%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL668+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n013.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 03:00:32 PM UTC 2026
% Result : Theorem 0.89s 1.19s
% Output : Proof 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL668+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 07:02:36 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.89/1.19 % SZS status Theorem
% 0.89/1.19 % SZS output start Proof
% 0.89/1.19 tff(p5_type, type, (
% 0.89/1.19 p5: $i > $o)).
% 0.89/1.19 tff(tptp_fun_Y_11_type, type, (
% 0.89/1.19 tptp_fun_Y_11: $i > $i)).
% 0.89/1.19 tff(tptp_fun_X_15_type, type, (
% 0.89/1.19 tptp_fun_X_15: $i)).
% 0.89/1.19 tff(p1_type, type, (
% 0.89/1.19 p1: $i > $o)).
% 0.89/1.19 tff(r1_type, type, (
% 0.89/1.19 r1: ( $i * $i ) > $o)).
% 0.89/1.19 tff(tptp_fun_Y_14_type, type, (
% 0.89/1.19 tptp_fun_Y_14: $i)).
% 0.89/1.19 tff(tptp_fun_X_13_type, type, (
% 0.89/1.19 tptp_fun_X_13: $i)).
% 0.89/1.19 tff(tptp_fun_Y_12_type, type, (
% 0.89/1.19 tptp_fun_Y_12: $i)).
% 0.89/1.19 tff(tptp_fun_X_8_type, type, (
% 0.89/1.19 tptp_fun_X_8: $i > $i)).
% 0.89/1.19 tff(p6_type, type, (
% 0.89/1.19 p6: $i > $o)).
% 0.89/1.19 tff(p2_type, type, (
% 0.89/1.19 p2: $i > $o)).
% 0.89/1.19 tff(p3_type, type, (
% 0.89/1.19 p3: $i > $o)).
% 0.89/1.19 tff(p4_type, type, (
% 0.89/1.19 p4: $i > $o)).
% 0.89/1.19 tff(tptp_fun_X_10_type, type, (
% 0.89/1.19 tptp_fun_X_10: $i > $i)).
% 0.89/1.19 tff(tptp_fun_Y_9_type, type, (
% 0.89/1.19 tptp_fun_Y_9: $i > $i)).
% 0.89/1.19 tff(tptp_fun_X_0_type, type, (
% 0.89/1.19 tptp_fun_X_0: $i)).
% 0.89/1.19 tff(tptp_fun_X_17_type, type, (
% 0.89/1.19 tptp_fun_X_17: $i)).
% 0.89/1.19 tff(tptp_fun_Y_16_type, type, (
% 0.89/1.19 tptp_fun_Y_16: $i)).
% 0.89/1.19 tff(tptp_fun_X_7_type, type, (
% 0.89/1.19 tptp_fun_X_7: $i)).
% 0.89/1.19 tff(p8_type, type, (
% 0.89/1.19 p8: $i > $o)).
% 0.89/1.19 tff(p10_type, type, (
% 0.89/1.19 p10: $i > $o)).
% 0.89/1.19 tff(p12_type, type, (
% 0.89/1.19 p12: $i > $o)).
% 0.89/1.19 tff(tptp_fun_Y_6_type, type, (
% 0.89/1.19 tptp_fun_Y_6: $i)).
% 0.89/1.19 tff(tptp_fun_X_5_type, type, (
% 0.89/1.19 tptp_fun_X_5: $i)).
% 0.89/1.19 tff(tptp_fun_Y_4_type, type, (
% 0.89/1.19 tptp_fun_Y_4: $i)).
% 0.89/1.19 tff(tptp_fun_X_3_type, type, (
% 0.89/1.19 tptp_fun_X_3: $i)).
% 0.89/1.19 tff(tptp_fun_Y_2_type, type, (
% 0.89/1.19 tptp_fun_Y_2: $i)).
% 0.89/1.19 tff(tptp_fun_Y_1_type, type, (
% 0.89/1.19 tptp_fun_Y_1: $i)).
% 0.89/1.19 tff(p7_type, type, (
% 0.89/1.19 p7: $i > $o)).
% 0.89/1.19 tff(1,assumption,(~r1(X!15, X!15)), introduced(assumption)).
% 0.89/1.19 tff(2,plain,
% 0.89/1.19 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.89/1.19 inference(bind,[status(th)],[])).
% 0.89/1.19 tff(3,plain,
% 0.89/1.19 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.89/1.19 inference(quant_intro,[status(thm)],[2])).
% 0.89/1.19 tff(4,plain,
% 0.89/1.19 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.89/1.19 inference(rewrite,[status(thm)],[])).
% 0.89/1.19 tff(5,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.89/1.19 tff(6,plain,
% 0.89/1.19 (![X: $i] : r1(X, X)),
% 0.89/1.19 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.89/1.19 tff(7,plain,(
% 0.89/1.19 ![X: $i] : r1(X, X)),
% 0.89/1.19 inference(skolemize,[status(sab)],[6])).
% 0.89/1.19 tff(8,plain,
% 0.89/1.19 (![X: $i] : r1(X, X)),
% 0.89/1.19 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.89/1.19 tff(9,plain,
% 0.89/1.19 ((~![X: $i] : r1(X, X)) | r1(X!15, X!15)),
% 0.89/1.19 inference(quant_inst,[status(thm)],[])).
% 0.89/1.19 tff(10,plain,
% 0.89/1.19 ($false),
% 0.89/1.19 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.89/1.19 tff(11,plain,(r1(X!15, X!15)), inference(lemma,lemma(discharge,[]))).
% 0.89/1.19 tff(12,plain,
% 0.89/1.19 (((~(p7(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) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & (r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> ((~(p7(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) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 0.89/1.20 inference(rewrite,[status(thm)],[])).
% 0.89/1.20 tff(13,plain,
% 0.89/1.20 ((r1(X!0, Y!12) & (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> (r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 0.89/1.20 inference(rewrite,[status(thm)],[])).
% 0.89/1.20 tff(14,plain,
% 0.89/1.20 ((r1(Y!12, X!13) & (r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 0.89/1.20 inference(rewrite,[status(thm)],[])).
% 0.89/1.20 tff(15,plain,
% 0.89/1.20 ((r1(X!13, Y!14) & (r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> (r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 0.89/1.20 inference(rewrite,[status(thm)],[])).
