%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL654+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n029.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 03:00:26 PM UTC 2026
% Result : Theorem 1.89s 2.14s
% Output : Proof 1.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL654+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.35 % Computer : n029.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 5 11:19:56 UTC 2026
% 0.07/0.35 % CPUTime :
% 1.89/2.14 % SZS status Theorem
% 1.89/2.14 % SZS output start Proof
% 1.89/2.14 tff(r1_type, type, (
% 1.89/2.14 r1: ( $i * $i ) > $o)).
% 1.89/2.14 tff(tptp_fun_Y_4_type, type, (
% 1.89/2.14 tptp_fun_Y_4: $i > $i)).
% 1.89/2.14 tff(tptp_fun_Y_10_type, type, (
% 1.89/2.14 tptp_fun_Y_10: $i)).
% 1.89/2.14 tff(p1_type, type, (
% 1.89/2.14 p1: $i > $o)).
% 1.89/2.14 tff(tptp_fun_Y_3_type, type, (
% 1.89/2.14 tptp_fun_Y_3: $i > $i)).
% 1.89/2.14 tff(tptp_fun_X_11_type, type, (
% 1.89/2.14 tptp_fun_X_11: $i)).
% 1.89/2.14 tff(tptp_fun_X_2_type, type, (
% 1.89/2.14 tptp_fun_X_2: $i > $i)).
% 1.89/2.14 tff(tptp_fun_Y_12_type, type, (
% 1.89/2.14 tptp_fun_Y_12: $i)).
% 1.89/2.14 tff(tptp_fun_X_5_type, type, (
% 1.89/2.14 tptp_fun_X_5: $i > $i)).
% 1.89/2.14 tff(tptp_fun_X_0_type, type, (
% 1.89/2.14 tptp_fun_X_0: $i)).
% 1.89/2.14 tff(tptp_fun_Y_1_type, type, (
% 1.89/2.14 tptp_fun_Y_1: $i > $i)).
% 1.89/2.14 tff(tptp_fun_Y_15_type, type, (
% 1.89/2.14 tptp_fun_Y_15: $i > $i)).
% 1.89/2.14 tff(tptp_fun_X_14_type, type, (
% 1.89/2.14 tptp_fun_X_14: $i > $i)).
% 1.89/2.14 tff(tptp_fun_X_13_type, type, (
% 1.89/2.14 tptp_fun_X_13: $i > $i)).
% 1.89/2.14 tff(tptp_fun_X_9_type, type, (
% 1.89/2.14 tptp_fun_X_9: $i)).
% 1.89/2.14 tff(tptp_fun_Y_8_type, type, (
% 1.89/2.14 tptp_fun_Y_8: $i)).
% 1.89/2.14 tff(tptp_fun_X_7_type, type, (
% 1.89/2.14 tptp_fun_X_7: $i)).
% 1.89/2.14 tff(tptp_fun_Y_6_type, type, (
% 1.89/2.14 tptp_fun_Y_6: $i)).
% 1.89/2.14 tff(1,assumption,(~r1(Y!10, Y!10)), introduced(assumption)).
% 1.89/2.14 tff(2,plain,
% 1.89/2.14 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 1.89/2.14 inference(bind,[status(th)],[])).
% 1.89/2.14 tff(3,plain,
% 1.89/2.14 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 1.89/2.14 inference(quant_intro,[status(thm)],[2])).
% 1.89/2.14 tff(4,plain,
% 1.89/2.14 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 1.89/2.14 inference(rewrite,[status(thm)],[])).
% 1.89/2.14 tff(5,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 1.89/2.14 tff(6,plain,
% 1.89/2.14 (![X: $i] : r1(X, X)),
% 1.89/2.14 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.89/2.14 tff(7,plain,(
% 1.89/2.14 ![X: $i] : r1(X, X)),
% 1.89/2.14 inference(skolemize,[status(sab)],[6])).
% 1.89/2.14 tff(8,plain,
% 1.89/2.14 (![X: $i] : r1(X, X)),
% 1.89/2.14 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.89/2.14 tff(9,plain,
% 1.89/2.14 ((~![X: $i] : r1(X, X)) | r1(Y!10, Y!10)),
% 1.89/2.14 inference(quant_inst,[status(thm)],[])).
% 1.89/2.14 tff(10,plain,
% 1.89/2.14 ($false),
% 1.89/2.14 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.89/2.14 tff(11,plain,(r1(Y!10, Y!10)), inference(lemma,lemma(discharge,[]))).
