%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL660+1.010 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:28 PM UTC 2026
% Result : Theorem 0.81s 1.09s
% Output : Proof 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL660+1.010 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.38 % Computer : n009.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 5 18:31:23 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.81/1.09 % SZS status Theorem
% 0.81/1.09 % SZS output start Proof
% 0.81/1.09 tff(r1_type, type, (
% 0.81/1.09 r1: ( $i * $i ) > $o)).
% 0.81/1.09 tff(tptp_fun_Y_14_type, type, (
% 0.81/1.09 tptp_fun_Y_14: $i > $i)).
% 0.81/1.09 tff(tptp_fun_X_12_type, type, (
% 0.81/1.09 tptp_fun_X_12: $i)).
% 0.81/1.09 tff(p2_type, type, (
% 0.81/1.09 p2: $i > $o)).
% 0.81/1.09 tff(tptp_fun_X_15_type, type, (
% 0.81/1.09 tptp_fun_X_15: $i > $i)).
% 0.81/1.09 tff(tptp_fun_Y_17_type, type, (
% 0.81/1.09 tptp_fun_Y_17: $i > $i)).
% 0.81/1.09 tff(tptp_fun_X_18_type, type, (
% 0.81/1.09 tptp_fun_X_18: $i > $i)).
% 0.81/1.09 tff(tptp_fun_Y_5_type, type, (
% 0.81/1.09 tptp_fun_Y_5: $i > $i)).
% 0.81/1.09 tff(tptp_fun_X_4_type, type, (
% 0.81/1.09 tptp_fun_X_4: $i > $i)).
% 0.81/1.09 tff(tptp_fun_Y_13_type, type, (
% 0.81/1.09 tptp_fun_Y_13: $i)).
% 0.81/1.09 tff(tptp_fun_Y_11_type, type, (
% 0.81/1.09 tptp_fun_Y_11: $i)).
% 0.81/1.09 tff(tptp_fun_X_16_type, type, (
% 0.81/1.09 tptp_fun_X_16: $i > $i)).
% 0.81/1.09 tff(tptp_fun_X_0_type, type, (
% 0.81/1.09 tptp_fun_X_0: $i)).
% 0.81/1.09 tff(tptp_fun_Y_19_type, type, (
% 0.81/1.09 tptp_fun_Y_19: $i)).
% 0.81/1.09 tff(tptp_fun_X_21_type, type, (
% 0.81/1.09 tptp_fun_X_21: $i)).
% 0.81/1.09 tff(tptp_fun_Y_20_type, type, (
% 0.81/1.09 tptp_fun_Y_20: $i)).
% 0.81/1.09 tff(tptp_fun_Y_3_type, type, (
% 0.81/1.09 tptp_fun_Y_3: $i)).
% 0.81/1.09 tff(tptp_fun_X_6_type, type, (
% 0.81/1.09 tptp_fun_X_6: $i > $i)).
% 0.81/1.09 tff(p5_type, type, (
% 0.81/1.09 p5: $i > $o)).
% 0.81/1.09 tff(tptp_fun_Y_45_type, type, (
% 0.81/1.09 tptp_fun_Y_45: $i > $i)).
% 0.81/1.09 tff(p1_type, type, (
% 0.81/1.09 p1: $i > $o)).
% 0.81/1.09 tff(tptp_fun_Y_50_type, type, (
% 0.81/1.09 tptp_fun_Y_50: $i)).
% 0.81/1.09 tff(tptp_fun_X_51_type, type, (
% 0.81/1.09 tptp_fun_X_51: $i)).
% 0.81/1.09 tff(tptp_fun_Y_48_type, type, (
% 0.81/1.09 tptp_fun_Y_48: $i)).
% 0.81/1.09 tff(tptp_fun_X_49_type, type, (
% 0.81/1.09 tptp_fun_X_49: $i)).
% 0.81/1.09 tff(p3_type, type, (
% 0.81/1.09 p3: $i > $o)).
% 0.81/1.09 tff(tptp_fun_Y_46_type, type, (
% 0.81/1.09 tptp_fun_Y_46: $i)).
% 0.81/1.09 tff(tptp_fun_X_47_type, type, (
% 0.81/1.09 tptp_fun_X_47: $i)).
% 0.81/1.09 tff(p4_type, type, (
% 0.81/1.09 p4: $i > $o)).
% 0.81/1.09 tff(tptp_fun_Y_43_type, type, (
% 0.81/1.09 tptp_fun_Y_43: $i)).
% 0.81/1.09 tff(tptp_fun_X_44_type, type, (
% 0.81/1.09 tptp_fun_X_44: $i)).
% 0.81/1.09 tff(tptp_fun_X_33_type, type, (
% 0.81/1.09 tptp_fun_X_33: $i > $i)).
% 0.81/1.09 tff(tptp_fun_Y_32_type, type, (
% 0.81/1.09 tptp_fun_Y_32: $i > $i)).
% 0.81/1.09 tff(tptp_fun_Y_40_type, type, (
% 0.81/1.09 tptp_fun_Y_40: $i)).
% 0.81/1.09 tff(tptp_fun_Y_42_type, type, (
% 0.81/1.09 tptp_fun_Y_42: $i)).
% 0.81/1.09 tff(tptp_fun_X_41_type, type, (
% 0.81/1.09 tptp_fun_X_41: $i)).
% 0.81/1.09 tff(tptp_fun_Y_37_type, type, (
% 0.81/1.09 tptp_fun_Y_37: $i)).
% 0.81/1.10 tff(tptp_fun_Y_39_type, type, (
% 0.81/1.10 tptp_fun_Y_39: $i)).
% 0.81/1.10 tff(tptp_fun_X_38_type, type, (
% 0.81/1.10 tptp_fun_X_38: $i)).
% 0.81/1.10 tff(tptp_fun_Y_34_type, type, (
% 0.81/1.10 tptp_fun_Y_34: $i)).
% 0.81/1.10 tff(tptp_fun_Y_36_type, type, (
% 0.81/1.10 tptp_fun_Y_36: $i)).
% 0.81/1.10 tff(tptp_fun_X_35_type, type, (
% 0.81/1.10 tptp_fun_X_35: $i)).
% 0.81/1.10 tff(tptp_fun_Y_29_type, type, (
% 0.81/1.10 tptp_fun_Y_29: $i)).
% 0.81/1.10 tff(tptp_fun_Y_31_type, type, (
% 0.81/1.10 tptp_fun_Y_31: $i)).
% 0.81/1.10 tff(tptp_fun_X_30_type, type, (
% 0.81/1.10 tptp_fun_X_30: $i)).
% 0.81/1.10 tff(tptp_fun_Y_28_type, type, (
% 0.81/1.10 tptp_fun_Y_28: $i > $i)).
% 0.81/1.10 tff(tptp_fun_X_27_type, type, (
% 0.81/1.10 tptp_fun_X_27: $i > $i)).
% 0.81/1.10 tff(tptp_fun_Y_26_type, type, (
% 0.81/1.10 tptp_fun_Y_26: $i > $i)).
% 0.81/1.10 tff(tptp_fun_Y_22_type, type, (
% 0.81/1.10 tptp_fun_Y_22: $i)).
% 0.81/1.10 tff(tptp_fun_X_25_type, type, (
% 0.81/1.10 tptp_fun_X_25: $i)).
% 0.81/1.10 tff(tptp_fun_Y_24_type, type, (
% 0.81/1.10 tptp_fun_Y_24: $i)).
% 0.81/1.10 tff(tptp_fun_X_23_type, type, (
% 0.81/1.10 tptp_fun_X_23: $i)).
% 0.81/1.10 tff(tptp_fun_Y_10_type, type, (
% 0.81/1.10 tptp_fun_Y_10: $i > $i)).
% 0.81/1.10 tff(tptp_fun_X_9_type, type, (
% 0.81/1.10 tptp_fun_X_9: $i > $i)).
% 0.81/1.10 tff(tptp_fun_Y_8_type, type, (
% 0.81/1.10 tptp_fun_Y_8: $i > $i)).
% 0.81/1.10 tff(tptp_fun_X_7_type, type, (
% 0.81/1.10 tptp_fun_X_7: $i > $i)).
