%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL660+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:28 PM UTC 2026
% Result : Theorem 0.39s 0.68s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL660+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n029.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 21:36:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.39/0.68 % SZS status Theorem
% 0.39/0.68 % SZS output start Proof
% 0.39/0.68 tff(r1_type, type, (
% 0.39/0.68 r1: ( $i * $i ) > $o)).
% 0.39/0.68 tff(tptp_fun_Y_14_type, type, (
% 0.39/0.68 tptp_fun_Y_14: $i > $i)).
% 0.39/0.68 tff(tptp_fun_X_12_type, type, (
% 0.39/0.68 tptp_fun_X_12: $i)).
% 0.39/0.68 tff(p2_type, type, (
% 0.39/0.68 p2: $i > $o)).
% 0.39/0.68 tff(tptp_fun_X_15_type, type, (
% 0.39/0.68 tptp_fun_X_15: $i > $i)).
% 0.39/0.68 tff(tptp_fun_Y_5_type, type, (
% 0.39/0.68 tptp_fun_Y_5: $i > $i)).
% 0.39/0.68 tff(tptp_fun_Y_13_type, type, (
% 0.39/0.68 tptp_fun_Y_13: $i)).
% 0.39/0.68 tff(tptp_fun_X_4_type, type, (
% 0.39/0.68 tptp_fun_X_4: $i > $i)).
% 0.39/0.68 tff(tptp_fun_Y_11_type, type, (
% 0.39/0.68 tptp_fun_Y_11: $i)).
% 0.39/0.68 tff(tptp_fun_X_16_type, type, (
% 0.39/0.68 tptp_fun_X_16: $i > $i)).
% 0.39/0.68 tff(tptp_fun_X_18_type, type, (
% 0.39/0.68 tptp_fun_X_18: $i > $i)).
% 0.39/0.68 tff(tptp_fun_Y_17_type, type, (
% 0.39/0.68 tptp_fun_Y_17: $i > $i)).
% 0.39/0.68 tff(tptp_fun_X_0_type, type, (
% 0.39/0.68 tptp_fun_X_0: $i)).
% 0.39/0.68 tff(tptp_fun_Y_19_type, type, (
% 0.39/0.68 tptp_fun_Y_19: $i)).
% 0.39/0.68 tff(tptp_fun_X_21_type, type, (
% 0.39/0.68 tptp_fun_X_21: $i)).
% 0.39/0.68 tff(tptp_fun_Y_20_type, type, (
% 0.39/0.68 tptp_fun_Y_20: $i)).
% 0.39/0.68 tff(tptp_fun_Y_3_type, type, (
% 0.39/0.68 tptp_fun_Y_3: $i)).
% 0.39/0.68 tff(tptp_fun_X_6_type, type, (
% 0.39/0.68 tptp_fun_X_6: $i > $i)).
% 0.39/0.68 tff(p5_type, type, (
% 0.39/0.68 p5: $i > $o)).
% 0.39/0.68 tff(tptp_fun_Y_24_type, type, (
% 0.39/0.68 tptp_fun_Y_24: $i > $i)).
% 0.39/0.68 tff(p1_type, type, (
% 0.39/0.68 p1: $i > $o)).
% 0.39/0.68 tff(tptp_fun_Y_29_type, type, (
% 0.39/0.68 tptp_fun_Y_29: $i)).
% 0.39/0.68 tff(tptp_fun_X_30_type, type, (
% 0.39/0.68 tptp_fun_X_30: $i)).
% 0.39/0.68 tff(tptp_fun_Y_27_type, type, (
% 0.39/0.68 tptp_fun_Y_27: $i)).
% 0.39/0.68 tff(tptp_fun_X_28_type, type, (
% 0.39/0.68 tptp_fun_X_28: $i)).
% 0.39/0.68 tff(p3_type, type, (
% 0.39/0.68 p3: $i > $o)).
% 0.39/0.68 tff(tptp_fun_Y_25_type, type, (
% 0.39/0.68 tptp_fun_Y_25: $i)).
% 0.39/0.68 tff(tptp_fun_X_26_type, type, (
% 0.39/0.68 tptp_fun_X_26: $i)).
% 0.39/0.68 tff(p4_type, type, (
% 0.39/0.68 p4: $i > $o)).
% 0.39/0.68 tff(tptp_fun_Y_22_type, type, (
% 0.39/0.68 tptp_fun_Y_22: $i)).
% 0.39/0.68 tff(tptp_fun_X_23_type, type, (
% 0.39/0.68 tptp_fun_X_23: $i)).
% 0.39/0.68 tff(tptp_fun_Y_10_type, type, (
% 0.39/0.68 tptp_fun_Y_10: $i > $i)).
% 0.39/0.68 tff(tptp_fun_X_9_type, type, (
% 0.39/0.68 tptp_fun_X_9: $i > $i)).
% 0.39/0.68 tff(tptp_fun_Y_8_type, type, (
% 0.39/0.68 tptp_fun_Y_8: $i > $i)).
% 0.39/0.68 tff(tptp_fun_X_7_type, type, (
% 0.39/0.68 tptp_fun_X_7: $i > $i)).
% 0.39/0.68 tff(tptp_fun_Y_2_type, type, (
% 0.39/0.68 tptp_fun_Y_2: $i)).
% 0.39/0.68 tff(tptp_fun_Y_1_type, type, (
% 0.39/0.68 tptp_fun_Y_1: $i)).
% 0.39/0.68 tff(1,assumption,(~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))), introduced(assumption)).
% 0.39/0.68 tff(2,plain,
% 0.39/0.68 ((p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))) | p2(tptp_fun_X_4(Y!13))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(3,plain,
% 0.39/0.68 (p2(tptp_fun_X_4(Y!13))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.39/0.68 tff(4,plain,
% 0.39/0.68 ((p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))) | r1(Y!13, tptp_fun_X_4(Y!13))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(5,plain,
% 0.39/0.68 (r1(Y!13, tptp_fun_X_4(Y!13))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.39/0.68 tff(6,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)).
% 0.39/0.68 tff(7,plain,
% 0.39/0.68 ((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)),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(8,plain,
% 0.39/0.68 (r1(X!0, Y!19)),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.39/0.68 tff(9,plain,
% 0.39/0.68 ((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))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(10,plain,
% 0.39/0.68 (~p2(Y!19)),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[9, 6])).
% 0.39/0.68 tff(11,assumption,(~r1(X!0, X!0)), introduced(assumption)).
% 0.39/0.68 tff(12,plain,
% 0.39/0.68 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.39/0.68 inference(bind,[status(th)],[])).
% 0.39/0.68 tff(13,plain,
% 0.39/0.68 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.39/0.68 inference(quant_intro,[status(thm)],[12])).