% 0.89/1.20 tff(16,plain,
% 0.89/1.20 ((r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))) <=> (r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 0.89/1.20 inference(rewrite,[status(thm)],[])).
% 0.89/1.20 tff(17,plain,
% 0.89/1.20 ((r1(X!13, Y!14) & (r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))) <=> (r1(X!13, Y!14) & (r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))),
% 0.89/1.20 inference(monotonicity,[status(thm)],[16])).
% 0.89/1.20 tff(18,plain,
% 0.89/1.20 ((r1(X!13, Y!14) & (r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))) <=> (r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 0.89/1.20 inference(transitivity,[status(thm)],[17, 15])).
% 0.89/1.20 tff(19,plain,
% 0.89/1.20 ((r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))))) <=> (r1(Y!12, X!13) & (r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[18])).
% 0.96/1.20 tff(20,plain,
% 0.96/1.20 ((r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))))) <=> (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 0.96/1.20 inference(transitivity,[status(thm)],[19, 14])).
% 0.96/1.20 tff(21,plain,
% 0.96/1.20 ((r1(X!0, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))))) <=> (r1(X!0, Y!12) & (r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[20])).
% 0.96/1.20 tff(22,plain,
% 0.96/1.20 ((r1(X!0, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))))) <=> (r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 0.96/1.20 inference(transitivity,[status(thm)],[21, 13])).
% 0.96/1.20 tff(23,plain,
% 0.96/1.20 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(24,plain,
% 0.96/1.20 ((r1(Y!2, X!3) & (r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(25,plain,
% 0.96/1.20 ((r1(X!3, Y!4) & (r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))) <=> (r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(26,plain,
% 0.96/1.20 ((r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))) <=> (r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(27,plain,
% 0.96/1.20 ((r1(X!3, Y!4) & (r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))) <=> (r1(X!3, Y!4) & (r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[26])).
% 0.96/1.20 tff(28,plain,
% 0.96/1.20 ((r1(X!3, Y!4) & (r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))) <=> (r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 0.96/1.20 inference(transitivity,[status(thm)],[27, 25])).
% 0.96/1.20 tff(29,plain,
% 0.96/1.20 ((r1(Y!2, X!3) & (r1(X!3, Y!4) & (r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))))) <=> (r1(Y!2, X!3) & (r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[28])).
% 0.96/1.20 tff(30,plain,
% 0.96/1.20 ((r1(Y!2, X!3) & (r1(X!3, Y!4) & (r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))))) <=> (r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 0.96/1.20 inference(transitivity,[status(thm)],[29, 24])).
% 0.96/1.20 tff(31,plain,
% 0.96/1.20 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))))) <=> (r1(X!0, Y!2) & (r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[30])).
% 0.96/1.20 tff(32,plain,
% 0.96/1.20 ((r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))))) <=> (r1(X!0, Y!2) & r1(Y!2, X!3) & r1(X!3, Y!4) & r1(Y!4, X!5) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))))),
% 0.96/1.20 inference(transitivity,[status(thm)],[31, 23])).
% 0.96/1.20 tff(33,plain,
% 0.96/1.20 ((~((~r1(X!0, Y!1)) | p7(Y!1))) <=> (~(p7(Y!1) | (~r1(X!0, Y!1))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(34,plain,
% 0.96/1.20 (((~((~r1(X!0, Y!1)) | p7(Y!1))) & (r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & (r1(X!0, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))))))) <=> ((~(p7(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) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & (r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))))),
% 0.96/1.21 inference(monotonicity,[status(thm)],[33, 32, 22])).
% 0.96/1.21 tff(35,plain,
% 0.96/1.21 (((~((~r1(X!0, Y!1)) | p7(Y!1))) & (r1(X!0, Y!2) & (r1(Y!2, X!3) & (r1(X!3, Y!4) & (r1(Y!4, X!5) & (r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & (r1(X!0, Y!12) & (r1(Y!12, X!13) & (r1(X!13, Y!14) & (r1(Y!14, X!15) & (r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))))))) <=> ((~(p7(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) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17)))))),
% 0.96/1.21 inference(transitivity,[status(thm)],[34, 12])).
% 0.96/1.21 tff(36,plain,
% 0.96/1.21 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X)))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 0.96/1.21 inference(rewrite,[status(thm)],[])).
% 0.96/1.21 tff(37,plain,
% 0.96/1.21 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X)))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 0.96/1.21 inference(rewrite,[status(thm)],[])).
% 0.96/1.21 tff(38,plain,
% 0.96/1.21 ((~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((~p12(X)) & (~p10(X))) & (~p8(X))) & (~p6(X))) & (~p4(X))) & (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p1(X))) | (p1(X) & p5(X)))))))))))) | ![X: $i] : ((~r1(Y, X)) | p6(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p5(X))) | (p5(X) & p4(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p4(X))) | (p4(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)) | ![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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((((p6(X) & p5(X)) & p4(X)) & p3(X)) & p2(X)) & p1(X))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X)))))))))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(39,plain,
% 0.96/1.22 ((~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((~p12(X)) & (~p10(X))) & (~p8(X))) & (~p6(X))) & (~p4(X))) & (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p1(X))) | (p1(X) & p5(X)))))))))))) | ![X: $i] : ((~r1(Y, X)) | p6(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p5(X))) | (p5(X) & p4(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p4(X))) | (p4(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)) | ![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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((((p6(X) & p5(X)) & p4(X)) & p3(X)) & p2(X)) & p1(X)))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))))),
% 0.96/1.22 inference(monotonicity,[status(thm)],[38])).
% 0.96/1.22 tff(40,plain,
% 0.96/1.22 ((~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((~p12(X)) & (~p10(X))) & (~p8(X))) & (~p6(X))) & (~p4(X))) & (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p1(X))) | (p1(X) & p5(X)))))))))))) | ![X: $i] : ((~r1(Y, X)) | p6(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p5(X))) | (p5(X) & p4(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p4(X))) | (p4(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)) | ![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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((((p6(X) & p5(X)) & p4(X)) & p3(X)) & p2(X)) & p1(X)))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 0.96/1.22 inference(transitivity,[status(thm)],[39, 37])).