% 0.81/1.10 tff(tptp_fun_Y_2_type, type, (
% 0.81/1.10 tptp_fun_Y_2: $i)).
% 0.81/1.10 tff(tptp_fun_Y_1_type, type, (
% 0.81/1.10 tptp_fun_Y_1: $i)).
% 0.81/1.10 tff(1,assumption,(![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))), introduced(assumption)).
% 0.81/1.10 tff(2,assumption,(~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))), introduced(assumption)).
% 0.81/1.10 tff(3,plain,
% 0.81/1.10 (((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))) | r1(Y!13, tptp_fun_X_4(Y!13))),
% 0.81/1.10 inference(tautology,[status(thm)],[])).
% 0.81/1.10 tff(4,plain,
% 0.81/1.10 (r1(Y!13, tptp_fun_X_4(Y!13))),
% 0.81/1.10 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.81/1.10 tff(5,plain,
% 0.81/1.10 (((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))) | p2(tptp_fun_X_4(Y!13))),
% 0.81/1.10 inference(tautology,[status(thm)],[])).
% 0.81/1.10 tff(6,plain,
% 0.81/1.10 (p2(tptp_fun_X_4(Y!13))),
% 0.81/1.10 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.81/1.10 tff(7,assumption,(~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))), introduced(assumption)).
% 0.81/1.10 tff(8,plain,
% 0.81/1.10 ((p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | r1(X!0, Y!19)),
% 0.81/1.10 inference(tautology,[status(thm)],[])).
% 0.81/1.10 tff(9,plain,
% 0.81/1.10 (r1(X!0, Y!19)),
% 0.81/1.10 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.81/1.10 tff(10,plain,
% 0.81/1.10 ((p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | (~p2(Y!19))),
% 0.81/1.10 inference(tautology,[status(thm)],[])).
% 0.81/1.10 tff(11,plain,
% 0.81/1.10 (~p2(Y!19)),
% 0.81/1.10 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.81/1.10 tff(12,assumption,(~r1(X!0, X!0)), introduced(assumption)).
% 0.81/1.10 tff(13,plain,
% 0.81/1.10 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.81/1.10 inference(bind,[status(th)],[])).
% 0.81/1.10 tff(14,plain,
% 0.81/1.10 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.81/1.10 inference(quant_intro,[status(thm)],[13])).
% 0.81/1.10 tff(15,plain,
% 0.81/1.10 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.81/1.10 inference(rewrite,[status(thm)],[])).
% 0.81/1.10 tff(16,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity')).
% 0.81/1.10 tff(17,plain,
% 0.81/1.10 (![X: $i] : r1(X, X)),
% 0.81/1.10 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.81/1.10 tff(18,plain,(
% 0.81/1.10 ![X: $i] : r1(X, X)),
% 0.81/1.10 inference(skolemize,[status(sab)],[17])).
% 0.81/1.10 tff(19,plain,
% 0.81/1.10 (![X: $i] : r1(X, X)),
% 0.81/1.10 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.81/1.10 tff(20,plain,
% 0.81/1.10 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.81/1.10 inference(quant_inst,[status(thm)],[])).
% 0.81/1.10 tff(21,plain,
% 0.81/1.10 ($false),
% 0.81/1.10 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.81/1.10 tff(22,plain,(r1(X!0, X!0)), inference(lemma,lemma(discharge,[]))).
% 0.81/1.10 tff(23,assumption,(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))), introduced(assumption)).
% 0.81/1.10 tff(24,plain,
% 0.81/1.10 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.81/1.10 inference(rewrite,[status(thm)],[])).
% 0.81/1.10 tff(25,plain,
% 0.81/1.10 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) <=> (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.81/1.10 inference(rewrite,[status(thm)],[])).
% 0.81/1.10 tff(26,plain,
% 0.81/1.10 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> (p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))),
% 0.81/1.10 inference(monotonicity,[status(thm)],[25])).
% 0.81/1.10 tff(27,plain,
% 0.81/1.10 ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.81/1.10 inference(monotonicity,[status(thm)],[26])).
% 0.81/1.10 tff(28,plain,
% 0.81/1.10 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.81/1.10 inference(monotonicity,[status(thm)],[27])).
% 0.81/1.10 tff(29,plain,
% 0.81/1.10 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.81/1.10 inference(transitivity,[status(thm)],[28, 24])).
% 0.81/1.10 tff(30,plain,
% 0.81/1.10 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.81/1.10 inference(rewrite,[status(thm)],[])).
% 0.81/1.10 tff(31,plain,
% 0.81/1.10 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.81/1.10 inference(rewrite,[status(thm)],[])).
% 0.81/1.10 tff(32,plain,
% 0.81/1.10 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) <=> (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.81/1.10 inference(rewrite,[status(thm)],[])).
% 0.81/1.10 tff(33,plain,
% 0.81/1.10 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.81/1.10 inference(bind,[status(th)],[])).
% 0.81/1.10 tff(34,plain,
% 0.81/1.10 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.81/1.10 inference(quant_intro,[status(thm)],[33])).
% 0.81/1.10 tff(35,plain,
% 0.81/1.10 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.81/1.10 inference(monotonicity,[status(thm)],[34])).
% 0.81/1.10 tff(36,plain,
% 0.81/1.10 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.81/1.10 inference(transitivity,[status(thm)],[35, 32])).
% 0.81/1.10 tff(37,plain,
% 0.81/1.10 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.81/1.10 inference(monotonicity,[status(thm)],[36])).
% 0.81/1.10 tff(38,plain,
% 0.81/1.10 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.81/1.10 inference(transitivity,[status(thm)],[37, 31])).
% 0.81/1.10 tff(39,plain,
% 0.81/1.10 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & ((((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & r1(X, tptp_fun_Y_17(X)) & (~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & r1(X, tptp_fun_Y_17(X)) & (~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 0.81/1.11 inference(rewrite,[status(thm)],[])).
% 0.81/1.11 tff(40,plain,
% 0.81/1.11 ((((r1(X!0, Y!11) & (((r1(Y!11, X!12) & ((~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & (r1(X, tptp_fun_Y_17(X)) & ((~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) | ((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21)))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!22) & (~p1(Y!22)) & ((~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & ((~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25))) & ![X: $i] : ((~r1(Y!22, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & ((~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & ((~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31)) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & ((~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36)) & ![X: $i] : ((~r1(Y!34, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & ((~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39)) & ![X: $i] : ((~r1(Y!37, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!40) & (~p1(Y!40)) & ((~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42)) & ![X: $i] : ((~r1(Y!40, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : ((~r1(Y!43, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : ((~r1(Y!46, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : ((~r1(Y!48, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : ((~r1(Y!50, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) <=> ((((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & r1(X, tptp_fun_Y_17(X)) & (~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 0.81/1.12 inference(rewrite,[status(thm)],[])).
% 0.81/1.12 tff(41,plain,
% 0.81/1.12 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))) <=> (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))), ((r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))) <=> (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))), (((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))))), rewrite(((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))), (((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))))),
% 0.81/1.12 inference(bind,[status(th)],[])).
% 0.81/1.12 tff(42,plain,
% 0.81/1.12 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y))))))),
% 0.81/1.12 inference(quant_intro,[status(thm)],[41])).
% 0.81/1.12 tff(43,plain,
% 0.81/1.12 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))) <=> (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y))))), ((r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y))))) <=> (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y))))))), (((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))))), rewrite(((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y))))))), (((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y))))))))),
% 0.81/1.12 inference(bind,[status(th)],[])).
% 0.81/1.12 tff(44,plain,
% 0.81/1.12 (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) <=> ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y))))))),
% 0.81/1.12 inference(quant_intro,[status(thm)],[43])).
% 0.81/1.12 tff(45,plain,
% 0.81/1.12 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.81/1.12 inference(rewrite,[status(thm)],[])).
% 0.81/1.12 tff(46,plain,
% 0.81/1.12 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) <=> ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))),
% 0.81/1.12 inference(rewrite,[status(thm)],[])).
% 0.81/1.12 tff(47,plain,
% 0.81/1.12 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.81/1.12 inference(monotonicity,[status(thm)],[46])).