% 0.39/0.68 tff(14,plain,
% 0.39/0.68 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.39/0.68 inference(rewrite,[status(thm)],[])).
% 0.39/0.68 tff(15,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.39/0.69 tff(16,plain,
% 0.39/0.69 (![X: $i] : r1(X, X)),
% 0.39/0.69 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.39/0.69 tff(17,plain,(
% 0.39/0.69 ![X: $i] : r1(X, X)),
% 0.39/0.69 inference(skolemize,[status(sab)],[16])).
% 0.39/0.69 tff(18,plain,
% 0.39/0.69 (![X: $i] : r1(X, X)),
% 0.39/0.69 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.39/0.69 tff(19,plain,
% 0.39/0.69 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.39/0.69 inference(quant_inst,[status(thm)],[])).
% 0.39/0.69 tff(20,plain,
% 0.39/0.69 ($false),
% 0.39/0.69 inference(unit_resolution,[status(thm)],[19, 18, 11])).
% 0.39/0.69 tff(21,plain,(r1(X!0, X!0)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.69 tff(22,assumption,(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))), introduced(assumption)).
% 0.39/0.69 tff(23,plain,
% 0.39/0.69 (((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)))))))),
% 0.39/0.69 inference(rewrite,[status(thm)],[])).
% 0.39/0.69 tff(24,plain,
% 0.39/0.69 ((((~(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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)))))))),
% 0.39/0.69 inference(rewrite,[status(thm)],[])).
% 0.39/0.69 tff(25,plain,
% 0.39/0.69 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~(p1(Y!2) | (~r1(X!0, 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))))))))) & (((~(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))))))) & ![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)))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p1(X!0) | p2(X!0) | ((~p2(Y!22)) & r1(X!0, Y!22) & (~p3(Y!22)) & (~p1(Y!22)) & (~p4(Y!22)) & r1(Y!22, X!23) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!22, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_24(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!25)) & r1(X!0, Y!25) & (~p3(Y!25)) & (~p1(Y!25)) & r1(Y!25, X!26) & ![X: $i] : ((~r1(Y!25, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!27)) & r1(X!0, Y!27) & (~p1(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_24(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))) & (~(p1(Y!2) | (~r1(X!0, 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))))))))) & (((~(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))))))) & ![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)))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p1(X!0) | p2(X!0) | ((~p2(Y!22)) & r1(X!0, Y!22) & (~p3(Y!22)) & (~p1(Y!22)) & (~p4(Y!22)) & r1(Y!22, X!23) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!22, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_24(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!25)) & r1(X!0, Y!25) & (~p3(Y!25)) & (~p1(Y!25)) & r1(Y!25, X!26) & ![X: $i] : ((~r1(Y!25, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!27)) & r1(X!0, Y!27) & (~p1(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_24(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)))))))),
% 0.39/0.69 inference(rewrite,[status(thm)],[])).
% 0.39/0.69 tff(26,plain,
% 0.39/0.69 ((((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)))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!22)) & r1(X!0, Y!22) & (~p3(Y!22)) & (~p1(Y!22)) & (~p4(Y!22)) & r1(Y!22, X!23) & ![X: $i] : ((~r1(Y!22, 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_24(X)))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!25)) & r1(X!0, Y!25) & (~p3(Y!25)) & (~p1(Y!25)) & r1(Y!25, X!26) & ![X: $i] : ((~r1(Y!25, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!27)) & r1(X!0, Y!27) & (~p1(Y!27)) & r1(Y!27, X!28) & ![X: $i] : ((~r1(Y!27, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & r1(Y!29, X!30) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_24(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)))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p1(X!0) | p2(X!0) | ((~p2(Y!22)) & r1(X!0, Y!22) & (~p3(Y!22)) & (~p1(Y!22)) & (~p4(Y!22)) & r1(Y!22, X!23) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!22, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_24(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!25)) & r1(X!0, Y!25) & (~p3(Y!25)) & (~p1(Y!25)) & r1(Y!25, X!26) & ![X: $i] : ((~r1(Y!25, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!27)) & r1(X!0, Y!27) & (~p1(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_24(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)))))))),
% 0.39/0.70 inference(rewrite,[status(thm)],[])).
% 0.39/0.70 tff(27,plain,
% 0.39/0.70 (^[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))))))))),
% 0.46/0.70 inference(bind,[status(th)],[])).
% 0.46/0.70 tff(28,plain,
% 0.46/0.70 (![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))))))),
% 0.46/0.70 inference(quant_intro,[status(thm)],[27])).
% 0.46/0.70 tff(29,plain,
% 0.46/0.70 (^[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))))))))),
% 0.46/0.70 inference(bind,[status(th)],[])).
% 0.46/0.70 tff(30,plain,
% 0.46/0.70 (![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))))))),
% 0.46/0.70 inference(quant_intro,[status(thm)],[29])).
% 0.46/0.70 tff(31,plain,
% 0.46/0.70 ((![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))))))))) <=> (((~(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)))))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(32,plain,
% 0.46/0.70 (((~(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))))))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(33,plain,
% 0.46/0.70 ((![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)))))))))),
% 0.46/0.70 inference(monotonicity,[status(thm)],[32])).
% 0.46/0.70 tff(34,plain,
% 0.46/0.70 ((![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))))))))) <=> (((~(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)))))))),
% 0.46/0.70 inference(transitivity,[status(thm)],[33, 31])).
% 0.46/0.70 tff(35,plain,
% 0.46/0.70 ((![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)))))))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(36,plain,
% 0.46/0.70 ((![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)))))))))),
% 0.46/0.70 inference(monotonicity,[status(thm)],[32])).
% 0.46/0.70 tff(37,plain,
% 0.46/0.70 ((![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)))))))))),
% 0.46/0.70 inference(transitivity,[status(thm)],[36, 35])).