% 1.89/2.14 tff(12,assumption,(~((~r1(X!11, tptp_fun_Y_3(X!11))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X)))))), introduced(assumption)).
% 1.89/2.14 tff(13,plain,
% 1.89/2.14 (((~r1(X!11, tptp_fun_Y_3(X!11))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X))))) | r1(X!11, tptp_fun_Y_3(X!11))),
% 1.89/2.14 inference(tautology,[status(thm)],[])).
% 1.89/2.14 tff(14,plain,
% 1.89/2.14 (r1(X!11, tptp_fun_Y_3(X!11))),
% 1.89/2.14 inference(unit_resolution,[status(thm)],[13, 12])).
% 1.89/2.14 tff(15,assumption,(![Y: $i] : (p1(Y) | (~r1(X!11, Y)))), introduced(assumption)).
% 1.89/2.14 tff(16,plain,
% 1.89/2.14 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & (r1(X!0, Y!6) & r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y)))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & r1(X!0, Y!6) & r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 1.89/2.15 inference(rewrite,[status(thm)],[])).
% 1.89/2.15 tff(17,plain,
% 1.89/2.15 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(18,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[17])).
% 1.89/2.15 tff(19,plain,
% 1.89/2.15 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(20,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[19])).
% 1.89/2.15 tff(21,plain,
% 1.89/2.15 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))) <=> ((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))))), rewrite(((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y)))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y)))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(22,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y)))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[21])).
% 1.89/2.15 tff(23,plain,
% 1.89/2.15 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(24,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y)))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[23])).
% 1.89/2.15 tff(25,plain,
% 1.89/2.15 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(26,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[25])).
% 1.89/2.15 tff(27,plain,
% 1.89/2.15 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))) | (~p1(X))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(28,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))) | (~p1(X))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[27])).
% 1.89/2.15 tff(29,plain,
% 1.89/2.15 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(30,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[29])).
% 1.89/2.15 tff(31,plain,
% 1.89/2.15 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(32,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[31])).
% 1.89/2.15 tff(33,plain,
% 1.89/2.15 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(34,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[33])).
% 1.89/2.15 tff(35,plain,
% 1.89/2.15 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(36,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y)))))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[35])).
% 1.89/2.15 tff(37,plain,
% 1.89/2.15 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(38,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[37])).
% 1.89/2.15 tff(39,plain,
% 1.89/2.15 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))) | (~p1(X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))))))),
% 1.89/2.15 inference(bind,[status(th)],[])).
% 1.89/2.15 tff(40,plain,
% 1.89/2.15 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))) | (~p1(X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y))))))))))),
% 1.89/2.15 inference(quant_intro,[status(thm)],[39])).
% 1.89/2.15 tff(41,plain,
% 1.89/2.15 ((r1(X!0, Y!6) & (r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))) <=> (r1(X!0, Y!6) & r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))),
% 1.89/2.16 inference(rewrite,[status(thm)],[])).
% 1.89/2.16 tff(42,plain,
% 1.89/2.16 ((r1(Y!6, X!7) & (r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))) <=> (r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))),
% 1.89/2.16 inference(rewrite,[status(thm)],[])).
% 1.89/2.16 tff(43,plain,
% 1.89/2.16 ((r1(X!7, Y!8) & (r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))) <=> (r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))),
% 1.89/2.16 inference(rewrite,[status(thm)],[])).
% 1.89/2.16 tff(44,plain,
% 1.89/2.16 ((r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))) <=> (r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))),
% 1.89/2.16 inference(rewrite,[status(thm)],[])).
% 1.89/2.16 tff(45,plain,
% 1.89/2.16 ((r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))) <=> (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))),
% 1.89/2.16 inference(rewrite,[status(thm)],[])).
% 1.89/2.16 tff(46,plain,
% 1.89/2.16 ((r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12))))))) <=> (r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12))))))),
% 1.89/2.16 inference(monotonicity,[status(thm)],[45])).
% 1.89/2.16 tff(47,plain,
% 1.89/2.16 ((r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12))))))) <=> (r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))),
% 1.89/2.16 inference(transitivity,[status(thm)],[46, 44])).
% 1.89/2.16 tff(48,plain,
% 1.89/2.16 ((r1(X!7, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))))) <=> (r1(X!7, Y!8) & (r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12))))))),
% 1.89/2.16 inference(monotonicity,[status(thm)],[47])).
% 1.89/2.16 tff(49,plain,
% 1.89/2.16 ((r1(X!7, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))))) <=> (r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))),
% 1.89/2.16 inference(transitivity,[status(thm)],[48, 43])).