% 0.81/1.12 tff(48,plain,
% 0.81/1.12 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.81/1.12 inference(transitivity,[status(thm)],[47, 45])).
% 0.81/1.12 tff(49,plain,
% 0.81/1.12 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.81/1.12 inference(rewrite,[status(thm)],[])).
% 0.81/1.12 tff(50,plain,
% 0.81/1.12 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.81/1.12 inference(monotonicity,[status(thm)],[46])).
% 0.81/1.12 tff(51,plain,
% 0.81/1.12 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.81/1.12 inference(transitivity,[status(thm)],[50, 49])).
% 0.81/1.12 tff(52,plain,
% 0.81/1.12 ((~((~r1(X!0, Y!2)) | p1(Y!2))) <=> (~((~r1(X!0, Y!2)) | p1(Y!2)))),
% 0.81/1.12 inference(rewrite,[status(thm)],[])).
% 0.81/1.13 tff(53,plain,
% 0.81/1.13 ((~((~r1(X!0, Y!1)) | p3(Y!1))) <=> (~((~r1(X!0, Y!1)) | p3(Y!1)))),
% 0.81/1.13 inference(rewrite,[status(thm)],[])).
% 0.81/1.13 tff(54,plain,
% 0.81/1.13 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((r1(X!0, Y!11) & (((r1(Y!11, X!12) & ((~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & (r1(X, tptp_fun_Y_17(X)) & ((~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) | ((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21)))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!22) & (~p1(Y!22)) & ((~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & ((~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25))) & ![X: $i] : ((~r1(Y!22, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & ((~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & ((~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31)) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & ((~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36)) & ![X: $i] : ((~r1(Y!34, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & ((~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39)) & ![X: $i] : ((~r1(Y!37, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!40) & (~p1(Y!40)) & ((~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42)) & ![X: $i] : ((~r1(Y!40, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : ((~r1(Y!43, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : ((~r1(Y!46, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : ((~r1(Y!48, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : ((~r1(Y!50, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & ((((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & r1(X, tptp_fun_Y_17(X)) & (~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.81/1.14 inference(monotonicity,[status(thm)],[53, 52, 51, 48, 44, 42, 40])).
% 0.81/1.14 tff(55,plain,
% 0.81/1.14 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((r1(X!0, Y!11) & (((r1(Y!11, X!12) & ((~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & (r1(X, tptp_fun_Y_17(X)) & ((~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) | ((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21)))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!22) & (~p1(Y!22)) & ((~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & ((~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25))) & ![X: $i] : ((~r1(Y!22, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & ((~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & ((~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31)) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & ((~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36)) & ![X: $i] : ((~r1(Y!34, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & ((~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39)) & ![X: $i] : ((~r1(Y!37, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!40) & (~p1(Y!40)) & ((~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42)) & ![X: $i] : ((~r1(Y!40, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : ((~r1(Y!43, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : ((~r1(Y!46, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : ((~r1(Y!48, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : ((~r1(Y!50, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & r1(X, tptp_fun_Y_17(X)) & (~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 0.81/1.15 inference(transitivity,[status(thm)],[54, 39])).
% 0.81/1.15 tff(56,plain,
% 0.81/1.15 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(57,plain,
% 0.91/1.16 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 0.91/1.17 inference(rewrite,[status(thm)],[])).
% 0.91/1.17 tff(58,plain,
% 0.91/1.17 ((~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))))),
% 0.91/1.18 inference(rewrite,[status(thm)],[])).
% 0.91/1.18 tff(59,plain,
% 0.91/1.18 ((~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))))),
% 0.91/1.18 inference(monotonicity,[status(thm)],[58])).
% 0.91/1.18 tff(60,plain,
% 0.91/1.18 ((~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 0.91/1.19 inference(transitivity,[status(thm)],[59, 57])).
% 0.91/1.19 tff(61,axiom,(~(~?[X: $i] : (~((((((((~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(X)))))) & (![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.91/1.20 tff(62,plain,
% 0.91/1.20 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 0.96/1.20 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.96/1.20 tff(63,plain,
% 0.96/1.20 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ((~![Y: $i] : ((~p5(Y)) | (~r1(X, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | ((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p5(X)) | (~r1(Y, X)))))) & (![Y: $i] : (p2(Y) | (~r1(X, Y))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(Y) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))))) | (~(((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))))) | (((~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p2(X)) | (~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p3(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~![X: $i] : (p2(X) | (~r1(Y, X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))))))),
% 0.96/1.21 inference(modus_ponens,[status(thm)],[62, 56])).
% 0.96/1.21 tff(64,plain,
% 0.96/1.21 ((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_7(Y)) & p3(tptp_fun_X_7(Y)) & (~((~r1(tptp_fun_X_7(Y), tptp_fun_Y_8(Y))) | p3(tptp_fun_Y_8(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p1(tptp_fun_Y_10(Y)))))) & (((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & r1(X, tptp_fun_Y_17(X)) & (~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!22) & (~p1(Y!22)) & (~p2(X!23)) & r1(Y!22, X!23) & (~p3(X!23)) & (~p1(X!23)) & (~p4(X!23)) & (~p2(Y!24)) & r1(X!23, Y!24) & (~p3(Y!24)) & (~p1(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!22, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_26(X))) & r1(X, tptp_fun_Y_26(X)) & (~p3(tptp_fun_Y_26(X))) & (~p1(tptp_fun_Y_26(X))) & (~p4(tptp_fun_Y_26(X))) & (~p2(tptp_fun_X_27(X))) & r1(tptp_fun_Y_26(X), tptp_fun_X_27(X)) & (~p3(tptp_fun_X_27(X))) & (~p1(tptp_fun_X_27(X))) & (~p4(tptp_fun_X_27(X))) & r1(tptp_fun_X_27(X), tptp_fun_Y_28(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!29)) & r1(X!0, Y!29) & (~p3(Y!29)) & (~p1(Y!29)) & (~p4(Y!29)) & (~p2(X!30)) & r1(Y!29, X!30) & (~p3(X!30)) & (~p1(X!30)) & (~p4(X!30)) & r1(X!30, Y!31) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!29, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!34)) & r1(X!0, Y!34) & (~p3(Y!34)) & (~p1(Y!34)) & (~p2(X!35)) & r1(Y!34, X!35) & (~p3(X!35)) & (~p1(X!35)) & (~p4(X!35)) & r1(X!35, Y!36) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!34, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(Y!37)) & r1(X!0, Y!37) & (~p1(Y!37)) & (~p2(X!38)) & r1(Y!37, X!38) & (~p3(X!38)) & (~p1(X!38)) & (~p4(X!38)) & r1(X!38, Y!39) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!37, X)) | ((~p2(X)) & (~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | ![Y: $i] : (p2(Y) | p3(Y) | p1(Y) | (~r1(X!0, Y)) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!40) & (~p1(Y!40)) & (~p2(X!41)) & r1(Y!40, X!41) & (~p3(X!41)) & (~p1(X!41)) & (~p4(X!41)) & r1(X!41, Y!42) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p2(X) | (~r1(Y, X)) | p3(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!40, X)) | ((~p1(X)) & (~p2(tptp_fun_Y_32(X))) & r1(X, tptp_fun_Y_32(X)) & (~p3(tptp_fun_Y_32(X))) & (~p1(tptp_fun_Y_32(X))) & (~p4(tptp_fun_Y_32(X))) & r1(tptp_fun_Y_32(X), tptp_fun_X_33(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!43)) & r1(X!0, Y!43) & (~p3(Y!43)) & (~p1(Y!43)) & (~p4(Y!43)) & r1(Y!43, X!44) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!43, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!46)) & r1(X!0, Y!46) & (~p3(Y!46)) & (~p1(Y!46)) & r1(Y!46, X!47) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!46, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!48)) & r1(X!0, Y!48) & (~p1(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_45(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 0.96/1.21 inference(modus_ponens,[status(thm)],[63, 55])).
% 0.96/1.21 tff(65,plain,
% 0.96/1.21 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))),
% 0.96/1.21 inference(and_elim,[status(thm)],[64])).
% 0.96/1.21 tff(66,plain,
% 0.96/1.21 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.96/1.21 inference(modus_ponens,[status(thm)],[65, 38])).