% 0.46/0.70 tff(38,plain,
% 0.46/0.70 ((~((~r1(X!0, Y!2)) | p1(Y!2))) <=> (~(p1(Y!2) | (~r1(X!0, Y!2))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(39,plain,
% 0.46/0.70 ((~((~r1(X!0, Y!1)) | p3(Y!1))) <=> (~((~r1(X!0, Y!1)) | p3(Y!1)))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(40,plain,
% 0.46/0.70 (((~((~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)))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!22)) & r1(X!0, Y!22) & (~p3(Y!22)) & (~p1(Y!22)) & (~p4(Y!22)) & r1(Y!22, X!23) & ![X: $i] : ((~r1(Y!22, 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_24(X)))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!25)) & r1(X!0, Y!25) & (~p3(Y!25)) & (~p1(Y!25)) & r1(Y!25, X!26) & ![X: $i] : ((~r1(Y!25, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!27)) & r1(X!0, Y!27) & (~p1(Y!27)) & r1(Y!27, X!28) & ![X: $i] : ((~r1(Y!27, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & r1(Y!29, X!30) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_24(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))) & (~(p1(Y!2) | (~r1(X!0, 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))))))))) & (((~(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))))))) & ![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)))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p1(X!0) | p2(X!0) | ((~p2(Y!22)) & r1(X!0, Y!22) & (~p3(Y!22)) & (~p1(Y!22)) & (~p4(Y!22)) & r1(Y!22, X!23) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!22, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_24(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!25)) & r1(X!0, Y!25) & (~p3(Y!25)) & (~p1(Y!25)) & r1(Y!25, X!26) & ![X: $i] : ((~r1(Y!25, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!27)) & r1(X!0, Y!27) & (~p1(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_24(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))))))))),
% 0.46/0.71 inference(monotonicity,[status(thm)],[39, 38, 37, 34, 30, 28, 26])).
% 0.46/0.71 tff(41,plain,
% 0.46/0.71 (((~((~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)))))))) & (p2(X!0) | p3(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!22)) & r1(X!0, Y!22) & (~p3(Y!22)) & (~p1(Y!22)) & (~p4(Y!22)) & r1(Y!22, X!23) & ![X: $i] : ((~r1(Y!22, 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_24(X)))))) & (p2(X!0) | p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!25)) & r1(X!0, Y!25) & (~p3(Y!25)) & (~p1(Y!25)) & r1(Y!25, X!26) & ![X: $i] : ((~r1(Y!25, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p2(Y!27)) & r1(X!0, Y!27) & (~p1(Y!27)) & r1(Y!27, X!28) & ![X: $i] : ((~r1(Y!27, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & r1(Y!29, X!30) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_24(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))) & (~(p1(Y!2) | (~r1(X!0, 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))))))))) & (((~(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))))))) & ![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)))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p1(X!0) | p2(X!0) | ((~p2(Y!22)) & r1(X!0, Y!22) & (~p3(Y!22)) & (~p1(Y!22)) & (~p4(Y!22)) & r1(Y!22, X!23) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!22, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_24(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!25)) & r1(X!0, Y!25) & (~p3(Y!25)) & (~p1(Y!25)) & r1(Y!25, X!26) & ![X: $i] : ((~r1(Y!25, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!27)) & r1(X!0, Y!27) & (~p1(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_24(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)))))))),
% 0.46/0.71 inference(transitivity,[status(thm)],[40, 25])).
% 0.46/0.71 tff(42,plain,
% 0.46/0.71 (?[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)))))))) & (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)) | (~(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)))))))) & (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)))))))) & (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)) | (~(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)))))))) & (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))))))))))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(43,plain,
% 0.46/0.72 ((~(~?[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)))))))) & (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)) | (~(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)))))))) & (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)))))))) & (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)) | (~(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)))))))) & (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))))))))))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(44,plain,
% 0.46/0.72 ((~?[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] : 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(((~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)))))))))))) & (((((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)) | 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(~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)))))))) & (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)) | (~(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)))))))) & (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)))))))))))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
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% 0.46/0.72 ((~(~?[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)))))))))))) & (((((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)))))))) & (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)) | (~(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)))))))) & (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))))))))))))))),
% 0.46/0.73 inference(monotonicity,[status(thm)],[44])).
% 0.46/0.73 tff(46,plain,
% 0.46/0.73 ((~(~?[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)))))))))))) & (((((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)))))))) & (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)) | (~(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)))))))) & (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))))))))))))),
% 0.46/0.74 inference(transitivity,[status(thm)],[45, 43])).
% 0.46/0.74 tff(47,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)))))))))))) & (((((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/sandbox/benchmark/theBenchmark.p','main')).
% 0.46/0.74 tff(48,plain,
% 0.46/0.74 (?[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)))))))) & (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)) | (~(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)))))))) & (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))))))))))))),
% 0.46/0.74 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.46/0.74 tff(49,plain,
% 0.46/0.74 (?[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)))))))) & (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)) | (~(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)))))))) & (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))))))))))))),
% 0.46/0.74 inference(modus_ponens,[status(thm)],[48, 42])).
% 0.46/0.74 tff(50,plain,
% 0.46/0.74 ((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~(p1(Y!2) | (~r1(X!0, 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))))))))) & (((~(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))))))) & ![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)))))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p1(X!0) | p2(X!0) | ((~p2(Y!22)) & r1(X!0, Y!22) & (~p3(Y!22)) & (~p1(Y!22)) & (~p4(Y!22)) & r1(Y!22, X!23) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!22, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_24(X)))))) & (p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!25)) & r1(X!0, Y!25) & (~p3(Y!25)) & (~p1(Y!25)) & r1(Y!25, X!26) & ![X: $i] : ((~r1(Y!25, X)) | ((~p2(X)) & (~p3(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X))) | ![Y: $i] : (p2(Y) | (~r1(X, Y)) | p3(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | p2(X!0) | ((~p2(Y!27)) & r1(X!0, Y!27) & (~p1(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : (p2(Y) | (~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_24(X)))))) & (![Y: $i] : (~r1(X!0, Y)) | p1(X!0) | (r1(X!0, Y!29) & (~p1(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_24(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))))))),
% 0.46/0.75 inference(modus_ponens,[status(thm)],[49, 41])).
% 0.46/0.75 tff(51,plain,
% 0.46/0.75 (((~(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))))))),
% 0.46/0.75 inference(and_elim,[status(thm)],[50])).
% 0.46/0.75 tff(52,plain,
% 0.46/0.75 ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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))))))),
% 0.46/0.75 inference(modus_ponens,[status(thm)],[51, 24])).
% 0.46/0.75 tff(53,plain,
% 0.46/0.75 ((~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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))))))),
% 0.46/0.75 inference(modus_ponens,[status(thm)],[52, 23])).
% 0.46/0.75 tff(54,plain,
% 0.46/0.75 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[53, 22])).
% 0.46/0.75 tff(55,plain,
% 0.46/0.75 (((~![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))))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(56,plain,
% 0.46/0.75 ((~![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))))))),
% 0.46/0.75 inference(quant_inst,[status(thm)],[])).
% 0.46/0.75 tff(57,plain,
% 0.46/0.75 ((~![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)))))),
% 0.46/0.75 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.46/0.75 tff(58,plain,
% 0.46/0.75 (~((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[57, 54, 21])).