% 1.89/2.16 tff(50,plain,
% 1.89/2.16 ((r1(Y!6, X!7) & (r1(X!7, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12))))))))) <=> (r1(Y!6, X!7) & (r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12))))))),
% 1.89/2.16 inference(monotonicity,[status(thm)],[49])).
% 1.89/2.16 tff(51,plain,
% 1.89/2.16 ((r1(Y!6, X!7) & (r1(X!7, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12))))))))) <=> (r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))),
% 1.89/2.16 inference(transitivity,[status(thm)],[50, 42])).
% 1.89/2.16 tff(52,plain,
% 1.89/2.16 ((r1(X!0, Y!6) & (r1(Y!6, X!7) & (r1(X!7, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))))))) <=> (r1(X!0, Y!6) & (r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12))))))),
% 1.89/2.16 inference(monotonicity,[status(thm)],[51])).
% 1.89/2.16 tff(53,plain,
% 1.89/2.16 ((r1(X!0, Y!6) & (r1(Y!6, X!7) & (r1(X!7, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))))))) <=> (r1(X!0, Y!6) & r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))),
% 1.89/2.16 inference(transitivity,[status(thm)],[52, 41])).
% 1.89/2.16 tff(54,plain,
% 1.89/2.16 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))))),
% 1.89/2.16 inference(bind,[status(th)],[])).
% 1.89/2.16 tff(55,plain,
% 1.89/2.16 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))))),
% 1.89/2.16 inference(quant_intro,[status(thm)],[54])).
% 1.89/2.16 tff(56,plain,
% 1.89/2.16 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $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)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))))),
% 1.89/2.16 inference(bind,[status(th)],[])).
% 1.89/2.16 tff(57,plain,
% 1.89/2.16 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))),
% 1.89/2.16 inference(quant_intro,[status(thm)],[56])).
% 1.89/2.16 tff(58,plain,
% 1.89/2.16 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))))))),
% 1.89/2.16 inference(bind,[status(th)],[])).
% 1.89/2.16 tff(59,plain,
% 1.89/2.16 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 1.89/2.16 inference(quant_intro,[status(thm)],[58])).
% 1.89/2.16 tff(60,plain,
% 1.89/2.16 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & (r1(X!0, Y!6) & (r1(Y!6, X!7) & (r1(X!7, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))) | (~p1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))) | (~p1(X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y)))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & (r1(X!0, Y!6) & r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 1.89/2.17 inference(monotonicity,[status(thm)],[59, 57, 55, 53, 40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18])).
% 1.89/2.17 tff(61,plain,
% 1.89/2.17 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & (r1(X!0, Y!6) & (r1(Y!6, X!7) & (r1(X!7, Y!8) & (r1(Y!8, X!9) & (r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & (r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))) | (~p1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))) | (~p1(X))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~p1(Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y)))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & r1(X!0, Y!6) & r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 1.89/2.18 inference(transitivity,[status(thm)],[60, 16])).
% 1.89/2.18 tff(62,plain,
% 1.89/2.18 (?[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)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~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)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) <=> ?[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)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~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)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))),
% 1.89/2.18 inference(rewrite,[status(thm)],[])).
% 1.89/2.18 tff(63,plain,
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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] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~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)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, X)))))) & 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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)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~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)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))),
% 1.89/2.19 inference(rewrite,[status(thm)],[])).
% 1.89/2.19 tff(64,plain,
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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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, 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] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, 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% 1.89/2.19 inference(rewrite,[status(thm)],[])).
% 1.89/2.19 tff(65,plain,
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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)) | $false)))))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, 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)) | (~p1(Y)))))) & p1(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)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(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)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, 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)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))) <=> (~(~?[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)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~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)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))))),
% 1.96/2.20 inference(monotonicity,[status(thm)],[64])).
% 1.96/2.20 tff(66,plain,
% 1.96/2.20 ((~(~?[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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(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)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(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)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(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)) | $false))))))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, 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)) | (~p1(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)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, 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)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, 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)) | $false)))))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, 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)) | (~p1(Y)))))) & p1(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)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(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)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, 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)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))) <=> ?[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)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~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)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))),
% 1.96/2.20 inference(transitivity,[status(thm)],[65, 63])).