% 0.96/1.21 tff(67,plain,
% 0.96/1.21 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.96/1.21 inference(modus_ponens,[status(thm)],[66, 30])).
% 0.96/1.21 tff(68,plain,
% 0.96/1.21 ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.96/1.21 inference(modus_ponens,[status(thm)],[67, 29])).
% 0.96/1.21 tff(69,plain,
% 0.96/1.21 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.96/1.21 inference(unit_resolution,[status(thm)],[68, 23])).
% 0.96/1.21 tff(70,plain,
% 0.96/1.21 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | ((~r1(X!0, X!0)) | (~((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~r1(X!0, X!0)) | (~((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))))),
% 0.96/1.21 inference(rewrite,[status(thm)],[])).
% 0.96/1.21 tff(71,plain,
% 0.96/1.21 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | ((~r1(X!0, X!0)) | (~((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))))),
% 0.96/1.21 inference(quant_inst,[status(thm)],[])).
% 0.96/1.21 tff(72,plain,
% 0.96/1.21 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~r1(X!0, X!0)) | (~((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))))),
% 0.96/1.21 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.96/1.21 tff(73,plain,
% 0.96/1.21 (~((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))),
% 0.96/1.21 inference(unit_resolution,[status(thm)],[72, 69, 22])).
% 0.96/1.21 tff(74,plain,
% 0.96/1.21 (((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))) | r1(X!0, tptp_fun_X_6(X!0))),
% 0.96/1.21 inference(tautology,[status(thm)],[])).
% 0.96/1.21 tff(75,plain,
% 0.96/1.21 (r1(X!0, tptp_fun_X_6(X!0))),
% 0.96/1.21 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.96/1.21 tff(76,plain,
% 0.96/1.21 (((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))) | p5(tptp_fun_X_6(X!0))),
% 0.96/1.21 inference(tautology,[status(thm)],[])).
% 0.96/1.21 tff(77,plain,
% 0.96/1.21 (p5(tptp_fun_X_6(X!0))),
% 0.96/1.21 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.96/1.21 tff(78,plain,
% 0.96/1.21 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.96/1.21 inference(rewrite,[status(thm)],[])).
% 0.96/1.21 tff(79,plain,
% 0.96/1.21 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.96/1.21 inference(rewrite,[status(thm)],[])).
% 0.96/1.21 tff(80,plain,
% 0.96/1.21 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.96/1.21 inference(monotonicity,[status(thm)],[36])).
% 0.96/1.21 tff(81,plain,
% 0.96/1.21 ((![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) <=> (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.96/1.21 inference(transitivity,[status(thm)],[80, 79])).
% 0.96/1.21 tff(82,plain,
% 0.96/1.21 (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | ((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))),
% 0.96/1.21 inference(and_elim,[status(thm)],[64])).
% 0.96/1.21 tff(83,plain,
% 0.96/1.21 (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.96/1.22 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.96/1.22 tff(84,plain,
% 0.96/1.22 (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y))) | (~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.96/1.22 inference(modus_ponens,[status(thm)],[83, 78])).
% 0.96/1.22 tff(85,plain,
% 0.96/1.22 (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[84, 23])).
% 0.96/1.22 tff(86,plain,
% 0.96/1.22 (((~![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))) | ((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))) <=> ((~![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))) | (~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(87,plain,
% 0.96/1.22 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))) | ((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))),
% 0.96/1.22 inference(quant_inst,[status(thm)],[])).
% 0.96/1.22 tff(88,plain,
% 0.96/1.22 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))) | (~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))),
% 0.96/1.22 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.96/1.22 tff(89,plain,
% 0.96/1.22 ($false),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[88, 85, 77, 75])).
% 0.96/1.22 tff(90,plain,(~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.22 tff(91,plain,
% 0.96/1.22 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.96/1.22 inference(tautology,[status(thm)],[])).
% 0.96/1.22 tff(92,plain,
% 0.96/1.22 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.96/1.22 tff(93,plain,
% 0.96/1.22 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19))))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(94,plain,
% 0.96/1.22 ((p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19)))))) <=> (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19))))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(95,plain,
% 0.96/1.22 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19)))))))),
% 0.96/1.22 inference(monotonicity,[status(thm)],[94])).
% 0.96/1.22 tff(96,plain,
% 0.96/1.22 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19))))))),
% 0.96/1.22 inference(transitivity,[status(thm)],[95, 93])).
% 0.96/1.22 tff(97,plain,
% 0.96/1.22 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))))),
% 0.96/1.22 inference(quant_inst,[status(thm)],[])).
% 0.96/1.22 tff(98,plain,
% 0.96/1.22 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19)))))),
% 0.96/1.22 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.96/1.22 tff(99,plain,
% 0.96/1.22 (~((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19))))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[98, 92, 11, 9])).
% 0.96/1.22 tff(100,plain,
% 0.96/1.22 (((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19)))) | p2(tptp_fun_X_4(Y!19))),
% 0.96/1.22 inference(tautology,[status(thm)],[])).
% 0.96/1.22 tff(101,plain,
% 0.96/1.22 (p2(tptp_fun_X_4(Y!19))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.96/1.22 tff(102,plain,
% 0.96/1.22 (((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19)))) | r1(Y!19, tptp_fun_X_4(Y!19))),
% 0.96/1.22 inference(tautology,[status(thm)],[])).
% 0.96/1.22 tff(103,plain,
% 0.96/1.22 (r1(Y!19, tptp_fun_X_4(Y!19))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.96/1.22 tff(104,plain,
% 0.96/1.22 ((p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.96/1.22 inference(tautology,[status(thm)],[])).
% 0.96/1.22 tff(105,plain,
% 0.96/1.22 (![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[104, 7])).
% 0.96/1.22 tff(106,plain,
% 0.96/1.22 (((~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!19))) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(107,plain,
% 0.96/1.22 ((~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!19))) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y))))),
% 0.96/1.22 inference(quant_inst,[status(thm)],[])).
% 0.96/1.22 tff(108,plain,
% 0.96/1.22 ((~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))),
% 0.96/1.22 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.96/1.22 tff(109,plain,
% 0.96/1.22 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[108, 105, 103, 101])).
% 0.96/1.22 tff(110,plain,
% 0.96/1.22 (((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19)))) | (~p2(tptp_fun_Y_5(Y!19)))),
% 0.96/1.22 inference(tautology,[status(thm)],[])).
% 0.96/1.22 tff(111,plain,
% 0.96/1.22 (~p2(tptp_fun_Y_5(Y!19))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[110, 99])).
% 0.96/1.22 tff(112,plain,
% 0.96/1.22 (((~r1(Y!19, tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~p2(tptp_fun_X_4(Y!19)))) | r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))),
% 0.96/1.22 inference(tautology,[status(thm)],[])).
% 0.96/1.22 tff(113,plain,
% 0.96/1.22 (r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[112, 99])).
% 0.96/1.22 tff(114,plain,
% 0.96/1.22 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))) | (p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(115,plain,
% 0.96/1.22 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))) | (p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))),
% 0.96/1.22 inference(quant_inst,[status(thm)],[])).
% 0.96/1.22 tff(116,plain,
% 0.96/1.22 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19)))),
% 0.96/1.22 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.96/1.22 tff(117,plain,
% 0.96/1.22 ($false),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[116, 113, 111, 109])).
% 0.96/1.22 tff(118,plain,(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.22 tff(119,assumption,(![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))), introduced(assumption)).
% 0.96/1.22 tff(120,assumption,(~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))), introduced(assumption)).
% 0.96/1.22 tff(121,plain,
% 0.96/1.22 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))) | p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.96/1.22 inference(tautology,[status(thm)],[])).
% 0.96/1.22 tff(122,plain,
% 0.96/1.22 (p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.96/1.22 tff(123,plain,
% 0.96/1.22 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))) | r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.96/1.22 inference(tautology,[status(thm)],[])).
% 0.96/1.22 tff(124,plain,
% 0.96/1.22 (r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[123, 120])).
% 0.96/1.22 tff(125,plain,
% 0.96/1.22 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))),
% 0.96/1.22 inference(bind,[status(th)],[])).