% 0.46/0.75 tff(59,plain,
% 0.46/0.75 (((~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))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(60,plain,
% 0.46/0.75 (r1(X!0, tptp_fun_X_6(X!0))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.46/0.75 tff(61,plain,
% 0.46/0.75 (((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))) | p5(tptp_fun_X_6(X!0))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(62,plain,
% 0.46/0.75 (p5(tptp_fun_X_6(X!0))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.46/0.75 tff(63,plain,
% 0.46/0.75 ((![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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(64,plain,
% 0.46/0.75 ((![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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(65,plain,
% 0.46/0.75 (((~(p2(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(66,plain,
% 0.46/0.75 (^[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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.46/0.75 inference(bind,[status(th)],[])).
% 0.46/0.75 tff(67,plain,
% 0.46/0.75 (![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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.46/0.75 inference(quant_intro,[status(thm)],[66])).
% 0.46/0.75 tff(68,plain,
% 0.46/0.75 (((~(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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))),
% 0.46/0.75 inference(monotonicity,[status(thm)],[67])).
% 0.46/0.75 tff(69,plain,
% 0.46/0.75 (((~(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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.46/0.75 inference(transitivity,[status(thm)],[68, 65])).
% 0.46/0.75 tff(70,plain,
% 0.46/0.75 ((![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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.46/0.75 inference(monotonicity,[status(thm)],[69])).
% 0.46/0.75 tff(71,plain,
% 0.46/0.75 ((![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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))),
% 0.46/0.75 inference(transitivity,[status(thm)],[70, 64])).
% 0.46/0.75 tff(72,plain,
% 0.46/0.75 (![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))))))))),
% 0.46/0.75 inference(and_elim,[status(thm)],[50])).
% 0.46/0.75 tff(73,plain,
% 0.46/0.75 (![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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.46/0.75 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.46/0.75 tff(74,plain,
% 0.46/0.75 (![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_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.46/0.75 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.46/0.75 tff(75,plain,
% 0.46/0.75 (![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[74, 22])).
% 0.46/0.75 tff(76,plain,
% 0.46/0.75 (((~![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))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(77,plain,
% 0.46/0.75 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))) | ((~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0))))),
% 0.46/0.75 inference(quant_inst,[status(thm)],[])).
% 0.46/0.75 tff(78,plain,
% 0.46/0.75 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!0, Y)))) | (~p5(tptp_fun_X_6(X!0))) | (~r1(X!0, tptp_fun_X_6(X!0)))),
% 0.46/0.75 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.46/0.75 tff(79,plain,
% 0.46/0.75 ($false),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[78, 75, 62, 60])).
% 0.46/0.75 tff(80,plain,(~(p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.75 tff(81,plain,
% 0.46/0.75 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(82,plain,
% 0.46/0.75 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.46/0.75 tff(83,plain,
% 0.46/0.75 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19))))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(84,plain,
% 0.46/0.75 ((p2(Y!19) | (~r1(X!0, Y!19)) | (~(p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19)))))) <=> (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19))))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(85,plain,
% 0.46/0.75 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~(p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19)))))))),
% 0.46/0.75 inference(monotonicity,[status(thm)],[84])).
% 0.46/0.75 tff(86,plain,
% 0.46/0.75 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~(p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19))))))),
% 0.46/0.75 inference(transitivity,[status(thm)],[85, 83])).
% 0.46/0.75 tff(87,plain,
% 0.46/0.75 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!19) | (~r1(X!0, Y!19)) | (~(p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))))))),
% 0.46/0.75 inference(quant_inst,[status(thm)],[])).
% 0.46/0.75 tff(88,plain,
% 0.46/0.75 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!19) | (~r1(X!0, Y!19)) | (~((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19)))))),
% 0.46/0.75 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.46/0.75 tff(89,plain,
% 0.46/0.75 (~((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19))))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[88, 82, 10, 8])).
% 0.46/0.75 tff(90,plain,
% 0.46/0.75 (((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19)))) | r1(Y!19, tptp_fun_X_4(Y!19))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(91,plain,
% 0.46/0.75 (r1(Y!19, tptp_fun_X_4(Y!19))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.46/0.75 tff(92,plain,
% 0.46/0.75 (((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19)))) | p2(tptp_fun_X_4(Y!19))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(93,plain,
% 0.46/0.75 (p2(tptp_fun_X_4(Y!19))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.46/0.75 tff(94,plain,
% 0.46/0.75 ((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))))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(95,plain,
% 0.46/0.75 (![X: $i] : ((~p2(X)) | (~r1(Y!19, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[94, 6])).
% 0.46/0.75 tff(96,plain,
% 0.46/0.75 (((~![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))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(97,plain,
% 0.46/0.75 ((~![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))))),
% 0.46/0.75 inference(quant_inst,[status(thm)],[])).
% 0.46/0.75 tff(98,plain,
% 0.46/0.75 ((~![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)))),
% 0.46/0.75 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.46/0.75 tff(99,plain,
% 0.46/0.75 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[98, 95, 93, 91])).
% 0.46/0.75 tff(100,plain,
% 0.46/0.75 (((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19)))) | (~p2(tptp_fun_Y_5(Y!19)))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(101,plain,
% 0.46/0.75 (~p2(tptp_fun_Y_5(Y!19))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[100, 89])).
% 0.46/0.75 tff(102,plain,
% 0.46/0.75 (((~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))) | (~p2(tptp_fun_X_4(Y!19))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(Y!19, tptp_fun_X_4(Y!19)))) | r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(103,plain,
% 0.46/0.75 (r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[102, 89])).
% 0.46/0.75 tff(104,plain,
% 0.46/0.75 (((~![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))))),
% 0.46/0.75 inference(rewrite,[status(thm)],[])).
% 0.46/0.75 tff(105,plain,
% 0.46/0.75 ((~![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))))),
% 0.46/0.75 inference(quant_inst,[status(thm)],[])).
% 0.46/0.75 tff(106,plain,
% 0.46/0.75 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!19), Y)))) | p2(tptp_fun_Y_5(Y!19)) | (~r1(tptp_fun_X_4(Y!19), tptp_fun_Y_5(Y!19)))),
% 0.46/0.75 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.46/0.75 tff(107,plain,
% 0.46/0.75 ($false),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[106, 103, 101, 99])).
% 0.46/0.75 tff(108,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,[]))).
% 0.46/0.75 tff(109,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)).
% 0.46/0.75 tff(110,assumption,(~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(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))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))))), introduced(assumption)).
% 0.46/0.75 tff(111,plain,
% 0.46/0.75 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(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))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3))))) | p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(112,plain,
% 0.46/0.75 (p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.46/0.75 tff(113,plain,
% 0.46/0.75 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(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))) | (~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)))),
% 0.46/0.75 inference(tautology,[status(thm)],[])).
% 0.46/0.75 tff(114,plain,
% 0.46/0.75 (r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))),
% 0.46/0.75 inference(unit_resolution,[status(thm)],[113, 110])).