% 0.96/1.22 tff(41,axiom,(~(~?[X: $i] : (~(((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((((((~p12(X)) & (~p10(X))) & (~p8(X))) & (~p6(X))) & (~p4(X))) & (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y))) | (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p5(X)) & (~p1(X))) | (p1(X) & p5(X)))))))))))) | ![X: $i] : ((~r1(Y, X)) | p6(X))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p4(X)) & (~p5(X))) | (p5(X) & p4(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(((~p3(X)) & (~p4(X))) | (p4(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)) | ![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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((((p6(X) & p5(X)) & p4(X)) & p3(X)) & p2(X)) & p1(X)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.96/1.22 tff(42,plain,
% 0.96/1.22 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 0.96/1.22 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.96/1.22 tff(43,plain,
% 0.96/1.22 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((~p12(X)) & (~p10(X)) & (~p8(X)) & (~p6(X)) & (~p4(X)) & (~p2(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p6(X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (p6(X) & p5(X) & p4(X) & p3(X) & p2(X) & p1(X))))))))))),
% 0.96/1.22 inference(modus_ponens,[status(thm)],[42, 36])).
% 0.96/1.22 tff(44,plain,
% 0.96/1.22 ((~(p7(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) & r1(X!5, Y!6) & (~((~r1(Y!6, X!7)) | ((~p12(X!7)) & (~p10(X!7)) & (~p8(X!7)) & (~p6(X!7)) & (~p4(X!7)) & (~p2(X!7))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X))))))))))))))))) & r1(X!0, Y!12) & r1(Y!12, X!13) & r1(X!13, Y!14) & r1(Y!14, X!15) & r1(X!15, Y!16) & (~((~r1(Y!16, X!17)) | (p6(X!17) & p5(X!17) & p4(X!17) & p3(X!17) & p2(X!17) & p1(X!17))))),
% 0.96/1.23 inference(modus_ponens,[status(thm)],[43, 35])).
% 0.96/1.23 tff(45,plain,
% 0.96/1.23 (r1(X!0, Y!12)),
% 0.96/1.23 inference(and_elim,[status(thm)],[44])).
% 0.96/1.23 tff(46,plain,
% 0.96/1.23 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))))),
% 0.96/1.23 inference(bind,[status(th)],[])).
% 0.96/1.23 tff(47,plain,
% 0.96/1.23 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 0.96/1.23 inference(quant_intro,[status(thm)],[46])).
% 0.96/1.23 tff(48,plain,
% 0.96/1.23 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))))),
% 0.96/1.23 inference(bind,[status(th)],[])).
% 0.96/1.23 tff(49,plain,
% 0.96/1.23 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 0.96/1.23 inference(quant_intro,[status(thm)],[48])).
% 0.96/1.23 tff(50,plain,
% 0.96/1.23 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 0.96/1.24 inference(transitivity,[status(thm)],[49, 47])).
% 0.96/1.24 tff(51,plain,
% 0.96/1.24 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))))),
% 0.96/1.24 inference(bind,[status(th)],[])).
% 0.96/1.24 tff(52,plain,
% 0.96/1.24 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 0.96/1.24 inference(quant_intro,[status(thm)],[51])).
% 0.96/1.24 tff(53,plain,
% 0.96/1.24 (![Y: $i] : ((~r1(X!0, Y)) | ((~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p1(X) & p5(X)) | ((~p5(X)) & (~p1(X)))))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p5(X) & p4(X)) | ((~p4(X)) & (~p5(X))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ((~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p4(X) & p3(X)) | ((~p3(X)) & (~p4(X)))))))))) & ![X: $i] : ((~r1(Y, X)) | ((~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((p2(X) & p1(X)) | ((~p1(X)) & (~p2(X)))))))))))))))))),
% 0.96/1.24 inference(and_elim,[status(thm)],[44])).
% 0.96/1.24 tff(54,plain,
% 0.96/1.24 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 0.96/1.24 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.96/1.24 tff(55,plain,
% 0.96/1.24 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 0.96/1.24 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.96/1.24 tff(56,plain,
% 0.96/1.24 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | ((~r1(X!0, Y!12)) | (~((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | p6(tptp_fun_X_8(Y!12)) | (~r1(Y!12, tptp_fun_X_8(Y!12))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | (~r1(X!0, Y!12)) | (~((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | p6(tptp_fun_X_8(Y!12)) | (~r1(Y!12, tptp_fun_X_8(Y!12))))))),
% 0.96/1.25 inference(rewrite,[status(thm)],[])).
% 0.96/1.25 tff(57,plain,
% 0.96/1.25 (((~r1(X!0, Y!12)) | (~((~r1(Y!12, tptp_fun_X_8(Y!12))) | p6(tptp_fun_X_8(Y!12)) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))))))) <=> ((~r1(X!0, Y!12)) | (~((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | p6(tptp_fun_X_8(Y!12)) | (~r1(Y!12, tptp_fun_X_8(Y!12))))))),
% 0.96/1.25 inference(rewrite,[status(thm)],[])).
% 0.96/1.25 tff(58,plain,
% 0.96/1.25 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | ((~r1(X!0, Y!12)) | (~((~r1(Y!12, tptp_fun_X_8(Y!12))) | p6(tptp_fun_X_8(Y!12)) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | ((~r1(X!0, Y!12)) | (~((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | p6(tptp_fun_X_8(Y!12)) | (~r1(Y!12, tptp_fun_X_8(Y!12)))))))),
% 0.96/1.25 inference(monotonicity,[status(thm)],[57])).
% 0.96/1.25 tff(59,plain,
% 0.96/1.25 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | ((~r1(X!0, Y!12)) | (~((~r1(Y!12, tptp_fun_X_8(Y!12))) | p6(tptp_fun_X_8(Y!12)) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![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_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | (~r1(X!0, Y!12)) | (~((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | p6(tptp_fun_X_8(Y!12)) | (~r1(Y!12, tptp_fun_X_8(Y!12))))))),
% 0.96/1.25 inference(transitivity,[status(thm)],[58, 56])).
% 0.96/1.25 tff(60,plain,
% 0.96/1.25 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | ((~r1(X!0, Y!12)) | (~((~r1(Y!12, tptp_fun_X_8(Y!12))) | p6(tptp_fun_X_8(Y!12)) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(61,plain,
% 0.96/1.26 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p6(tptp_fun_X_8(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))))))) | (~r1(X!0, Y!12)) | (~((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | p6(tptp_fun_X_8(Y!12)) | (~r1(Y!12, tptp_fun_X_8(Y!12)))))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.96/1.26 tff(62,plain,
% 0.96/1.26 (~((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | p6(tptp_fun_X_8(Y!12)) | (~r1(Y!12, tptp_fun_X_8(Y!12))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[61, 55, 45])).