% 0.96/1.22 tff(126,plain,
% 0.96/1.22 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.96/1.22 inference(quant_intro,[status(thm)],[125])).
% 0.96/1.22 tff(127,plain,
% 0.96/1.22 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))),
% 0.96/1.22 inference(bind,[status(th)],[])).
% 0.96/1.22 tff(128,plain,
% 0.96/1.22 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.96/1.22 inference(quant_intro,[status(thm)],[127])).
% 0.96/1.22 tff(129,plain,
% 0.96/1.22 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.96/1.22 inference(transitivity,[status(thm)],[128, 126])).
% 0.96/1.22 tff(130,plain,
% 0.96/1.22 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))))),
% 0.96/1.22 inference(bind,[status(th)],[])).
% 0.96/1.22 tff(131,plain,
% 0.96/1.22 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.96/1.22 inference(quant_intro,[status(thm)],[130])).
% 0.96/1.22 tff(132,plain,
% 0.96/1.22 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 0.96/1.22 inference(and_elim,[status(thm)],[64])).
% 0.96/1.22 tff(133,plain,
% 0.96/1.22 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.96/1.22 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.96/1.22 tff(134,plain,
% 0.96/1.22 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.96/1.22 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.96/1.22 tff(135,plain,
% 0.96/1.22 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | r1(X!0, Y!3)),
% 0.96/1.22 inference(tautology,[status(thm)],[])).
% 0.96/1.22 tff(136,plain,
% 0.96/1.22 (r1(X!0, Y!3)),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[135, 90])).
% 0.96/1.22 tff(137,plain,
% 0.96/1.22 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | (~p2(Y!3))),
% 0.96/1.22 inference(tautology,[status(thm)],[])).
% 0.96/1.22 tff(138,plain,
% 0.96/1.22 (~p2(Y!3)),
% 0.96/1.22 inference(unit_resolution,[status(thm)],[137, 90])).
% 0.96/1.22 tff(139,plain,
% 0.96/1.22 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | (p2(Y!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | p2(Y!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(140,plain,
% 0.96/1.22 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | (p2(Y!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.96/1.23 inference(quant_inst,[status(thm)],[])).
% 0.96/1.23 tff(141,plain,
% 0.96/1.23 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | p2(Y!3) | (~r1(X!0, Y!3)) | (~(p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 0.96/1.23 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.96/1.23 tff(142,plain,
% 0.96/1.23 (~(p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[141, 138, 136, 134])).
% 0.96/1.23 tff(143,plain,
% 0.96/1.23 ((p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.96/1.23 inference(tautology,[status(thm)],[])).
% 0.96/1.23 tff(144,plain,
% 0.96/1.23 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.96/1.23 tff(145,plain,
% 0.96/1.23 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X))))),
% 0.96/1.23 inference(rewrite,[status(thm)],[])).
% 0.96/1.23 tff(146,plain,
% 0.96/1.23 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X))))),
% 0.96/1.23 inference(quant_inst,[status(thm)],[])).
% 0.96/1.23 tff(147,plain,
% 0.96/1.23 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))),
% 0.96/1.23 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.96/1.23 tff(148,plain,
% 0.96/1.23 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[147, 144, 124, 122])).
% 0.96/1.23 tff(149,plain,
% 0.96/1.23 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))) | r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))),
% 0.96/1.23 inference(tautology,[status(thm)],[])).
% 0.96/1.23 tff(150,plain,
% 0.96/1.23 (r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[149, 120])).
% 0.96/1.23 tff(151,plain,
% 0.96/1.23 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))) | (~p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))))),
% 0.96/1.23 inference(tautology,[status(thm)],[])).
% 0.96/1.23 tff(152,plain,
% 0.96/1.23 (~p2(tptp_fun_X_15(tptp_fun_X_16(Y!3)))),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[151, 120])).
% 0.96/1.23 tff(153,plain,
% 0.96/1.23 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))) | (p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))),
% 0.96/1.23 inference(rewrite,[status(thm)],[])).
% 0.96/1.23 tff(154,plain,
% 0.96/1.23 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))) | (p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))),
% 0.96/1.23 inference(quant_inst,[status(thm)],[])).
% 0.96/1.23 tff(155,plain,
% 0.96/1.23 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))),
% 0.96/1.23 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.96/1.23 tff(156,plain,
% 0.96/1.23 ($false),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[155, 152, 150, 148])).
% 0.96/1.23 tff(157,plain,((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.23 tff(158,plain,
% 0.96/1.23 ((p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | r1(Y!3, tptp_fun_X_16(Y!3))),
% 0.96/1.23 inference(tautology,[status(thm)],[])).
% 0.96/1.23 tff(159,plain,
% 0.96/1.23 (r1(Y!3, tptp_fun_X_16(Y!3))),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[158, 142])).
% 0.96/1.23 tff(160,plain,
% 0.96/1.23 ((p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(tptp_fun_X_16(Y!3)))),
% 0.96/1.23 inference(tautology,[status(thm)],[])).
% 0.96/1.23 tff(161,plain,
% 0.96/1.23 (~p2(tptp_fun_X_16(Y!3))),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[160, 142])).
% 0.96/1.23 tff(162,plain,
% 0.96/1.23 (((~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | (p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))))),
% 0.96/1.23 inference(rewrite,[status(thm)],[])).
% 0.96/1.23 tff(163,plain,
% 0.96/1.23 ((~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | (p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))))))),
% 0.96/1.23 inference(quant_inst,[status(thm)],[])).
% 0.96/1.23 tff(164,plain,
% 0.96/1.23 ((~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))))),
% 0.96/1.23 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.96/1.23 tff(165,plain,
% 0.96/1.23 ($false),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[164, 161, 159, 157, 119])).
% 0.96/1.23 tff(166,plain,(~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.23 tff(167,assumption,(![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))), introduced(assumption)).
% 0.96/1.23 tff(168,plain,
% 0.96/1.23 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | (~r1(X!0, Y!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))),
% 0.96/1.23 inference(rewrite,[status(thm)],[])).
% 0.96/1.23 tff(169,plain,
% 0.96/1.23 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ((~r1(X!0, Y!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))),
% 0.96/1.23 inference(quant_inst,[status(thm)],[])).
% 0.96/1.23 tff(170,plain,
% 0.96/1.23 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | (~r1(X!0, Y!3)) | ![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))),
% 0.96/1.23 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.96/1.23 tff(171,plain,
% 0.96/1.23 ($false),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[170, 136, 167, 166])).
% 0.96/1.23 tff(172,plain,(~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.23 tff(173,plain,
% 0.96/1.23 ((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))),
% 0.96/1.23 inference(tautology,[status(thm)],[])).
% 0.96/1.23 tff(174,plain,
% 0.96/1.23 (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[173, 172, 118])).
% 0.96/1.23 tff(175,plain,
% 0.96/1.23 (((~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))) | (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))))) | ((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))),
% 0.96/1.23 inference(tautology,[status(thm)],[])).
% 0.96/1.23 tff(176,plain,
% 0.96/1.23 ((~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))) | (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))))),
% 0.96/1.23 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.96/1.23 tff(177,plain,
% 0.96/1.23 (((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) <=> ((~((~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))) | (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))))),
% 0.96/1.24 inference(rewrite,[status(thm)],[])).
% 0.96/1.24 tff(178,plain,
% 0.96/1.24 (((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) <=> ((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.96/1.24 inference(rewrite,[status(thm)],[])).
% 0.96/1.24 tff(179,plain,
% 0.96/1.24 ((((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & r1(X, tptp_fun_Y_17(X)) & (~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))) <=> ((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.96/1.24 inference(rewrite,[status(thm)],[])).