% 1.96/2.20 tff(67,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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(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)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(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)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(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)) | $false))))))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, 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)) | (~p1(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)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, 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)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, 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)) | $false)))))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, 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)) | (~p1(Y)))))) & p1(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)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(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)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, 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)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![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)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 1.96/2.21 tff(68,plain,
% 1.96/2.21 (?[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)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~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)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))),
% 1.96/2.21 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.96/2.21 tff(69,plain,
% 1.96/2.21 (?[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)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~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)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(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] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, 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] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~p1(X)) | (~r1(Y, 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] : (p1(Y) | (~r1(X, Y)))))) & (~![X: $i] : (p1(X) | (~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] : (p1(Y) | (~r1(X, Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X)))))))),
% 1.96/2.22 inference(modus_ponens,[status(thm)],[68, 62])).
% 1.96/2.22 tff(70,plain,
% 1.96/2.22 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & r1(X!0, Y!6) & r1(Y!6, X!7) & r1(X!7, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & ![X: $i] : (p1(X) | (~r1(Y!10, X))) & r1(Y!10, X!11) & (~(p1(Y!12) | (~r1(X!11, Y!12)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~p1(X)) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_13(Y))) | (~r1(Y, tptp_fun_X_13(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_14(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_14(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_15(X)))) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~p1(tptp_fun_Y_1(X))) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y)))),
% 1.96/2.22 inference(modus_ponens,[status(thm)],[69, 61])).
% 1.96/2.22 tff(71,plain,
% 1.96/2.22 (~(p1(Y!12) | (~r1(X!11, Y!12)))),
% 1.96/2.22 inference(and_elim,[status(thm)],[70])).
% 1.96/2.22 tff(72,plain,
% 1.96/2.22 (r1(X!11, Y!12)),
% 1.96/2.22 inference(or_elim,[status(thm)],[71])).
% 1.96/2.22 tff(73,plain,
% 1.96/2.22 (~p1(Y!12)),
% 1.96/2.22 inference(or_elim,[status(thm)],[71])).
% 1.96/2.22 tff(74,plain,
% 1.96/2.22 (((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)))) | (p1(Y!12) | (~r1(X!11, Y!12)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)))) | p1(Y!12) | (~r1(X!11, Y!12)))),
% 1.96/2.22 inference(rewrite,[status(thm)],[])).
% 1.96/2.22 tff(75,plain,
% 1.96/2.22 ((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)))) | (p1(Y!12) | (~r1(X!11, Y!12)))),
% 1.96/2.22 inference(quant_inst,[status(thm)],[])).
% 1.96/2.22 tff(76,plain,
% 1.96/2.22 ((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)))) | p1(Y!12) | (~r1(X!11, Y!12))),
% 1.96/2.22 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.96/2.22 tff(77,plain,
% 1.96/2.22 ($false),
% 1.96/2.22 inference(unit_resolution,[status(thm)],[76, 73, 72, 15])).
% 1.96/2.22 tff(78,plain,(~![Y: $i] : (p1(Y) | (~r1(X!11, Y)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.22 tff(79,plain,
% 1.96/2.22 (r1(X!0, Y!6)),
% 1.96/2.22 inference(and_elim,[status(thm)],[70])).
% 1.96/2.22 tff(80,plain,
% 1.96/2.22 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) <=> ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))))),
% 1.96/2.22 inference(bind,[status(th)],[])).
% 1.96/2.22 tff(81,plain,
% 1.96/2.22 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))),
% 1.96/2.22 inference(quant_intro,[status(thm)],[80])).
% 1.96/2.22 tff(82,plain,
% 1.96/2.22 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) <=> ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))))),
% 1.96/2.22 inference(bind,[status(th)],[])).
% 1.96/2.22 tff(83,plain,
% 1.96/2.22 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))),
% 1.96/2.22 inference(quant_intro,[status(thm)],[82])).
% 1.96/2.22 tff(84,plain,
% 1.96/2.22 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))),
% 1.96/2.22 inference(transitivity,[status(thm)],[83, 81])).
% 1.96/2.22 tff(85,plain,
% 1.96/2.22 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))),
% 1.96/2.22 inference(and_elim,[status(thm)],[70])).
% 1.96/2.22 tff(86,plain,
% 1.96/2.22 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))),
% 1.96/2.22 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.96/2.22 tff(87,plain,
% 1.96/2.22 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))),
% 1.96/2.22 inference(rewrite,[status(thm)],[])).
% 1.96/2.22 tff(88,plain,
% 1.96/2.22 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))),
% 1.96/2.22 inference(quant_inst,[status(thm)],[])).
% 1.96/2.22 tff(89,plain,
% 1.96/2.22 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 1.96/2.22 inference(modus_ponens,[status(thm)],[88, 87])).