% 0.46/0.75 tff(115,plain,
% 0.46/0.75 (^[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)))))))))),
% 0.46/0.75 inference(bind,[status(th)],[])).
% 0.46/0.75 tff(116,plain,
% 0.46/0.75 (![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))))))))),
% 0.46/0.75 inference(quant_intro,[status(thm)],[115])).
% 0.46/0.75 tff(117,plain,
% 0.46/0.75 (^[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)))))))))),
% 0.46/0.75 inference(bind,[status(th)],[])).
% 0.46/0.75 tff(118,plain,
% 0.46/0.75 (![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))))))))),
% 0.46/0.75 inference(quant_intro,[status(thm)],[117])).
% 0.46/0.75 tff(119,plain,
% 0.46/0.75 (![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))))))))),
% 0.46/0.76 inference(transitivity,[status(thm)],[118, 116])).
% 0.46/0.76 tff(120,plain,
% 0.46/0.76 (^[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)))))))))),
% 0.46/0.76 inference(bind,[status(th)],[])).
% 0.46/0.76 tff(121,plain,
% 0.46/0.76 (![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))))))))),
% 0.46/0.76 inference(quant_intro,[status(thm)],[120])).
% 0.46/0.76 tff(122,plain,
% 0.46/0.76 (![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))))))),
% 0.46/0.76 inference(and_elim,[status(thm)],[50])).
% 0.46/0.76 tff(123,plain,
% 0.46/0.76 (![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))))))))),
% 0.46/0.76 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.46/0.76 tff(124,plain,
% 0.46/0.76 (![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))))))))),
% 0.46/0.76 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.46/0.76 tff(125,plain,
% 0.46/0.76 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | r1(X!0, Y!3)),
% 0.46/0.76 inference(tautology,[status(thm)],[])).
% 0.46/0.76 tff(126,plain,
% 0.46/0.76 (r1(X!0, Y!3)),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[125, 80])).
% 0.46/0.76 tff(127,plain,
% 0.46/0.76 ((p2(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))) | (~p2(Y!3))),
% 0.46/0.76 inference(tautology,[status(thm)],[])).
% 0.46/0.76 tff(128,plain,
% 0.46/0.76 (~p2(Y!3)),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[127, 80])).
% 0.46/0.76 tff(129,plain,
% 0.46/0.76 (((~![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))))))))),
% 0.46/0.76 inference(rewrite,[status(thm)],[])).
% 0.46/0.76 tff(130,plain,
% 0.46/0.76 ((~![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))))))))),
% 0.46/0.76 inference(quant_inst,[status(thm)],[])).
% 0.46/0.76 tff(131,plain,
% 0.46/0.76 ((~![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)))))))),
% 0.46/0.76 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.46/0.76 tff(132,plain,
% 0.46/0.76 (~(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))))))),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[131, 128, 126, 124])).
% 0.46/0.76 tff(133,plain,
% 0.46/0.76 ((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))))),
% 0.46/0.76 inference(tautology,[status(thm)],[])).
% 0.46/0.76 tff(134,plain,
% 0.46/0.76 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!3), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.46/0.76 tff(135,plain,
% 0.46/0.76 (((~![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))))),
% 0.46/0.76 inference(rewrite,[status(thm)],[])).
% 0.46/0.76 tff(136,plain,
% 0.46/0.76 ((~![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))))),
% 0.46/0.76 inference(quant_inst,[status(thm)],[])).
% 0.46/0.76 tff(137,plain,
% 0.46/0.76 ((~![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)))),
% 0.46/0.76 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.46/0.76 tff(138,plain,
% 0.46/0.76 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[137, 134, 114, 112])).
% 0.46/0.76 tff(139,plain,
% 0.46/0.76 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(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))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3))))) | (~p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))))),
% 0.46/0.76 inference(tautology,[status(thm)],[])).
% 0.46/0.76 tff(140,plain,
% 0.46/0.76 (~p2(tptp_fun_X_15(tptp_fun_X_16(Y!3)))),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[139, 110])).
% 0.46/0.76 tff(141,plain,
% 0.46/0.76 (((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(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))) | (~p2(tptp_fun_Y_14(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)))),
% 0.46/0.76 inference(tautology,[status(thm)],[])).
% 0.46/0.76 tff(142,plain,
% 0.46/0.76 (r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[141, 110])).
% 0.46/0.76 tff(143,plain,
% 0.46/0.76 (((~![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)))))),
% 0.46/0.76 inference(rewrite,[status(thm)],[])).
% 0.46/0.76 tff(144,plain,
% 0.46/0.76 ((~![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)))))),
% 0.46/0.76 inference(quant_inst,[status(thm)],[])).
% 0.46/0.76 tff(145,plain,
% 0.46/0.76 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), X)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3))))),
% 0.46/0.76 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.46/0.76 tff(146,plain,
% 0.46/0.76 ($false),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[145, 142, 140, 138])).
% 0.46/0.76 tff(147,plain,((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(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))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.76 tff(148,plain,
% 0.46/0.76 ((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))),
% 0.46/0.76 inference(tautology,[status(thm)],[])).
% 0.46/0.76 tff(149,plain,
% 0.46/0.76 (r1(Y!3, tptp_fun_X_16(Y!3))),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[148, 132])).
% 0.46/0.76 tff(150,plain,
% 0.46/0.76 ((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)))),
% 0.46/0.76 inference(tautology,[status(thm)],[])).
% 0.46/0.76 tff(151,plain,
% 0.46/0.76 (~p2(tptp_fun_X_16(Y!3))),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[150, 132])).
% 0.46/0.76 tff(152,plain,
% 0.46/0.76 (((~![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)))) | (~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))) | (~p2(tptp_fun_Y_14(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)))) | (~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))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))))))),
% 0.46/0.76 inference(rewrite,[status(thm)],[])).
% 0.46/0.76 tff(153,plain,
% 0.46/0.76 ((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))))))) <=> (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)))) | (~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))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))))))),
% 0.46/0.76 inference(rewrite,[status(thm)],[])).
% 0.46/0.76 tff(154,plain,
% 0.46/0.76 (((~![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)))) | (~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))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3))))))))),
% 0.46/0.76 inference(monotonicity,[status(thm)],[153])).
% 0.46/0.76 tff(155,plain,
% 0.46/0.76 (((~![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)))) | (~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))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3)))))))),
% 0.46/0.76 inference(transitivity,[status(thm)],[154, 152])).
% 0.46/0.76 tff(156,plain,
% 0.46/0.76 ((~![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)))))))),
% 0.46/0.76 inference(quant_inst,[status(thm)],[])).