% 0.96/1.26 tff(63,plain,
% 0.96/1.26 (((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | p6(tptp_fun_X_8(Y!12)) | (~r1(Y!12, tptp_fun_X_8(Y!12)))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(64,plain,
% 0.96/1.26 (![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.96/1.26 tff(65,plain,
% 0.96/1.26 (r1(Y!12, X!13)),
% 0.96/1.26 inference(and_elim,[status(thm)],[44])).
% 0.96/1.26 tff(66,plain,
% 0.96/1.26 (((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | ((~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) <=> ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(67,plain,
% 0.96/1.26 ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | ((~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(68,plain,
% 0.96/1.26 ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | (~r1(Y!12, X!13)) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.96/1.26 tff(69,plain,
% 0.96/1.26 (![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[68, 65, 64])).
% 0.96/1.26 tff(70,plain,
% 0.96/1.26 (r1(X!13, Y!14)),
% 0.96/1.26 inference(and_elim,[status(thm)],[44])).
% 0.96/1.26 tff(71,plain,
% 0.96/1.26 (((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))) | ((~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))) | (~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(72,plain,
% 0.96/1.26 ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))) | ((~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(73,plain,
% 0.96/1.26 ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))))) | (~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.96/1.26 tff(74,plain,
% 0.96/1.26 (![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[73, 70, 69])).
% 0.96/1.26 tff(75,plain,
% 0.96/1.26 (r1(Y!14, X!15)),
% 0.96/1.26 inference(and_elim,[status(thm)],[44])).
% 0.96/1.26 tff(76,plain,
% 0.96/1.26 (((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))) | ((~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))) | (~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(77,plain,
% 0.96/1.26 ((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))) | ((~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(78,plain,
% 0.96/1.26 ((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))) | (~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.96/1.26 tff(79,plain,
% 0.96/1.26 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[78, 75, 74])).
% 0.96/1.26 tff(80,plain,
% 0.96/1.26 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(81,plain,
% 0.96/1.26 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(82,plain,
% 0.96/1.26 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.96/1.26 tff(83,plain,
% 0.96/1.26 (![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[82, 79, 11])).
% 0.96/1.26 tff(84,plain,
% 0.96/1.26 (((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))) | ((~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))) | (~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(85,plain,
% 0.96/1.26 ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))) | ((~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(86,plain,
% 0.96/1.26 ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))) | (~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.96/1.26 tff(87,plain,
% 0.96/1.26 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))),
% 0.96/1.27 inference(unit_resolution,[status(thm)],[86, 11, 83])).
% 0.96/1.27 tff(88,plain,
% 0.96/1.27 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))),
% 0.96/1.27 inference(rewrite,[status(thm)],[])).
% 0.96/1.27 tff(89,plain,
% 0.96/1.27 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))),
% 0.96/1.27 inference(quant_inst,[status(thm)],[])).
% 0.96/1.27 tff(90,plain,
% 0.96/1.27 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X)))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))),
% 0.96/1.27 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.96/1.27 tff(91,plain,
% 0.96/1.27 (![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))),
% 0.96/1.27 inference(unit_resolution,[status(thm)],[90, 11, 87])).
% 0.96/1.27 tff(92,plain,
% 0.96/1.27 (((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))))))))) | p6(tptp_fun_X_8(Y!12)) | (~r1(Y!12, tptp_fun_X_8(Y!12)))) | ![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))),
% 0.96/1.27 inference(tautology,[status(thm)],[])).
% 0.96/1.27 tff(93,plain,
% 0.96/1.27 (![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))),
% 0.96/1.27 inference(unit_resolution,[status(thm)],[92, 62])).
% 0.96/1.27 tff(94,plain,
% 0.96/1.27 (((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | ((~r1(Y!12, X!13)) | (~((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | p5(tptp_fun_Y_9(X!13)) | (~r1(X!13, tptp_fun_Y_9(X!13))))))) <=> ((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~r1(Y!12, X!13)) | (~((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | p5(tptp_fun_Y_9(X!13)) | (~r1(X!13, tptp_fun_Y_9(X!13))))))),
% 0.96/1.27 inference(rewrite,[status(thm)],[])).
% 0.96/1.27 tff(95,plain,
% 0.96/1.27 (((~r1(Y!12, X!13)) | (~((~r1(X!13, tptp_fun_Y_9(X!13))) | p5(tptp_fun_Y_9(X!13)) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))))))) <=> ((~r1(Y!12, X!13)) | (~((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | p5(tptp_fun_Y_9(X!13)) | (~r1(X!13, tptp_fun_Y_9(X!13))))))),
% 0.96/1.27 inference(rewrite,[status(thm)],[])).
% 0.96/1.27 tff(96,plain,
% 0.96/1.27 (((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | ((~r1(Y!12, X!13)) | (~((~r1(X!13, tptp_fun_Y_9(X!13))) | p5(tptp_fun_Y_9(X!13)) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) <=> ((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | ((~r1(Y!12, X!13)) | (~((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | p5(tptp_fun_Y_9(X!13)) | (~r1(X!13, tptp_fun_Y_9(X!13)))))))),
% 0.96/1.27 inference(monotonicity,[status(thm)],[95])).
% 0.96/1.27 tff(97,plain,
% 0.96/1.27 (((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | ((~r1(Y!12, X!13)) | (~((~r1(X!13, tptp_fun_Y_9(X!13))) | p5(tptp_fun_Y_9(X!13)) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) <=> ((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~r1(Y!12, X!13)) | (~((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | p5(tptp_fun_Y_9(X!13)) | (~r1(X!13, tptp_fun_Y_9(X!13))))))),
% 0.96/1.28 inference(transitivity,[status(thm)],[96, 94])).
% 0.96/1.28 tff(98,plain,
% 0.96/1.28 ((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | ((~r1(Y!12, X!13)) | (~((~r1(X!13, tptp_fun_Y_9(X!13))) | p5(tptp_fun_Y_9(X!13)) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))),
% 0.96/1.28 inference(quant_inst,[status(thm)],[])).