% 0.96/1.24 tff(180,plain,
% 0.96/1.24 (((((~p2(Y!19)) & r1(X!0, Y!19) & ![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & (p2(X!0) | (p2(Y!20) & r1(X!0, Y!20) & (~(p2(X!21) | (~r1(Y!20, X!21))))))) | (r1(X!0, Y!11) & (((~p2(Y!11)) & ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (r1(Y!11, X!12) & (~p2(Y!13)) & r1(X!12, Y!13) & ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))) & ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (p2(tptp_fun_Y_14(X)) & r1(X, tptp_fun_Y_14(X)) & (~(p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) & ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ((~p2(tptp_fun_X_16(Y))) & r1(Y, tptp_fun_X_16(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) & (p2(Y) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ((~p2(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (![Y: $i] : (p2(Y) | (~r1(X, Y)) | (p2(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & r1(X, tptp_fun_Y_17(X)) & (~p2(tptp_fun_X_18(X))) & r1(tptp_fun_Y_17(X), tptp_fun_X_18(X)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 0.96/1.24 inference(and_elim,[status(thm)],[64])).
% 0.96/1.24 tff(181,plain,
% 0.96/1.24 ((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.96/1.24 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.96/1.24 tff(182,plain,
% 0.96/1.24 ((~((~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.96/1.24 inference(modus_ponens,[status(thm)],[181, 178])).
% 0.96/1.24 tff(183,plain,
% 0.96/1.24 ((~((~(p2(X!0) | (~((~r1(X!0, Y!20)) | (~p2(Y!20)) | p2(X!21) | (~r1(Y!20, X!21)))))) | (~((~(p2(Y!19) | (~r1(X!0, Y!19)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))))),
% 0.96/1.24 inference(modus_ponens,[status(thm)],[182, 177])).
% 0.96/1.24 tff(184,plain,
% 0.96/1.24 (~((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.96/1.24 inference(unit_resolution,[status(thm)],[183, 176])).
% 0.96/1.25 tff(185,plain,
% 0.96/1.25 (((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) | ((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))),
% 0.96/1.25 inference(tautology,[status(thm)],[])).
% 0.96/1.25 tff(186,plain,
% 0.96/1.25 ((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.96/1.25 tff(187,plain,
% 0.96/1.25 (((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) | r1(X!0, Y!11)),
% 0.96/1.25 inference(tautology,[status(thm)],[])).
% 0.96/1.25 tff(188,plain,
% 0.96/1.25 (r1(X!0, Y!11)),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[187, 184])).
% 0.96/1.25 tff(189,assumption,(~p2(Y!11)), introduced(assumption)).
% 0.96/1.25 tff(190,assumption,(p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))), introduced(assumption)).
% 0.96/1.25 tff(191,assumption,(r1(X!0, Y!11)), introduced(assumption)).
% 0.96/1.25 tff(192,assumption,(![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))), introduced(assumption)).
% 0.96/1.25 tff(193,plain,
% 0.96/1.25 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))),
% 0.96/1.25 inference(rewrite,[status(thm)],[])).
% 0.96/1.25 tff(194,plain,
% 0.96/1.25 ((p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))))) <=> (p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))),
% 0.96/1.25 inference(rewrite,[status(thm)],[])).
% 0.96/1.25 tff(195,plain,
% 0.96/1.25 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))))))),
% 0.96/1.25 inference(monotonicity,[status(thm)],[194])).
% 0.96/1.25 tff(196,plain,
% 0.96/1.25 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))),
% 0.96/1.25 inference(transitivity,[status(thm)],[195, 193])).
% 0.96/1.25 tff(197,plain,
% 0.96/1.25 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))),
% 0.96/1.25 inference(quant_inst,[status(thm)],[])).
% 0.96/1.25 tff(198,plain,
% 0.96/1.25 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))))),
% 0.96/1.25 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.96/1.25 tff(199,plain,
% 0.96/1.25 ($false),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[198, 192, 191, 189, 190])).
% 0.96/1.25 tff(200,plain,((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~r1(X!0, Y!11)) | p2(Y!11) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.25 tff(201,plain,
% 0.96/1.25 (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[200, 189, 92, 188])).
% 0.96/1.25 tff(202,assumption,(~(p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))))), introduced(assumption)).
% 0.96/1.25 tff(203,plain,
% 0.96/1.25 ((p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | r1(Y!11, tptp_fun_X_4(Y!11))),
% 0.96/1.25 inference(tautology,[status(thm)],[])).
% 0.96/1.25 tff(204,plain,
% 0.96/1.25 (r1(Y!11, tptp_fun_X_4(Y!11))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.96/1.25 tff(205,plain,
% 0.96/1.25 ((p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | p2(tptp_fun_X_4(Y!11))),
% 0.96/1.25 inference(tautology,[status(thm)],[])).
% 0.96/1.25 tff(206,plain,
% 0.96/1.25 (p2(tptp_fun_X_4(Y!11))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[205, 202])).
% 0.96/1.25 tff(207,assumption,(![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))), introduced(assumption)).
% 0.96/1.25 tff(208,plain,
% 0.96/1.25 (((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y))))),
% 0.96/1.25 inference(rewrite,[status(thm)],[])).
% 0.96/1.25 tff(209,plain,
% 0.96/1.25 ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y))))),
% 0.96/1.25 inference(quant_inst,[status(thm)],[])).
% 0.96/1.25 tff(210,plain,
% 0.96/1.25 ((~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))),
% 0.96/1.25 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.96/1.25 tff(211,plain,
% 0.96/1.25 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[210, 207, 206, 204])).
% 0.96/1.25 tff(212,plain,
% 0.96/1.25 ((p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))),
% 0.96/1.25 inference(tautology,[status(thm)],[])).
% 0.96/1.25 tff(213,plain,
% 0.96/1.25 (r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[212, 202])).
% 0.96/1.25 tff(214,plain,
% 0.96/1.25 ((p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | (~p2(tptp_fun_Y_5(Y!11)))),
% 0.96/1.25 inference(tautology,[status(thm)],[])).
% 0.96/1.25 tff(215,plain,
% 0.96/1.25 (~p2(tptp_fun_Y_5(Y!11))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[214, 202])).
% 0.96/1.25 tff(216,plain,
% 0.96/1.25 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | (p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))),
% 0.96/1.25 inference(rewrite,[status(thm)],[])).
% 0.96/1.25 tff(217,plain,
% 0.96/1.25 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | (p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))),
% 0.96/1.25 inference(quant_inst,[status(thm)],[])).
% 0.96/1.25 tff(218,plain,
% 0.96/1.25 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))),
% 0.96/1.25 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.96/1.25 tff(219,plain,
% 0.96/1.25 ($false),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[218, 215, 213, 211])).
% 0.96/1.25 tff(220,plain,((p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.25 tff(221,plain,
% 0.96/1.25 (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[220, 201])).
% 0.96/1.25 tff(222,plain,
% 0.96/1.25 ((p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.96/1.25 inference(tautology,[status(thm)],[])).
% 0.96/1.25 tff(223,plain,
% 0.96/1.25 (p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.96/1.25 tff(224,plain,
% 0.96/1.25 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.96/1.25 inference(rewrite,[status(thm)],[])).
% 0.96/1.25 tff(225,plain,
% 0.96/1.25 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))),
% 0.96/1.25 inference(quant_inst,[status(thm)],[])).
% 0.96/1.25 tff(226,plain,
% 0.96/1.25 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 0.96/1.25 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.96/1.25 tff(227,plain,
% 0.96/1.25 (p2(Y!11) | (~(p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[226, 188, 134])).
% 0.96/1.25 tff(228,plain,
% 0.96/1.25 (~(p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[227, 189])).
% 0.96/1.25 tff(229,assumption,(~(p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))), introduced(assumption)).
% 0.96/1.25 tff(230,plain,
% 0.96/1.25 ((p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | r1(Y!11, tptp_fun_X_16(Y!11))),
% 0.96/1.25 inference(tautology,[status(thm)],[])).
% 0.96/1.25 tff(231,plain,
% 0.96/1.25 (r1(Y!11, tptp_fun_X_16(Y!11))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.96/1.25 tff(232,plain,
% 0.96/1.25 ((p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(tptp_fun_X_16(Y!11)))),
% 0.96/1.25 inference(tautology,[status(thm)],[])).
% 0.96/1.25 tff(233,plain,
% 0.96/1.25 (~p2(tptp_fun_X_16(Y!11))),
% 0.96/1.25 inference(unit_resolution,[status(thm)],[232, 229])).
% 0.96/1.25 tff(234,assumption,(![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))), introduced(assumption)).