% 0.46/0.76 tff(157,plain,
% 0.46/0.76 ((~![X: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))) | p2(tptp_fun_X_16(Y!3)) | (~r1(Y!3, tptp_fun_X_16(Y!3))) | (~((~r1(tptp_fun_X_16(Y!3), tptp_fun_Y_14(tptp_fun_X_16(Y!3)))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!3)), tptp_fun_X_15(tptp_fun_X_16(Y!3)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!3))) | (~p2(tptp_fun_Y_14(tptp_fun_X_16(Y!3))))))),
% 0.46/0.76 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.46/0.76 tff(158,plain,
% 0.46/0.76 ($false),
% 0.46/0.76 inference(unit_resolution,[status(thm)],[157, 151, 149, 147, 109])).
% 0.46/0.76 tff(159,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,[]))).
% 0.46/0.76 tff(160,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)).
% 0.46/0.76 tff(161,plain,
% 0.46/0.76 (((~![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)))))))),
% 0.46/0.76 inference(rewrite,[status(thm)],[])).
% 0.46/0.76 tff(162,plain,
% 0.46/0.76 ((~![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)))))))),
% 0.46/0.76 inference(quant_inst,[status(thm)],[])).
% 0.46/0.76 tff(163,plain,
% 0.46/0.76 ((~![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: $i] : (p2(X) | (~r1(Y!3, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))))))),
% 0.46/0.77 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.46/0.77 tff(164,plain,
% 0.46/0.77 ($false),
% 0.46/0.77 inference(unit_resolution,[status(thm)],[163, 126, 160, 159])).
% 0.46/0.77 tff(165,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,[]))).
% 0.46/0.77 tff(166,plain,
% 0.46/0.77 ((~((~(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)))))))),
% 0.46/0.77 inference(tautology,[status(thm)],[])).
% 0.46/0.77 tff(167,plain,
% 0.46/0.77 ((~((~(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)))))))),
% 0.46/0.77 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.46/0.77 tff(168,plain,
% 0.46/0.77 (~((~(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))))))))),
% 0.46/0.77 inference(unit_resolution,[status(thm)],[167, 108])).
% 0.46/0.77 tff(169,plain,
% 0.46/0.77 (((~(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))))))))),
% 0.46/0.77 inference(tautology,[status(thm)],[])).
% 0.46/0.77 tff(170,plain,
% 0.46/0.77 ((~(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)))))))))),
% 0.46/0.77 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.46/0.77 tff(171,plain,
% 0.46/0.77 (((~((~((~(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)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))))),
% 0.46/0.77 inference(rewrite,[status(thm)],[])).
% 0.46/0.77 tff(172,plain,
% 0.46/0.77 (((~((~((~(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)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.46/0.77 inference(rewrite,[status(thm)],[])).
% 0.46/0.77 tff(173,plain,
% 0.46/0.77 ((((((~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)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.46/0.77 inference(rewrite,[status(thm)],[])).
% 0.46/0.77 tff(174,plain,
% 0.46/0.77 (((((~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)))))))),
% 0.46/0.77 inference(and_elim,[status(thm)],[50])).
% 0.46/0.77 tff(175,plain,
% 0.46/0.77 ((~((~((~(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)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.46/0.78 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.46/0.78 tff(176,plain,
% 0.46/0.78 ((~((~((~(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)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | (~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.46/0.78 inference(modus_ponens,[status(thm)],[175, 172])).
% 0.46/0.78 tff(177,plain,
% 0.46/0.78 ((~((~(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)) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))))),
% 0.46/0.78 inference(modus_ponens,[status(thm)],[176, 171])).
% 0.46/0.78 tff(178,plain,
% 0.46/0.78 (~((~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)) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))))),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[177, 170])).
% 0.46/0.78 tff(179,plain,
% 0.46/0.78 (((~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)) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~r1(X!12, Y!13)) | p2(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))))))))))),
% 0.46/0.78 inference(tautology,[status(thm)],[])).
% 0.46/0.78 tff(180,plain,
% 0.46/0.78 ((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(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)))))))))),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.46/0.78 tff(181,plain,
% 0.46/0.78 (((~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)) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))) | r1(X!0, Y!11)),
% 0.46/0.78 inference(tautology,[status(thm)],[])).
% 0.46/0.78 tff(182,plain,
% 0.46/0.78 (r1(X!0, Y!11)),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[181, 178])).
% 0.46/0.78 tff(183,assumption,(~p2(Y!11)), introduced(assumption)).
% 0.46/0.78 tff(184,assumption,((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11)))), introduced(assumption)).
% 0.46/0.78 tff(185,assumption,(r1(X!0, Y!11)), introduced(assumption)).
% 0.46/0.78 tff(186,assumption,(![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))), introduced(assumption)).
% 0.46/0.78 tff(187,plain,
% 0.46/0.78 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))),
% 0.46/0.78 inference(rewrite,[status(thm)],[])).
% 0.46/0.78 tff(188,plain,
% 0.46/0.78 ((p2(Y!11) | (~r1(X!0, Y!11)) | (~(p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(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_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))),
% 0.46/0.78 inference(rewrite,[status(thm)],[])).
% 0.46/0.78 tff(189,plain,
% 0.46/0.78 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11)))))))),
% 0.46/0.78 inference(monotonicity,[status(thm)],[188])).
% 0.46/0.78 tff(190,plain,
% 0.46/0.78 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))))))),
% 0.46/0.78 inference(transitivity,[status(thm)],[189, 187])).
% 0.46/0.78 tff(191,plain,
% 0.46/0.78 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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(Y!11, tptp_fun_X_4(Y!11))) | (~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))))))),
% 0.46/0.78 inference(quant_inst,[status(thm)],[])).
% 0.46/0.78 tff(192,plain,
% 0.46/0.78 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!11) | (~r1(X!0, Y!11)) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11)))))),
% 0.46/0.78 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.46/0.78 tff(193,plain,
% 0.46/0.78 ($false),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[192, 186, 185, 183, 184])).
% 0.46/0.78 tff(194,plain,((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (~r1(X!0, Y!11)) | p2(Y!11) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11)))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.78 tff(195,plain,
% 0.46/0.78 ((~r1(X!0, Y!11)) | p2(Y!11) | (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11)))))),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[194, 82])).
% 0.46/0.78 tff(196,plain,
% 0.46/0.78 (~((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))))),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[195, 183, 182])).
% 0.46/0.78 tff(197,assumption,(~((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11))))), introduced(assumption)).
% 0.46/0.78 tff(198,plain,
% 0.46/0.78 (((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | r1(Y!11, tptp_fun_X_4(Y!11))),
% 0.46/0.78 inference(tautology,[status(thm)],[])).