% 1.96/2.22 tff(90,plain,
% 1.96/2.22 (![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 1.96/2.22 inference(unit_resolution,[status(thm)],[89, 86, 79])).
% 1.96/2.22 tff(91,plain,
% 1.96/2.22 (r1(Y!6, X!7)),
% 1.96/2.22 inference(and_elim,[status(thm)],[70])).
% 1.96/2.22 tff(92,plain,
% 1.96/2.22 (((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) <=> ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) | (~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 1.96/2.22 inference(rewrite,[status(thm)],[])).
% 1.96/2.22 tff(93,plain,
% 1.96/2.22 ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 1.96/2.22 inference(quant_inst,[status(thm)],[])).
% 1.96/2.22 tff(94,plain,
% 1.96/2.22 ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))) | (~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 1.96/2.22 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.96/2.22 tff(95,plain,
% 1.96/2.22 (![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 1.96/2.22 inference(unit_resolution,[status(thm)],[94, 91, 90])).
% 1.96/2.22 tff(96,plain,
% 1.96/2.22 (r1(X!7, Y!8)),
% 1.96/2.22 inference(and_elim,[status(thm)],[70])).
% 1.96/2.22 tff(97,plain,
% 1.96/2.22 (((~![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) | ((~r1(X!7, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) <=> ((~![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) | (~r1(X!7, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 1.96/2.22 inference(rewrite,[status(thm)],[])).
% 1.96/2.22 tff(98,plain,
% 1.96/2.22 ((~![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) | ((~r1(X!7, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 1.96/2.22 inference(quant_inst,[status(thm)],[])).
% 1.96/2.22 tff(99,plain,
% 1.96/2.22 ((~![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) | (~r1(X!7, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))),
% 1.96/2.23 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.96/2.23 tff(100,plain,
% 1.96/2.23 (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[99, 96, 95])).
% 1.96/2.23 tff(101,plain,
% 1.96/2.23 (r1(Y!8, X!9)),
% 1.96/2.23 inference(and_elim,[status(thm)],[70])).
% 1.96/2.23 tff(102,plain,
% 1.96/2.23 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))),
% 1.96/2.23 inference(rewrite,[status(thm)],[])).
% 1.96/2.23 tff(103,plain,
% 1.96/2.23 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))),
% 1.96/2.23 inference(quant_inst,[status(thm)],[])).
% 1.96/2.23 tff(104,plain,
% 1.96/2.23 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))),
% 1.96/2.23 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.96/2.23 tff(105,plain,
% 1.96/2.23 (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[104, 101, 100])).
% 1.96/2.23 tff(106,plain,
% 1.96/2.23 (r1(X!9, Y!10)),
% 1.96/2.23 inference(and_elim,[status(thm)],[70])).
% 1.96/2.23 tff(107,plain,
% 1.96/2.23 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))),
% 1.96/2.23 inference(rewrite,[status(thm)],[])).
% 1.96/2.23 tff(108,plain,
% 1.96/2.23 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))),
% 1.96/2.23 inference(quant_inst,[status(thm)],[])).
% 1.96/2.23 tff(109,plain,
% 1.96/2.23 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))),
% 1.96/2.23 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.96/2.23 tff(110,plain,
% 1.96/2.23 (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[109, 106, 105])).
% 1.96/2.23 tff(111,plain,
% 1.96/2.23 (r1(Y!10, X!11)),
% 1.96/2.23 inference(and_elim,[status(thm)],[70])).
% 1.96/2.23 tff(112,plain,
% 1.96/2.23 (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y))))),
% 1.96/2.23 inference(rewrite,[status(thm)],[])).
% 1.96/2.23 tff(113,plain,
% 1.96/2.23 (((~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y))) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y))))),
% 1.96/2.23 inference(rewrite,[status(thm)],[])).
% 1.96/2.23 tff(114,plain,
% 1.96/2.23 (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y))) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)))))),
% 1.96/2.23 inference(monotonicity,[status(thm)],[113])).
% 1.96/2.23 tff(115,plain,
% 1.96/2.23 (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y))) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y))))),
% 1.96/2.23 inference(transitivity,[status(thm)],[114, 112])).
% 1.96/2.23 tff(116,plain,
% 1.96/2.23 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y))) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))),
% 1.96/2.23 inference(quant_inst,[status(thm)],[])).
% 1.96/2.23 tff(117,plain,
% 1.96/2.23 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)))),
% 1.96/2.23 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.96/2.23 tff(118,plain,
% 1.96/2.23 (![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)))),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[117, 111, 110])).