% 0.96/1.28 tff(99,plain,
% 0.96/1.28 ((~![X: $i] : ((~r1(Y!12, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | p5(tptp_fun_Y_9(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))))))) | (~r1(Y!12, X!13)) | (~((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | p5(tptp_fun_Y_9(X!13)) | (~r1(X!13, tptp_fun_Y_9(X!13)))))),
% 0.96/1.28 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.96/1.28 tff(100,plain,
% 0.96/1.28 (~((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | p5(tptp_fun_Y_9(X!13)) | (~r1(X!13, tptp_fun_Y_9(X!13))))),
% 0.96/1.28 inference(unit_resolution,[status(thm)],[99, 65, 93])).
% 0.96/1.28 tff(101,plain,
% 0.96/1.28 (((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | p5(tptp_fun_Y_9(X!13)) | (~r1(X!13, tptp_fun_Y_9(X!13)))) | ![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))),
% 0.96/1.28 inference(tautology,[status(thm)],[])).
% 0.96/1.28 tff(102,plain,
% 0.96/1.28 (![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))),
% 0.96/1.28 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.96/1.28 tff(103,plain,
% 0.96/1.28 (((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | ((~r1(X!13, Y!14)) | (~((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | p4(tptp_fun_X_10(Y!14)) | (~r1(Y!14, tptp_fun_X_10(Y!14))))))) <=> ((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~r1(X!13, Y!14)) | (~((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | p4(tptp_fun_X_10(Y!14)) | (~r1(Y!14, tptp_fun_X_10(Y!14))))))),
% 0.96/1.28 inference(rewrite,[status(thm)],[])).
% 0.96/1.28 tff(104,plain,
% 0.96/1.28 (((~r1(X!13, Y!14)) | (~((~r1(Y!14, tptp_fun_X_10(Y!14))) | p4(tptp_fun_X_10(Y!14)) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))))))) <=> ((~r1(X!13, Y!14)) | (~((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | p4(tptp_fun_X_10(Y!14)) | (~r1(Y!14, tptp_fun_X_10(Y!14))))))),
% 0.96/1.28 inference(rewrite,[status(thm)],[])).
% 0.96/1.28 tff(105,plain,
% 0.96/1.28 (((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | ((~r1(X!13, Y!14)) | (~((~r1(Y!14, tptp_fun_X_10(Y!14))) | p4(tptp_fun_X_10(Y!14)) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | ((~r1(X!13, Y!14)) | (~((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | p4(tptp_fun_X_10(Y!14)) | (~r1(Y!14, tptp_fun_X_10(Y!14)))))))),
% 0.96/1.29 inference(monotonicity,[status(thm)],[104])).
% 0.96/1.29 tff(106,plain,
% 0.96/1.29 (((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | ((~r1(X!13, Y!14)) | (~((~r1(Y!14, tptp_fun_X_10(Y!14))) | p4(tptp_fun_X_10(Y!14)) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~r1(X!13, Y!14)) | (~((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | p4(tptp_fun_X_10(Y!14)) | (~r1(Y!14, tptp_fun_X_10(Y!14))))))),
% 0.96/1.29 inference(transitivity,[status(thm)],[105, 103])).
% 0.96/1.29 tff(107,plain,
% 0.96/1.29 ((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | ((~r1(X!13, Y!14)) | (~((~r1(Y!14, tptp_fun_X_10(Y!14))) | p4(tptp_fun_X_10(Y!14)) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))),
% 0.96/1.29 inference(quant_inst,[status(thm)],[])).
% 0.96/1.29 tff(108,plain,
% 0.96/1.29 ((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~r1(X!13, Y!14)) | (~((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | p4(tptp_fun_X_10(Y!14)) | (~r1(Y!14, tptp_fun_X_10(Y!14)))))),
% 0.96/1.29 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.96/1.29 tff(109,plain,
% 0.96/1.29 (~((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | p4(tptp_fun_X_10(Y!14)) | (~r1(Y!14, tptp_fun_X_10(Y!14))))),
% 0.96/1.29 inference(unit_resolution,[status(thm)],[108, 70, 102])).
% 0.96/1.29 tff(110,plain,
% 0.96/1.29 (((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | p4(tptp_fun_X_10(Y!14)) | (~r1(Y!14, tptp_fun_X_10(Y!14)))) | ![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))),
% 0.96/1.29 inference(tautology,[status(thm)],[])).
% 0.96/1.29 tff(111,plain,
% 0.96/1.29 (![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))),
% 0.96/1.29 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.96/1.29 tff(112,plain,
% 0.96/1.29 (((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | ((~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15))))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15))))))),
% 0.96/1.29 inference(rewrite,[status(thm)],[])).
% 0.96/1.29 tff(113,plain,
% 0.96/1.29 (((~r1(Y!14, X!15)) | (~((~r1(X!15, tptp_fun_Y_11(X!15))) | p3(tptp_fun_Y_11(X!15)) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))))))) <=> ((~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15))))))),
% 0.96/1.29 inference(rewrite,[status(thm)],[])).
% 0.96/1.29 tff(114,plain,
% 0.96/1.29 (((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | ((~r1(Y!14, X!15)) | (~((~r1(X!15, tptp_fun_Y_11(X!15))) | p3(tptp_fun_Y_11(X!15)) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | ((~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15)))))))),
% 0.96/1.29 inference(monotonicity,[status(thm)],[113])).
% 0.96/1.29 tff(115,plain,
% 0.96/1.29 (((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | ((~r1(Y!14, X!15)) | (~((~r1(X!15, tptp_fun_Y_11(X!15))) | p3(tptp_fun_Y_11(X!15)) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15))))))),
% 0.96/1.29 inference(transitivity,[status(thm)],[114, 112])).
% 0.96/1.29 tff(116,plain,
% 0.96/1.29 ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | ((~r1(Y!14, X!15)) | (~((~r1(X!15, tptp_fun_Y_11(X!15))) | p3(tptp_fun_Y_11(X!15)) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))),
% 0.96/1.30 inference(quant_inst,[status(thm)],[])).
% 0.96/1.30 tff(117,plain,
% 0.96/1.30 ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~r1(Y!14, X!15)) | (~((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15)))))),
% 0.96/1.30 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.96/1.30 tff(118,plain,
% 0.96/1.30 (~((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15))))),
% 0.96/1.30 inference(unit_resolution,[status(thm)],[117, 75, 111])).