% 0.46/0.78 tff(199,plain,
% 0.46/0.78 (r1(Y!11, tptp_fun_X_4(Y!11))),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.46/0.78 tff(200,plain,
% 0.46/0.78 (((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | p2(tptp_fun_X_4(Y!11))),
% 0.46/0.78 inference(tautology,[status(thm)],[])).
% 0.46/0.78 tff(201,plain,
% 0.46/0.78 (p2(tptp_fun_X_4(Y!11))),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[200, 197])).
% 0.46/0.78 tff(202,assumption,(![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))), introduced(assumption)).
% 0.46/0.78 tff(203,plain,
% 0.46/0.78 (((~![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))))),
% 0.46/0.78 inference(rewrite,[status(thm)],[])).
% 0.46/0.78 tff(204,plain,
% 0.46/0.78 ((~![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))))),
% 0.46/0.78 inference(quant_inst,[status(thm)],[])).
% 0.46/0.78 tff(205,plain,
% 0.46/0.78 ((~![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)))),
% 0.46/0.78 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.46/0.78 tff(206,plain,
% 0.46/0.78 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[205, 202, 201, 199])).
% 0.46/0.78 tff(207,plain,
% 0.46/0.78 (((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | (~p2(tptp_fun_Y_5(Y!11)))),
% 0.46/0.78 inference(tautology,[status(thm)],[])).
% 0.46/0.78 tff(208,plain,
% 0.46/0.78 (~p2(tptp_fun_Y_5(Y!11))),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[207, 197])).
% 0.46/0.78 tff(209,plain,
% 0.46/0.78 (((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(Y!11, tptp_fun_X_4(Y!11)))) | r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))),
% 0.46/0.78 inference(tautology,[status(thm)],[])).
% 0.46/0.78 tff(210,plain,
% 0.46/0.78 (r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))),
% 0.46/0.78 inference(unit_resolution,[status(thm)],[209, 197])).
% 0.46/0.78 tff(211,plain,
% 0.46/0.78 (((~![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))))),
% 0.46/0.79 inference(rewrite,[status(thm)],[])).
% 0.46/0.79 tff(212,plain,
% 0.46/0.79 ((~![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))))),
% 0.46/0.79 inference(quant_inst,[status(thm)],[])).
% 0.46/0.79 tff(213,plain,
% 0.46/0.79 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!11), Y)))) | p2(tptp_fun_Y_5(Y!11)) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11)))),
% 0.46/0.79 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.46/0.79 tff(214,plain,
% 0.46/0.79 ($false),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[213, 210, 208, 206])).
% 0.46/0.79 tff(215,plain,(((~p2(tptp_fun_X_4(Y!11))) | (~r1(tptp_fun_X_4(Y!11), tptp_fun_Y_5(Y!11))) | p2(tptp_fun_Y_5(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,[]))).
% 0.46/0.79 tff(216,plain,
% 0.46/0.79 (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[215, 196])).
% 0.46/0.79 tff(217,plain,
% 0.46/0.79 ((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))))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(218,plain,
% 0.46/0.79 (p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.46/0.79 tff(219,plain,
% 0.46/0.79 (((~![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))))))))),
% 0.46/0.79 inference(rewrite,[status(thm)],[])).
% 0.46/0.79 tff(220,plain,
% 0.46/0.79 ((~![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))))))))),
% 0.46/0.79 inference(quant_inst,[status(thm)],[])).
% 0.46/0.79 tff(221,plain,
% 0.46/0.79 ((~![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)))))))),
% 0.46/0.79 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.46/0.79 tff(222,plain,
% 0.46/0.79 (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)))))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[221, 182, 124])).
% 0.46/0.79 tff(223,plain,
% 0.46/0.79 (~(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))))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[222, 183])).
% 0.46/0.79 tff(224,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)).
% 0.46/0.79 tff(225,plain,
% 0.46/0.79 ((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))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(226,plain,
% 0.46/0.79 (r1(Y!11, tptp_fun_X_16(Y!11))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.46/0.79 tff(227,plain,
% 0.46/0.79 ((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)))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(228,plain,
% 0.46/0.79 (~p2(tptp_fun_X_16(Y!11))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[227, 224])).
% 0.46/0.79 tff(229,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)).
% 0.46/0.79 tff(230,plain,
% 0.46/0.79 (((~![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)))))))),
% 0.46/0.79 inference(rewrite,[status(thm)],[])).
% 0.46/0.79 tff(231,plain,
% 0.46/0.79 ((~![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)))))))),
% 0.46/0.79 inference(quant_inst,[status(thm)],[])).
% 0.46/0.79 tff(232,plain,
% 0.46/0.79 ((~![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))))))),
% 0.46/0.79 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.46/0.79 tff(233,plain,
% 0.46/0.79 (~((~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)))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[232, 229, 228, 226])).
% 0.46/0.79 tff(234,plain,
% 0.46/0.79 (((~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)))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(235,plain,
% 0.46/0.79 (p2(tptp_fun_Y_14(tptp_fun_X_16(Y!11)))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.46/0.79 tff(236,plain,
% 0.46/0.79 (((~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)))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(237,plain,
% 0.46/0.79 (r1(tptp_fun_X_16(Y!11), tptp_fun_Y_14(tptp_fun_X_16(Y!11)))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[236, 233])).
% 0.46/0.79 tff(238,plain,
% 0.46/0.79 ((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))))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(239,plain,
% 0.46/0.79 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_16(Y!11), Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[238, 224])).
% 0.46/0.79 tff(240,plain,
% 0.46/0.79 (((~![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))))),
% 0.46/0.79 inference(rewrite,[status(thm)],[])).
% 0.46/0.79 tff(241,plain,
% 0.46/0.79 ((~![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))))),
% 0.46/0.79 inference(quant_inst,[status(thm)],[])).
% 0.46/0.79 tff(242,plain,
% 0.46/0.79 ((~![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)))),
% 0.46/0.79 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.46/0.79 tff(243,plain,
% 0.46/0.79 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X)))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[242, 239, 237, 235])).
% 0.46/0.79 tff(244,plain,
% 0.46/0.79 (((~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)))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(245,plain,
% 0.46/0.79 (r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11)))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[244, 233])).
% 0.46/0.79 tff(246,plain,
% 0.46/0.79 (((~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))))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(247,plain,
% 0.46/0.79 (~p2(tptp_fun_X_15(tptp_fun_X_16(Y!11)))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[246, 233])).
% 0.46/0.79 tff(248,plain,
% 0.46/0.79 (((~![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)))))),
% 0.46/0.79 inference(rewrite,[status(thm)],[])).
% 0.46/0.79 tff(249,plain,
% 0.46/0.79 ((~![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)))))),
% 0.46/0.79 inference(quant_inst,[status(thm)],[])).