% 1.96/2.23 tff(119,plain,
% 1.96/2.23 (![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[118, 78])).
% 1.96/2.23 tff(120,plain,
% 1.96/2.23 (((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ((~r1(X!11, tptp_fun_Y_3(X!11))) | (~(p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11)))))))) <=> ((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (~r1(X!11, tptp_fun_Y_3(X!11))) | (~(p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11)))))))),
% 1.96/2.23 inference(rewrite,[status(thm)],[])).
% 1.96/2.23 tff(121,plain,
% 1.96/2.23 ((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ((~r1(X!11, tptp_fun_Y_3(X!11))) | (~(p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11)))))))),
% 1.96/2.23 inference(quant_inst,[status(thm)],[])).
% 1.96/2.23 tff(122,plain,
% 1.96/2.23 ((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (~r1(X!11, tptp_fun_Y_3(X!11))) | (~(p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11))))))),
% 1.96/2.23 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.96/2.23 tff(123,plain,
% 1.96/2.23 (~(p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11)))))),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[122, 119, 14])).
% 1.96/2.23 tff(124,plain,
% 1.96/2.23 ((p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11))))) | r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11)))),
% 1.96/2.23 inference(tautology,[status(thm)],[])).
% 1.96/2.23 tff(125,plain,
% 1.96/2.23 (r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11)))),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[124, 123])).
% 1.96/2.23 tff(126,plain,
% 1.96/2.23 ((p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11))))) | (~p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))))),
% 1.96/2.23 inference(tautology,[status(thm)],[])).
% 1.96/2.23 tff(127,plain,
% 1.96/2.23 (~p1(tptp_fun_X_2(tptp_fun_Y_3(X!11)))),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[126, 123])).
% 1.96/2.23 tff(128,plain,
% 1.96/2.23 (((~r1(X!11, tptp_fun_Y_3(X!11))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X))))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X)))),
% 1.96/2.23 inference(tautology,[status(thm)],[])).
% 1.96/2.23 tff(129,plain,
% 1.96/2.23 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X)))),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[128, 12])).
% 1.96/2.23 tff(130,plain,
% 1.96/2.23 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X)))) | (p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X)))) | p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11)))))),
% 1.96/2.23 inference(rewrite,[status(thm)],[])).
% 1.96/2.23 tff(131,plain,
% 1.96/2.23 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X)))) | (p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11)))))),
% 1.96/2.23 inference(quant_inst,[status(thm)],[])).
% 1.96/2.23 tff(132,plain,
% 1.96/2.23 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X)))) | p1(tptp_fun_X_2(tptp_fun_Y_3(X!11))) | (~r1(tptp_fun_Y_3(X!11), tptp_fun_X_2(tptp_fun_Y_3(X!11))))),
% 1.96/2.23 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.96/2.23 tff(133,plain,
% 1.96/2.23 ($false),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[132, 129, 127, 125])).
% 1.96/2.23 tff(134,plain,((~r1(X!11, tptp_fun_Y_3(X!11))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.23 tff(135,assumption,(![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))), introduced(assumption)).
% 1.96/2.23 tff(136,plain,
% 1.96/2.23 (((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))) | ((~r1(Y!10, X!11)) | (~((~r1(X!11, tptp_fun_Y_3(X!11))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X)))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))) | (~r1(Y!10, X!11)) | (~((~r1(X!11, tptp_fun_Y_3(X!11))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X)))))))),
% 1.96/2.23 inference(rewrite,[status(thm)],[])).
% 1.96/2.23 tff(137,plain,
% 1.96/2.23 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))) | ((~r1(Y!10, X!11)) | (~((~r1(X!11, tptp_fun_Y_3(X!11))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X)))))))),
% 1.96/2.23 inference(quant_inst,[status(thm)],[])).
% 1.96/2.23 tff(138,plain,
% 1.96/2.23 ((~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))) | (~r1(Y!10, X!11)) | (~((~r1(X!11, tptp_fun_Y_3(X!11))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X!11), X))))))),
% 1.96/2.23 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.96/2.23 tff(139,plain,
% 1.96/2.23 ($false),
% 1.96/2.23 inference(unit_resolution,[status(thm)],[138, 111, 135, 134])).
% 1.96/2.23 tff(140,plain,(~![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.23 tff(141,plain,
% 1.96/2.23 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))) <=> ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))))),
% 1.96/2.23 inference(bind,[status(th)],[])).