% 0.96/1.26 tff(235,plain,
% 0.96/1.26 (((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | (p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~((~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11)))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~((~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11)))))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(236,plain,
% 0.96/1.26 ((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | (p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~((~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11)))))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(237,plain,
% 0.96/1.26 ((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~((~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11))))))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.96/1.26 tff(238,plain,
% 0.96/1.26 (~((~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11)))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[237, 234, 233, 231])).
% 0.96/1.26 tff(239,plain,
% 0.96/1.26 (((~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11))))) | p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(240,plain,
% 0.96/1.26 (p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.96/1.26 tff(241,plain,
% 0.96/1.26 (((~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11))))) | r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(242,plain,
% 0.96/1.26 (r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[241, 238])).
% 0.96/1.26 tff(243,plain,
% 0.96/1.26 ((p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(244,plain,
% 0.96/1.26 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[243, 229])).
% 0.96/1.26 tff(245,plain,
% 0.96/1.26 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(246,plain,
% 0.96/1.26 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(247,plain,
% 0.96/1.26 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X)))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.96/1.26 tff(248,plain,
% 0.96/1.26 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X)))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[247, 244, 242, 240])).
% 0.96/1.26 tff(249,plain,
% 0.96/1.26 (((~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11))))) | r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11)))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(250,plain,
% 0.96/1.26 (r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11)))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[249, 238])).
% 0.96/1.26 tff(251,plain,
% 0.96/1.26 (((~r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11))))) | (~p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(252,plain,
% 0.96/1.26 (~p2(tptp_fun_X_15(tptp_fun_X_16(Y!11)))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[251, 238])).
% 0.96/1.26 tff(253,plain,
% 0.96/1.26 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X)))) | (p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11)))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(254,plain,
% 0.96/1.26 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X)))) | (p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11)))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(255,plain,
% 0.96/1.26 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11))))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.96/1.26 tff(256,plain,
% 0.96/1.26 ($false),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[255, 252, 250, 248])).
% 0.96/1.26 tff(257,plain,((p2(tptp_fun_X_16(Y!11)) | (~r1(Y!11, tptp_fun_X_16(Y!11))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.26 tff(258,plain,
% 0.96/1.26 (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[257, 228])).
% 0.96/1.26 tff(259,plain,
% 0.96/1.26 (((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(260,plain,
% 0.96/1.26 ((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[259, 258])).
% 0.96/1.26 tff(261,plain,
% 0.96/1.26 ((~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(262,plain,
% 0.96/1.26 ($false),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[261, 260, 223, 186])).
% 0.96/1.26 tff(263,plain,(p2(Y!11)), inference(lemma,lemma(discharge,[]))).
% 0.96/1.26 tff(264,plain,
% 0.96/1.26 ((p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | (~p2(Y!11))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(265,plain,
% 0.96/1.26 (p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.96/1.26 tff(266,plain,
% 0.96/1.26 (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[261, 265, 186])).
% 0.96/1.26 tff(267,plain,
% 0.96/1.26 (((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(268,plain,
% 0.96/1.26 (![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[267, 266])).
% 0.96/1.26 tff(269,plain,
% 0.96/1.26 (((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(270,plain,
% 0.96/1.26 ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | ((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(271,plain,
% 0.96/1.26 ((~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.96/1.26 tff(272,plain,
% 0.96/1.26 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[271, 268, 6, 4])).
% 0.96/1.26 tff(273,plain,
% 0.96/1.26 (((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))) | r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(274,plain,
% 0.96/1.26 (r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[273, 2])).
% 0.96/1.26 tff(275,plain,
% 0.96/1.26 (((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))) | (~p2(tptp_fun_Y_5(Y!13)))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(276,plain,
% 0.96/1.26 (~p2(tptp_fun_Y_5(Y!13))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[275, 2])).
% 0.96/1.26 tff(277,plain,
% 0.96/1.26 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))) | (p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(278,plain,
% 0.96/1.26 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))) | (p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(279,plain,
% 0.96/1.26 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.96/1.26 tff(280,plain,
% 0.96/1.26 ($false),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[279, 276, 274, 272])).
% 0.96/1.26 tff(281,plain,((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.26 tff(282,plain,
% 0.96/1.26 (((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | r1(X!12, Y!13)),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(283,plain,
% 0.96/1.26 (r1(X!12, Y!13)),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[282, 266])).
% 0.96/1.26 tff(284,plain,
% 0.96/1.26 (((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | (~p2(Y!13))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(285,plain,
% 0.96/1.26 (~p2(Y!13)),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[284, 266])).
% 0.96/1.26 tff(286,plain,
% 0.96/1.26 (((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!13) | (~r1(X!12, Y!13)) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(287,plain,
% 0.96/1.26 ((p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))))) <=> (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(288,plain,
% 0.96/1.26 (((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))))))),
% 0.96/1.26 inference(monotonicity,[status(thm)],[287])).
% 0.96/1.26 tff(289,plain,
% 0.96/1.26 (((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!13) | (~r1(X!12, Y!13)) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.96/1.26 inference(transitivity,[status(thm)],[288, 286])).
% 0.96/1.26 tff(290,plain,
% 0.96/1.26 ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.96/1.26 inference(quant_inst,[status(thm)],[])).
% 0.96/1.26 tff(291,plain,
% 0.96/1.26 ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!13) | (~r1(X!12, Y!13)) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))))),
% 0.96/1.26 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.96/1.26 tff(292,plain,
% 0.96/1.26 ($false),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[291, 285, 283, 281, 1])).
% 0.96/1.26 tff(293,plain,(~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.26 tff(294,plain,
% 0.96/1.26 (((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12)))) | ![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(295,plain,
% 0.96/1.26 ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12)))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[294, 293])).
% 0.96/1.26 tff(296,plain,
% 0.96/1.26 ((~(p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))))),
% 0.96/1.26 inference(tautology,[status(thm)],[])).
% 0.96/1.26 tff(297,plain,
% 0.96/1.26 (~(p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.96/1.26 inference(unit_resolution,[status(thm)],[296, 285, 281])).
% 0.96/1.26 tff(298,plain,
% 0.96/1.26 (((~(p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) | (p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.96/1.27 inference(tautology,[status(thm)],[])).
% 0.96/1.27 tff(299,plain,
% 0.96/1.27 ((~(p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.96/1.27 inference(unit_resolution,[status(thm)],[298, 297])).
% 0.96/1.27 tff(300,assumption,(![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))), introduced(assumption)).
% 0.96/1.27 tff(301,plain,
% 0.96/1.27 (((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.96/1.27 inference(rewrite,[status(thm)],[])).
% 0.96/1.27 tff(302,plain,
% 0.96/1.27 (((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))) <=> ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.96/1.27 inference(rewrite,[status(thm)],[])).
% 0.96/1.27 tff(303,plain,
% 0.96/1.27 (((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.96/1.27 inference(monotonicity,[status(thm)],[302])).
% 0.96/1.27 tff(304,plain,
% 0.96/1.27 (((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.96/1.27 inference(transitivity,[status(thm)],[303, 301])).
% 0.96/1.27 tff(305,plain,
% 0.96/1.27 ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.96/1.27 inference(quant_inst,[status(thm)],[])).
% 0.96/1.27 tff(306,plain,
% 0.96/1.27 ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~((~p2(tptp_fun_X_4(Y!13))) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | (~((~(p2(tptp_fun_X_16(Y!13)) | (~r1(Y!13, tptp_fun_X_16(Y!13))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!13), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))),
% 0.96/1.27 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.96/1.27 tff(307,plain,
% 0.96/1.27 ($false),
% 0.96/1.27 inference(unit_resolution,[status(thm)],[306, 283, 300, 299])).
% 0.96/1.27 tff(308,plain,(~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.27 tff(309,plain,
% 0.96/1.27 (((~r1(X!0, Y!11)) | (~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))))))) | (~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) | ![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.96/1.27 inference(tautology,[status(thm)],[])).
% 0.96/1.27 tff(310,plain,
% 0.96/1.27 (![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.96/1.27 inference(unit_resolution,[status(thm)],[309, 184])).