% 0.96/1.30 tff(119,plain,
% 0.96/1.30 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15)))) | r1(X!15, tptp_fun_Y_11(X!15))),
% 0.96/1.30 inference(tautology,[status(thm)],[])).
% 0.96/1.30 tff(120,plain,
% 0.96/1.30 (r1(X!15, tptp_fun_Y_11(X!15))),
% 0.96/1.30 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.96/1.30 tff(121,plain,
% 0.96/1.30 (((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))))))),
% 0.96/1.30 inference(rewrite,[status(thm)],[])).
% 0.96/1.30 tff(122,plain,
% 0.96/1.30 (((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p5(tptp_fun_Y_11(X!15)) | p1(tptp_fun_Y_11(X!15))))))) <=> ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))))))),
% 0.96/1.30 inference(rewrite,[status(thm)],[])).
% 0.96/1.30 tff(123,plain,
% 0.96/1.30 (((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p5(tptp_fun_Y_11(X!15)) | p1(tptp_fun_Y_11(X!15)))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15))))))))),
% 0.96/1.30 inference(monotonicity,[status(thm)],[122])).
% 0.96/1.30 tff(124,plain,
% 0.96/1.30 (((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p5(tptp_fun_Y_11(X!15)) | p1(tptp_fun_Y_11(X!15)))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))))))),
% 1.06/1.30 inference(transitivity,[status(thm)],[123, 121])).
% 1.06/1.30 tff(125,plain,
% 1.06/1.30 ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p5(tptp_fun_Y_11(X!15)) | p1(tptp_fun_Y_11(X!15)))))))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(126,plain,
% 1.06/1.30 ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p1(X)) | (~p5(X)))) | (~(p5(X) | p1(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15))))))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.06/1.30 tff(127,plain,
% 1.06/1.30 (~((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[126, 120, 91])).
% 1.06/1.30 tff(128,plain,
% 1.06/1.30 (((~((~p1(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15))))) | (p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))),
% 1.06/1.30 inference(tautology,[status(thm)],[])).
% 1.06/1.30 tff(129,plain,
% 1.06/1.30 (p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[128, 127])).
% 1.06/1.30 tff(130,plain,
% 1.06/1.30 (((~![Y: $i] : ((~r1(X!13, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | p4(tptp_fun_X_10(Y)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))))))) | (~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | p5(tptp_fun_Y_9(X!13)) | (~r1(X!13, tptp_fun_Y_9(X!13)))) | ![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))),
% 1.06/1.30 inference(tautology,[status(thm)],[])).
% 1.06/1.30 tff(131,plain,
% 1.06/1.30 (![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[130, 100])).
% 1.06/1.30 tff(132,plain,
% 1.06/1.30 (((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | ((~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(133,plain,
% 1.06/1.30 ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | ((~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(134,plain,
% 1.06/1.30 ((~![Y: $i] : ((~r1(X!13, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))))) | (~r1(X!13, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.06/1.30 tff(135,plain,
% 1.06/1.30 (![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[134, 70, 131])).
% 1.06/1.30 tff(136,plain,
% 1.06/1.30 (((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))) | ((~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))) | (~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(137,plain,
% 1.06/1.30 ((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))) | ((~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(138,plain,
% 1.06/1.30 ((~![X: $i] : ((~r1(Y!14, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))))) | (~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.06/1.30 tff(139,plain,
% 1.06/1.30 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[138, 75, 135])).
% 1.06/1.30 tff(140,plain,
% 1.06/1.30 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(141,plain,
% 1.06/1.30 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(142,plain,
% 1.06/1.30 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.06/1.30 tff(143,plain,
% 1.06/1.30 (![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[142, 139, 11])).
% 1.06/1.30 tff(144,plain,
% 1.06/1.30 (((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))) | ((~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))) | (~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(145,plain,
% 1.06/1.30 ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))) | ((~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(146,plain,
% 1.06/1.30 ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))))) | (~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.06/1.30 tff(147,plain,
% 1.06/1.30 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[146, 11, 143])).
% 1.06/1.30 tff(148,plain,
% 1.06/1.30 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(149,plain,
% 1.06/1.30 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))),
% 1.06/1.30 inference(quant_inst,[status(thm)],[])).
% 1.06/1.30 tff(150,plain,
% 1.06/1.30 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X)))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.06/1.30 tff(151,plain,
% 1.06/1.30 (![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))),
% 1.06/1.30 inference(unit_resolution,[status(thm)],[150, 11, 147])).
% 1.06/1.30 tff(152,plain,
% 1.06/1.30 (((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p4(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p4(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p4(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p4(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))))))),
% 1.06/1.30 inference(rewrite,[status(thm)],[])).
% 1.06/1.30 tff(153,plain,
% 1.06/1.30 ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p4(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p4(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))))))),
% 1.06/1.31 inference(quant_inst,[status(thm)],[])).
% 1.06/1.31 tff(154,plain,
% 1.06/1.31 ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p5(X)))) | (~(p4(X) | p5(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p4(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p4(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.06/1.31 tff(155,plain,
% 1.06/1.31 (~((~((~p4(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p4(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[154, 120, 151])).
% 1.06/1.31 tff(156,plain,
% 1.06/1.31 (((~((~p4(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~(p4(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15))))) | ((~p4(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))),
% 1.06/1.31 inference(tautology,[status(thm)],[])).
% 1.06/1.31 tff(157,plain,
% 1.06/1.31 ((~p4(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15)))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[156, 155])).
% 1.06/1.31 tff(158,plain,
% 1.06/1.31 (((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | p3(tptp_fun_Y_11(X)) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))))))) | (~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | p4(tptp_fun_X_10(Y!14)) | (~r1(Y!14, tptp_fun_X_10(Y!14)))) | ![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))),
% 1.06/1.31 inference(tautology,[status(thm)],[])).
% 1.06/1.31 tff(159,plain,
% 1.06/1.31 (![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[158, 109])).
% 1.06/1.31 tff(160,plain,
% 1.06/1.31 (((~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | ((~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))) <=> ((~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | (~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(161,plain,
% 1.06/1.31 ((~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | ((~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))))),
% 1.06/1.31 inference(quant_inst,[status(thm)],[])).