% 1.96/2.23 tff(142,plain,
% 1.96/2.23 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))),
% 1.96/2.23 inference(quant_intro,[status(thm)],[141])).
% 1.96/2.23 tff(143,plain,
% 1.96/2.23 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))) <=> ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))))),
% 1.96/2.23 inference(bind,[status(th)],[])).
% 1.96/2.23 tff(144,plain,
% 1.96/2.23 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))),
% 1.96/2.23 inference(quant_intro,[status(thm)],[143])).
% 1.96/2.23 tff(145,plain,
% 1.96/2.23 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))),
% 1.96/2.24 inference(transitivity,[status(thm)],[144, 142])).
% 1.96/2.24 tff(146,plain,
% 1.96/2.24 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) <=> ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))))),
% 1.96/2.24 inference(bind,[status(th)],[])).
% 1.96/2.24 tff(147,plain,
% 1.96/2.24 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))),
% 1.96/2.24 inference(quant_intro,[status(thm)],[146])).
% 1.96/2.24 tff(148,plain,
% 1.96/2.24 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_3(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))))))))),
% 1.96/2.24 inference(and_elim,[status(thm)],[70])).
% 1.96/2.24 tff(149,plain,
% 1.96/2.24 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))),
% 1.96/2.24 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.96/2.24 tff(150,plain,
% 1.96/2.24 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))),
% 1.96/2.24 inference(modus_ponens,[status(thm)],[149, 145])).
% 1.96/2.24 tff(151,plain,
% 1.96/2.24 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))),
% 1.96/2.24 inference(rewrite,[status(thm)],[])).
% 1.96/2.24 tff(152,plain,
% 1.96/2.24 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))) | ((~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))),
% 1.96/2.24 inference(quant_inst,[status(thm)],[])).
% 1.96/2.24 tff(153,plain,
% 1.96/2.24 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $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(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))))) | (~r1(X!0, Y!6)) | ![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))),
% 1.96/2.24 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.96/2.24 tff(154,plain,
% 1.96/2.24 (![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))),
% 1.96/2.24 inference(unit_resolution,[status(thm)],[153, 150, 79])).
% 1.96/2.24 tff(155,plain,
% 1.96/2.24 (((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))) <=> ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))) | (~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))),
% 1.96/2.24 inference(rewrite,[status(thm)],[])).
% 1.96/2.24 tff(156,plain,
% 1.96/2.24 ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))) | ((~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))),
% 1.96/2.24 inference(quant_inst,[status(thm)],[])).
% 1.96/2.24 tff(157,plain,
% 1.96/2.24 ((~![X: $i] : ((~r1(Y!6, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))))) | (~r1(Y!6, X!7)) | ![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))),
% 1.96/2.24 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.96/2.24 tff(158,plain,
% 1.96/2.24 (![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))),
% 1.96/2.24 inference(unit_resolution,[status(thm)],[157, 91, 154])).
% 1.96/2.24 tff(159,plain,
% 1.96/2.24 (((~![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))) | ((~r1(X!7, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))) <=> ((~![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))) | (~r1(X!7, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))),
% 1.96/2.24 inference(rewrite,[status(thm)],[])).
% 1.96/2.24 tff(160,plain,
% 1.96/2.24 ((~![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))) | ((~r1(X!7, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))),
% 1.96/2.24 inference(quant_inst,[status(thm)],[])).
% 1.96/2.24 tff(161,plain,
% 1.96/2.24 ((~![Y: $i] : ((~r1(X!7, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))))) | (~r1(X!7, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))),
% 1.96/2.24 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.96/2.24 tff(162,plain,
% 1.96/2.24 (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))),
% 1.96/2.24 inference(unit_resolution,[status(thm)],[161, 96, 158])).
% 1.96/2.24 tff(163,plain,
% 1.96/2.24 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))),
% 1.96/2.24 inference(rewrite,[status(thm)],[])).
% 1.96/2.24 tff(164,plain,
% 1.96/2.24 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))),
% 1.96/2.24 inference(quant_inst,[status(thm)],[])).
% 1.96/2.24 tff(165,plain,
% 1.96/2.24 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))),
% 1.96/2.24 inference(modus_ponens,[status(thm)],[164, 163])).
% 1.96/2.24 tff(166,plain,
% 1.96/2.24 (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))),
% 1.96/2.24 inference(unit_resolution,[status(thm)],[165, 101, 162])).
% 1.96/2.24 tff(167,plain,
% 1.96/2.24 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))),
% 1.96/2.24 inference(rewrite,[status(thm)],[])).
