) & (p1(X!5) & ![Y: $i] : (p1(Y) | (~r1(X!5, Y)))))) | ((~p2(Y!6)) & (~p1(Y!6)) & r1(X!0, Y!6) & (p2(Y!6) & ![X: $i] : (p2(X) | (~r1(Y!6, X)))) & (p1(Y!6) & ![X: $i] : (p1(X) | (~r1(Y!6, X)))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p1(Y)) | (~(p1(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ((~p1(Y!8)) & r1(X!0, Y!8) & (![X: $i] : (p1(X) | (~r1(Y!8, X))) & p1(Y!8)))) <=> $false),
% 0.12/0.43 inference(transitivity,[status(thm)],[37, 1])).
% 0.12/0.43 tff(39,plain,
% 0.12/0.43 (?[X: $i] : (~((~(![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~(p2(X) & ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~(p1(X) & ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p2(Y) | p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(![X: $i] : (p1(X) | (~r1(Y, X))) & p1(Y)))))) <=> ?[X: $i] : (~((~(![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~(p2(X) & ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~(p1(X) & ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p2(Y) | p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(![X: $i] : (p1(X) | (~r1(Y, X))) & p1(Y))))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(40,plain,
% 0.12/0.43 ((~(~?[X: $i] : (~((~(![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~(p2(X) & ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~(p1(X) & ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p2(Y) | p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(![X: $i] : (p1(X) | (~r1(Y, X))) & p1(Y)))))))) <=> ?[X: $i] : (~((~(![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~(p2(X) & ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~(p1(X) & ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p2(Y) | p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(![X: $i] : (p1(X) | (~r1(Y, X))) & p1(Y))))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(41,plain,
% 0.12/0.43 ((~?[X: $i] : (~(((~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) & p1(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) & p1(Y))))))) <=> (~?[X: $i] : (~((~(![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~(p2(X) & ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~(p1(X) & ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p2(Y) | p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(![X: $i] : (p1(X) | (~r1(Y, X))) & p1(Y)))))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(42,plain,
% 0.12/0.43 ((~(~?[X: $i] : (~(((~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) & p1(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) & p1(Y)))))))) <=> (~(~?[X: $i] : (~((~(![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~(p2(X) & ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~(p1(X) & ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p2(Y) | p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(![X: $i] : (p1(X) | (~r1(Y, X))) & p1(Y))))))))),
% 0.12/0.43 inference(monotonicity,[status(thm)],[41])).
% 0.12/0.43 tff(43,plain,
% 0.12/0.43 ((~(~?[X: $i] : (~(((~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) & p1(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) & p1(Y)))))))) <=> ?[X: $i] : (~((~(![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~(p2(X) & ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~(p1(X) & ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p2(Y) | p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(![X: $i] : (p1(X) | (~r1(Y, X))) & p1(Y))))))),
% 0.12/0.43 inference(transitivity,[status(thm)],[42, 40])).
% 0.12/0.43 tff(44,axiom,(~(~?[X: $i] : (~(((~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) & p1(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) & p1(Y)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.12/0.43 tff(45,plain,
% 0.12/0.43 (?[X: $i] : (~((~(![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~(p2(X) & ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~(p1(X) & ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p2(Y) | p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(![X: $i] : (p1(X) | (~r1(Y, X))) & p1(Y))))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.43 tff(46,plain,
% 0.12/0.43 (?[X: $i] : (~((~(![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~(p2(X) & ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~(p1(X) & ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p2(Y) | p1(Y) | (~r1(X, Y)) | (~(p2(Y) & ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~(p1(Y) & ![X: $i] : (p1(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~(![X: $i] : (p1(X) | (~r1(Y, X))) & p1(Y))))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[45, 39])).
% 0.12/0.43 tff(47,plain,
% 0.12/0.43 ($false),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[46, 38])).
% 0.12/0.43 % SZS output end Proof
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------