% 1.06/1.31 tff(162,plain,
% 1.06/1.31 ((~![X: $i] : ((~r1(Y!14, 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)))) | (~(p3(X) | p4(X))))))))))) | (~r1(Y!14, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.06/1.31 tff(163,plain,
% 1.06/1.31 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[162, 75, 159])).
% 1.06/1.31 tff(164,plain,
% 1.06/1.31 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(165,plain,
% 1.06/1.31 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))),
% 1.06/1.31 inference(quant_inst,[status(thm)],[])).
% 1.06/1.31 tff(166,plain,
% 1.06/1.31 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.06/1.31 tff(167,plain,
% 1.06/1.31 (![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[166, 163, 11])).
% 1.06/1.31 tff(168,plain,
% 1.06/1.31 (((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))) | ((~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))) | (~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(169,plain,
% 1.06/1.31 ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))) | ((~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))),
% 1.06/1.31 inference(quant_inst,[status(thm)],[])).
% 1.06/1.31 tff(170,plain,
% 1.06/1.31 ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))))) | (~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.06/1.31 tff(171,plain,
% 1.06/1.31 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[170, 167, 11])).
% 1.06/1.31 tff(172,plain,
% 1.06/1.31 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(173,plain,
% 1.06/1.31 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))),
% 1.06/1.31 inference(quant_inst,[status(thm)],[])).
% 1.06/1.31 tff(174,plain,
% 1.06/1.31 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X)))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.06/1.31 tff(175,plain,
% 1.06/1.31 (![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[174, 11, 171])).
% 1.06/1.31 tff(176,plain,
% 1.06/1.31 (((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))) | (~((~p3(tptp_fun_Y_11(X!15))) | (~p4(tptp_fun_Y_11(X!15))))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))) | (~((~p3(tptp_fun_Y_11(X!15))) | (~p4(tptp_fun_Y_11(X!15))))))))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(177,plain,
% 1.06/1.31 (((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p4(tptp_fun_Y_11(X!15))) | (~p3(tptp_fun_Y_11(X!15))))) | (~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15))))))) <=> ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))) | (~((~p3(tptp_fun_Y_11(X!15))) | (~p4(tptp_fun_Y_11(X!15))))))))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(178,plain,
% 1.06/1.31 (((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p4(tptp_fun_Y_11(X!15))) | (~p3(tptp_fun_Y_11(X!15))))) | (~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))) | (~((~p3(tptp_fun_Y_11(X!15))) | (~p4(tptp_fun_Y_11(X!15)))))))))),
% 1.06/1.31 inference(monotonicity,[status(thm)],[177])).
% 1.06/1.31 tff(179,plain,
% 1.06/1.31 (((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p4(tptp_fun_Y_11(X!15))) | (~p3(tptp_fun_Y_11(X!15))))) | (~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))) | (~((~p3(tptp_fun_Y_11(X!15))) | (~p4(tptp_fun_Y_11(X!15))))))))),
% 1.06/1.31 inference(transitivity,[status(thm)],[178, 176])).
% 1.06/1.31 tff(180,plain,
% 1.06/1.31 ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p4(tptp_fun_Y_11(X!15))) | (~p3(tptp_fun_Y_11(X!15))))) | (~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))))))),
% 1.06/1.31 inference(quant_inst,[status(thm)],[])).
% 1.06/1.31 tff(181,plain,
% 1.06/1.31 ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p4(X)) | (~p3(X)))) | (~(p3(X) | p4(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))) | (~((~p3(tptp_fun_Y_11(X!15))) | (~p4(tptp_fun_Y_11(X!15)))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[180, 179])).
% 1.06/1.31 tff(182,plain,
% 1.06/1.31 (~((~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))) | (~((~p3(tptp_fun_Y_11(X!15))) | (~p4(tptp_fun_Y_11(X!15))))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[181, 120, 175])).
% 1.06/1.31 tff(183,plain,
% 1.06/1.31 (((~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))) | (~((~p3(tptp_fun_Y_11(X!15))) | (~p4(tptp_fun_Y_11(X!15)))))) | (p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))),
% 1.06/1.31 inference(tautology,[status(thm)],[])).
% 1.06/1.31 tff(184,plain,
% 1.06/1.31 (p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[183, 182])).
% 1.06/1.31 tff(185,plain,
% 1.06/1.31 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15)))) | (~p3(tptp_fun_Y_11(X!15)))),
% 1.06/1.31 inference(tautology,[status(thm)],[])).
% 1.06/1.31 tff(186,plain,
% 1.06/1.31 (~p3(tptp_fun_Y_11(X!15))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[185, 118])).
% 1.06/1.31 tff(187,plain,
% 1.06/1.31 ((~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))) | p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15))),
% 1.06/1.31 inference(tautology,[status(thm)],[])).
% 1.06/1.31 tff(188,plain,
% 1.06/1.31 ((~(p3(tptp_fun_Y_11(X!15)) | p4(tptp_fun_Y_11(X!15)))) | p4(tptp_fun_Y_11(X!15))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[187, 186])).
% 1.06/1.31 tff(189,plain,
% 1.06/1.31 (p4(tptp_fun_Y_11(X!15))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[188, 184])).
% 1.06/1.31 tff(190,plain,
% 1.06/1.31 ((~((~p4(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15))))) | (~p4(tptp_fun_Y_11(X!15))) | (~p5(tptp_fun_Y_11(X!15)))),
% 1.06/1.31 inference(tautology,[status(thm)],[])).
% 1.06/1.31 tff(191,plain,
% 1.06/1.31 (~p5(tptp_fun_Y_11(X!15))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[190, 189, 157])).
% 1.06/1.31 tff(192,plain,
% 1.06/1.31 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15)))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))),
% 1.06/1.31 inference(tautology,[status(thm)],[])).
% 1.06/1.31 tff(193,plain,
% 1.06/1.31 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[192, 118])).
% 1.06/1.31 tff(194,plain,
% 1.06/1.31 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(195,plain,
% 1.06/1.31 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))),
% 1.06/1.31 inference(quant_inst,[status(thm)],[])).
% 1.06/1.31 tff(196,plain,
% 1.06/1.31 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[195, 194])).
% 1.06/1.31 tff(197,plain,
% 1.06/1.31 ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[196, 193])).
% 1.06/1.31 tff(198,plain,
% 1.06/1.31 (![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[197, 11])).