% 1.96/2.24 tff(168,plain,
% 1.96/2.24 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))),
% 1.96/2.24 inference(quant_inst,[status(thm)],[])).
% 1.96/2.24 tff(169,plain,
% 1.96/2.24 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X))))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))),
% 1.96/2.26 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.96/2.26 tff(170,plain,
% 1.96/2.26 (![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X)))))) | ![X: $i] : ((~r1(Y!10, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_3(X), X)))))))),
% 1.96/2.26 inference(unit_resolution,[status(thm)],[169, 106, 166])).
% 1.96/2.26 tff(171,plain,
% 1.96/2.26 (![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))),
% 1.96/2.26 inference(unit_resolution,[status(thm)],[170, 140])).
% 1.96/2.26 tff(172,plain,
% 1.96/2.26 (((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))) | ((~r1(Y!10, Y!10)) | (~(p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))) | (~r1(Y!10, Y!10)) | (~(p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10))))))),
% 1.96/2.26 inference(rewrite,[status(thm)],[])).
% 1.96/2.26 tff(173,plain,
% 1.96/2.26 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))) | ((~r1(Y!10, Y!10)) | (~(p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10))))))),
% 1.96/2.26 inference(quant_inst,[status(thm)],[])).
% 1.96/2.26 tff(174,plain,
% 1.96/2.26 ((~![X: $i] : ((~r1(Y!10, X)) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))))))) | (~r1(Y!10, Y!10)) | (~(p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10)))))),
% 1.96/2.26 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.96/2.26 tff(175,plain,
% 1.96/2.26 (~(p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10))))),
% 1.96/2.26 inference(unit_resolution,[status(thm)],[174, 171, 11])).
% 1.96/2.26 tff(176,plain,
% 1.96/2.26 ((p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10)))) | r1(Y!10, tptp_fun_Y_4(Y!10))),
% 1.96/2.26 inference(tautology,[status(thm)],[])).
% 1.96/2.26 tff(177,plain,
% 1.96/2.26 (r1(Y!10, tptp_fun_Y_4(Y!10))),
% 1.96/2.26 inference(unit_resolution,[status(thm)],[176, 175])).
% 1.96/2.26 tff(178,plain,
% 1.96/2.26 ((p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10)))) | (~p1(tptp_fun_Y_4(Y!10)))),
% 1.96/2.26 inference(tautology,[status(thm)],[])).
% 1.96/2.26 tff(179,plain,
% 1.96/2.26 (~p1(tptp_fun_Y_4(Y!10))),
% 1.96/2.26 inference(unit_resolution,[status(thm)],[178, 175])).
% 1.96/2.26 tff(180,plain,
% 1.96/2.26 (^[X: $i] : refl((p1(X) | (~r1(Y!10, X))) <=> (p1(X) | (~r1(Y!10, X))))),
% 1.96/2.26 inference(bind,[status(th)],[])).
% 1.96/2.26 tff(181,plain,
% 1.96/2.26 (![X: $i] : (p1(X) | (~r1(Y!10, X))) <=> ![X: $i] : (p1(X) | (~r1(Y!10, X)))),
% 1.96/2.26 inference(quant_intro,[status(thm)],[180])).
% 1.96/2.26 tff(182,plain,
% 1.96/2.26 (![X: $i] : (p1(X) | (~r1(Y!10, X)))),
% 1.96/2.26 inference(and_elim,[status(thm)],[70])).
% 1.96/2.26 tff(183,plain,
% 1.96/2.26 (![X: $i] : (p1(X) | (~r1(Y!10, X)))),
% 1.96/2.26 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.96/2.26 tff(184,plain,
% 1.96/2.26 (((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | (p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10))))),
% 1.96/2.26 inference(rewrite,[status(thm)],[])).
% 1.96/2.26 tff(185,plain,
% 1.96/2.26 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | (p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10))))),
% 1.96/2.26 inference(quant_inst,[status(thm)],[])).
% 1.96/2.26 tff(186,plain,
% 1.96/2.26 ((~![X: $i] : (p1(X) | (~r1(Y!10, X)))) | p1(tptp_fun_Y_4(Y!10)) | (~r1(Y!10, tptp_fun_Y_4(Y!10)))),
% 1.96/2.26 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.96/2.26 tff(187,plain,
% 1.96/2.26 ($false),
% 1.96/2.26 inference(unit_resolution,[status(thm)],[186, 183, 179, 177])).
% 1.96/2.26 % SZS output end Proof
% 1.96/2.27 % E exiting
%------------------------------------------------------------------------------