% 0.96/1.27 tff(311,plain,
% 0.96/1.27 (((~r1(Y!11, X!12)) | p2(Y!13) | (~r1(X!12, Y!13)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))) | r1(Y!11, X!12)),
% 0.96/1.27 inference(tautology,[status(thm)],[])).
% 0.96/1.27 tff(312,plain,
% 0.96/1.27 (r1(Y!11, X!12)),
% 0.96/1.27 inference(unit_resolution,[status(thm)],[311, 266])).
% 0.96/1.27 tff(313,plain,
% 0.96/1.27 (((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | (~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.96/1.28 inference(rewrite,[status(thm)],[])).
% 0.96/1.28 tff(314,plain,
% 0.96/1.28 (((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!12, tptp_fun_Y_17(X!12))) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | p2(tptp_fun_X_18(X!12)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.96/1.28 inference(rewrite,[status(thm)],[])).
% 0.96/1.28 tff(315,plain,
% 0.96/1.28 (((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!12, tptp_fun_Y_17(X!12))) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | p2(tptp_fun_X_18(X!12)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.96/1.28 inference(monotonicity,[status(thm)],[314])).
% 0.96/1.28 tff(316,plain,
% 0.96/1.28 (((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!12, tptp_fun_Y_17(X!12))) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | p2(tptp_fun_X_18(X!12)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | (~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.96/1.28 inference(transitivity,[status(thm)],[315, 313])).
% 0.96/1.28 tff(317,plain,
% 0.96/1.28 ((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | ((~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X!12, tptp_fun_Y_17(X!12))) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | p2(tptp_fun_X_18(X!12)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.96/1.28 inference(quant_inst,[status(thm)],[])).
% 0.96/1.28 tff(318,plain,
% 0.96/1.28 ((~![X: $i] : ((~r1(Y!11, X)) | (~(p2(X) | (~![Y: $i] : ((~p2(Y)) | (~r1(X, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~r1(X, tptp_fun_Y_17(X))) | (~r1(tptp_fun_Y_17(X), tptp_fun_X_18(X))) | p2(tptp_fun_X_18(X)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))) | (~r1(Y!11, X!12)) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.96/1.28 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.96/1.28 tff(319,plain,
% 0.96/1.28 ((~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(X!12), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | p2(tptp_fun_X_18(X!12)) | (~r1(tptp_fun_Y_17(X!12), tptp_fun_X_18(X!12))) | (~r1(X!12, tptp_fun_Y_17(X!12))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~((~(p2(tptp_fun_X_16(Y)) | (~r1(Y, tptp_fun_X_16(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | p2(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.96/1.28 inference(unit_resolution,[status(thm)],[318, 312, 310])).
% 0.96/1.28 tff(320,plain,
% 0.96/1.28 (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 0.96/1.28 inference(unit_resolution,[status(thm)],[319, 308, 295])).
% 0.96/1.28 tff(321,plain,
% 0.96/1.28 ((p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(X!12))),
% 0.96/1.28 inference(tautology,[status(thm)],[])).
% 0.96/1.28 tff(322,plain,
% 0.96/1.28 (~p2(X!12)),
% 0.96/1.28 inference(unit_resolution,[status(thm)],[321, 320])).
% 0.96/1.28 tff(323,plain,
% 0.96/1.28 (![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))),
% 0.96/1.28 inference(unit_resolution,[status(thm)],[259, 266])).
% 0.96/1.28 tff(324,plain,
% 0.96/1.28 (((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | (p2(X!12) | (~r1(Y!11, X!12)) | (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(X!12) | (~r1(Y!11, X!12)) | (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))))),
% 0.96/1.29 inference(rewrite,[status(thm)],[])).
% 0.96/1.29 tff(325,plain,
% 0.96/1.29 ((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | (p2(X!12) | (~r1(Y!11, X!12)) | (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))))),
% 0.96/1.29 inference(quant_inst,[status(thm)],[])).
% 0.96/1.29 tff(326,plain,
% 0.96/1.29 ((~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(X!12) | (~r1(Y!11, X!12)) | (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))))),
% 0.96/1.29 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.96/1.29 tff(327,plain,
% 0.96/1.29 (p2(X!12) | (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))))),
% 0.96/1.29 inference(unit_resolution,[status(thm)],[326, 312, 323])).
% 0.96/1.29 tff(328,plain,
% 0.96/1.29 (~((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))),
% 0.96/1.29 inference(unit_resolution,[status(thm)],[327, 322])).
% 0.96/1.29 tff(329,plain,
% 0.96/1.29 (((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))) | p2(tptp_fun_Y_14(X!12))),
% 0.96/1.29 inference(tautology,[status(thm)],[])).
% 0.96/1.29 tff(330,plain,
% 0.96/1.29 (p2(tptp_fun_Y_14(X!12))),
% 0.96/1.29 inference(unit_resolution,[status(thm)],[329, 328])).
% 0.96/1.29 tff(331,plain,
% 0.96/1.29 (((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))) | r1(X!12, tptp_fun_Y_14(X!12))),
% 0.96/1.29 inference(tautology,[status(thm)],[])).
% 0.96/1.29 tff(332,plain,
% 0.96/1.29 (r1(X!12, tptp_fun_Y_14(X!12))),
% 0.96/1.29 inference(unit_resolution,[status(thm)],[331, 328])).
% 0.96/1.29 tff(333,plain,
% 0.96/1.29 ((p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.96/1.29 inference(tautology,[status(thm)],[])).
% 0.96/1.29 tff(334,plain,
% 0.96/1.29 (![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.96/1.29 inference(unit_resolution,[status(thm)],[333, 320])).
% 0.96/1.29 tff(335,plain,
% 0.96/1.29 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_14(X!12))) | (~r1(X!12, tptp_fun_Y_14(X!12))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_14(X!12))) | (~r1(X!12, tptp_fun_Y_14(X!12))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X))))),
% 0.96/1.29 inference(rewrite,[status(thm)],[])).
% 0.96/1.29 tff(336,plain,
% 0.96/1.29 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | ((~p2(tptp_fun_Y_14(X!12))) | (~r1(X!12, tptp_fun_Y_14(X!12))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X))))),
% 0.96/1.29 inference(quant_inst,[status(thm)],[])).
% 0.96/1.29 tff(337,plain,
% 0.96/1.29 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))) | (~p2(tptp_fun_Y_14(X!12))) | (~r1(X!12, tptp_fun_Y_14(X!12))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))),
% 0.96/1.29 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.96/1.29 tff(338,plain,
% 0.96/1.29 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))),
% 0.96/1.29 inference(unit_resolution,[status(thm)],[337, 334, 332, 330])).
% 0.96/1.29 tff(339,plain,
% 0.96/1.29 (((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))) | r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))),
% 0.96/1.29 inference(tautology,[status(thm)],[])).
% 0.96/1.29 tff(340,plain,
% 0.96/1.29 (r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))),
% 0.96/1.29 inference(unit_resolution,[status(thm)],[339, 328])).
% 0.96/1.29 tff(341,plain,
% 0.96/1.29 (((~r1(X!12, tptp_fun_Y_14(X!12))) | (~p2(tptp_fun_Y_14(X!12))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))) | (~p2(tptp_fun_X_15(X!12)))),
% 0.96/1.30 inference(tautology,[status(thm)],[])).
% 0.96/1.30 tff(342,plain,
% 0.96/1.30 (~p2(tptp_fun_X_15(X!12))),
% 0.96/1.30 inference(unit_resolution,[status(thm)],[341, 328])).
% 0.96/1.30 tff(343,plain,
% 0.96/1.30 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))) | (p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))),
% 0.96/1.30 inference(rewrite,[status(thm)],[])).
% 0.96/1.30 tff(344,plain,
% 0.96/1.30 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))) | (p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))))),
% 0.96/1.30 inference(quant_inst,[status(thm)],[])).
% 0.96/1.30 tff(345,plain,
% 0.96/1.30 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))),
% 0.96/1.30 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.96/1.30 tff(346,plain,
% 0.96/1.30 ($false),
% 0.96/1.30 inference(unit_resolution,[status(thm)],[345, 342, 340, 338])).
% 0.96/1.30 % SZS output end Proof
% 0.17/1.30 % E exiting
%------------------------------------------------------------------------------