% 1.06/1.31 tff(199,plain,
% 1.06/1.31 (((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) | ((~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) | (~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(200,plain,
% 1.06/1.32 ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) | ((~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(201,plain,
% 1.06/1.32 ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))))) | (~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.06/1.32 tff(202,plain,
% 1.06/1.32 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[201, 11, 198])).
% 1.06/1.32 tff(203,plain,
% 1.06/1.32 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(204,plain,
% 1.06/1.32 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(205,plain,
% 1.06/1.32 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[204, 203])).
% 1.06/1.32 tff(206,plain,
% 1.06/1.32 (![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[205, 11, 202])).
% 1.06/1.32 tff(207,plain,
% 1.06/1.32 (((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p2(tptp_fun_Y_11(X!15))) | (~p1(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p2(tptp_fun_Y_11(X!15)))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p2(tptp_fun_Y_11(X!15))) | (~p1(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p2(tptp_fun_Y_11(X!15)))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(208,plain,
% 1.06/1.32 ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p2(tptp_fun_Y_11(X!15))) | (~p1(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p2(tptp_fun_Y_11(X!15)))))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(209,plain,
% 1.06/1.32 ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p2(tptp_fun_Y_11(X!15))) | (~p1(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p2(tptp_fun_Y_11(X!15))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[208, 207])).
% 1.06/1.32 tff(210,plain,
% 1.06/1.32 (~((~((~p2(tptp_fun_Y_11(X!15))) | (~p1(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p2(tptp_fun_Y_11(X!15)))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[209, 120, 206])).
% 1.06/1.32 tff(211,plain,
% 1.06/1.32 (((~((~p2(tptp_fun_Y_11(X!15))) | (~p1(tptp_fun_Y_11(X!15))))) | (~(p1(tptp_fun_Y_11(X!15)) | p2(tptp_fun_Y_11(X!15))))) | ((~p2(tptp_fun_Y_11(X!15))) | (~p1(tptp_fun_Y_11(X!15))))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(212,plain,
% 1.06/1.32 ((~p2(tptp_fun_Y_11(X!15))) | (~p1(tptp_fun_Y_11(X!15)))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[211, 210])).
% 1.06/1.32 tff(213,plain,
% 1.06/1.32 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p1(X)))) | (~(p1(X) | p2(X)))))))))) | (~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | p3(tptp_fun_Y_11(X!15)) | (~r1(X!15, tptp_fun_Y_11(X!15)))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(214,plain,
% 1.06/1.32 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[213, 118])).
% 1.06/1.32 tff(215,plain,
% 1.06/1.32 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(216,plain,
% 1.06/1.32 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(217,plain,
% 1.06/1.32 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[216, 215])).
% 1.06/1.32 tff(218,plain,
% 1.06/1.32 (![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[217, 214, 11])).
% 1.06/1.32 tff(219,plain,
% 1.06/1.32 (((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))) | ((~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))) | (~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(220,plain,
% 1.06/1.32 ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))) | ((~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(221,plain,
% 1.06/1.32 ((~![X: $i] : ((~r1(X!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))))) | (~r1(X!15, X!15)) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.06/1.32 tff(222,plain,
% 1.06/1.32 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[221, 11, 218])).
% 1.06/1.32 tff(223,plain,
% 1.06/1.32 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(224,plain,
% 1.06/1.32 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | ((~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(225,plain,
% 1.06/1.32 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X)))))))) | (~r1(X!15, X!15)) | ![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.06/1.32 tff(226,plain,
% 1.06/1.32 (![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[225, 11, 222])).
% 1.06/1.32 tff(227,plain,
% 1.06/1.32 (((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p2(tptp_fun_Y_11(X!15))) | (~p3(tptp_fun_Y_11(X!15))))) | (~(p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15)))))))) <=> ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p2(tptp_fun_Y_11(X!15))) | (~p3(tptp_fun_Y_11(X!15))))) | (~(p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15)))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(228,plain,
% 1.06/1.32 ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | ((~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p2(tptp_fun_Y_11(X!15))) | (~p3(tptp_fun_Y_11(X!15))))) | (~(p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15)))))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(229,plain,
% 1.06/1.32 ((~![X: $i] : ((~r1(X!15, X)) | (~((~((~p2(X)) | (~p3(X)))) | (~(p2(X) | p3(X))))))) | (~r1(X!15, tptp_fun_Y_11(X!15))) | (~((~((~p2(tptp_fun_Y_11(X!15))) | (~p3(tptp_fun_Y_11(X!15))))) | (~(p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.06/1.32 tff(230,plain,
% 1.06/1.32 (~((~((~p2(tptp_fun_Y_11(X!15))) | (~p3(tptp_fun_Y_11(X!15))))) | (~(p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15)))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[229, 120, 226])).
% 1.06/1.32 tff(231,plain,
% 1.06/1.32 (((~((~p2(tptp_fun_Y_11(X!15))) | (~p3(tptp_fun_Y_11(X!15))))) | (~(p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15))))) | (p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15)))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(232,plain,
% 1.06/1.32 (p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[231, 230])).
% 1.06/1.32 tff(233,plain,
% 1.06/1.32 ((~(p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15)))) | p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(234,plain,
% 1.06/1.32 ((~(p2(tptp_fun_Y_11(X!15)) | p3(tptp_fun_Y_11(X!15)))) | p2(tptp_fun_Y_11(X!15))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[233, 186])).
% 1.06/1.32 tff(235,plain,
% 1.06/1.32 (p2(tptp_fun_Y_11(X!15))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[234, 232])).
% 1.06/1.32 tff(236,plain,
% 1.06/1.32 ((~((~p2(tptp_fun_Y_11(X!15))) | (~p1(tptp_fun_Y_11(X!15))))) | (~p2(tptp_fun_Y_11(X!15))) | (~p1(tptp_fun_Y_11(X!15)))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(237,plain,
% 1.06/1.32 (~p1(tptp_fun_Y_11(X!15))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[236, 235, 212])).
% 1.06/1.32 tff(238,plain,
% 1.06/1.32 ((~(p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15)))) | p1(tptp_fun_Y_11(X!15)) | p5(tptp_fun_Y_11(X!15))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(239,plain,
% 1.06/1.32 ($false),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[238, 237, 191, 129])).
% 1.06/1.32 % SZS output end Proof
% 1.06/1.33 % E exiting
%------------------------------------------------------------------------------