% 0.46/0.79 tff(250,plain,
% 0.46/0.79 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), X)))) | p2(tptp_fun_X_15(tptp_fun_X_16(Y!11))) | (~r1(tptp_fun_Y_14(tptp_fun_X_16(Y!11)), tptp_fun_X_15(tptp_fun_X_16(Y!11))))),
% 0.46/0.79 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.46/0.79 tff(251,plain,
% 0.46/0.79 ($false),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[250, 247, 245, 243])).
% 0.46/0.79 tff(252,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,[]))).
% 0.46/0.79 tff(253,plain,
% 0.46/0.79 (~![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))))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[252, 223])).
% 0.46/0.79 tff(254,plain,
% 0.46/0.79 (((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(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))))))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(255,plain,
% 0.46/0.79 ((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(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)))))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.46/0.79 tff(256,plain,
% 0.46/0.79 ((~((~(p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))))) | (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(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)) | (~r1(X!12, Y!13)) | p2(Y!13) | (~![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))) | (~![X: $i] : (p2(X) | (~r1(Y!11, X)) | (~((~r1(X, tptp_fun_Y_14(X))) | (~p2(tptp_fun_Y_14(X))) | p2(tptp_fun_X_15(X)) | (~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X)))))))))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(257,plain,
% 0.46/0.79 ($false),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[256, 255, 218, 180])).
% 0.46/0.79 tff(258,plain,(p2(Y!11)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.79 tff(259,plain,
% 0.46/0.79 ((p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))) | (~p2(Y!11))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(260,plain,
% 0.46/0.79 (p2(Y!11) | (~![X: $i] : ((~p2(X)) | (~r1(Y!11, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y)))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[259, 258])).
% 0.46/0.79 tff(261,plain,
% 0.46/0.79 (~((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(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))))))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[256, 260, 180])).
% 0.46/0.79 tff(262,plain,
% 0.46/0.79 (((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(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))))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(263,plain,
% 0.46/0.79 (![X: $i] : ((~p2(X)) | (~r1(Y!13, X)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.46/0.79 tff(264,plain,
% 0.46/0.79 (((~![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))))),
% 0.46/0.79 inference(rewrite,[status(thm)],[])).
% 0.46/0.79 tff(265,plain,
% 0.46/0.79 ((~![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))))),
% 0.46/0.79 inference(quant_inst,[status(thm)],[])).
% 0.46/0.79 tff(266,plain,
% 0.46/0.79 ((~![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)))),
% 0.46/0.79 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.46/0.79 tff(267,plain,
% 0.46/0.79 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[266, 263, 5, 3])).
% 0.46/0.79 tff(268,plain,
% 0.46/0.79 ((p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(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))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(269,plain,
% 0.46/0.79 (r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[268, 1])).
% 0.46/0.79 tff(270,plain,
% 0.46/0.79 ((p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))) | (~p2(tptp_fun_Y_5(Y!13)))),
% 0.46/0.79 inference(tautology,[status(thm)],[])).
% 0.46/0.79 tff(271,plain,
% 0.46/0.79 (~p2(tptp_fun_Y_5(Y!13))),
% 0.46/0.79 inference(unit_resolution,[status(thm)],[270, 1])).
% 0.46/0.79 tff(272,plain,
% 0.46/0.79 (((~![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))))),
% 0.46/0.79 inference(rewrite,[status(thm)],[])).
% 0.46/0.79 tff(273,plain,
% 0.46/0.79 ((~![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))))),
% 0.46/0.79 inference(quant_inst,[status(thm)],[])).
% 0.46/0.80 tff(274,plain,
% 0.46/0.80 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!13), Y)))) | p2(tptp_fun_Y_5(Y!13)) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))),
% 0.46/0.80 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.46/0.80 tff(275,plain,
% 0.46/0.80 ($false),
% 0.46/0.80 inference(unit_resolution,[status(thm)],[274, 271, 269, 267])).
% 0.46/0.80 tff(276,plain,(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.80 tff(277,assumption,(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))), introduced(assumption)).
% 0.46/0.80 tff(278,assumption,(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))), introduced(assumption)).
% 0.46/0.80 tff(279,plain,
% 0.46/0.80 (((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(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))),
% 0.46/0.80 inference(tautology,[status(thm)],[])).
% 0.46/0.80 tff(280,plain,
% 0.46/0.80 (~p2(Y!13)),
% 0.46/0.80 inference(unit_resolution,[status(thm)],[279, 261])).
% 0.46/0.80 tff(281,plain,
% 0.46/0.80 ((~(p2(Y!13) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) | p2(Y!13) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))))),
% 0.46/0.80 inference(tautology,[status(thm)],[])).
% 0.46/0.80 tff(282,plain,
% 0.46/0.80 (~(p2(Y!13) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.46/0.80 inference(unit_resolution,[status(thm)],[281, 280, 278])).
% 0.46/0.80 tff(283,plain,
% 0.46/0.80 (((~(p2(Y!13) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))) | (p2(Y!13) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.46/0.80 inference(tautology,[status(thm)],[])).
% 0.46/0.80 tff(284,plain,
% 0.46/0.80 ((~(p2(Y!13) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))),
% 0.46/0.80 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.46/0.80 tff(285,assumption,(![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))), introduced(assumption)).
% 0.46/0.80 tff(286,plain,
% 0.46/0.80 (((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(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)),
% 0.56/0.80 inference(tautology,[status(thm)],[])).
% 0.56/0.80 tff(287,plain,
% 0.56/0.80 (r1(X!12, Y!13)),
% 0.56/0.80 inference(unit_resolution,[status(thm)],[286, 261])).
% 0.56/0.80 tff(288,plain,
% 0.56/0.80 (((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.56/0.80 inference(rewrite,[status(thm)],[])).
% 0.56/0.80 tff(289,plain,
% 0.56/0.80 ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | ((~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.56/0.80 inference(quant_inst,[status(thm)],[])).
% 0.56/0.80 tff(290,plain,
% 0.56/0.80 ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~r1(X!12, Y!13)) | (~((~(p2(Y!13) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(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: $i] : (p2(Y) | (~r1(X, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))),
% 0.56/0.80 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.56/0.80 tff(291,plain,
% 0.56/0.80 ($false),
% 0.56/0.80 inference(unit_resolution,[status(thm)],[290, 287, 285, 284])).
% 0.56/0.80 tff(292,plain,((~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.80 tff(293,plain,
% 0.56/0.80 (~![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.56/0.80 inference(unit_resolution,[status(thm)],[292, 278])).
% 0.56/0.80 tff(294,plain,
% 0.56/0.80 (((~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)) | (~r1(X!12, Y!13)) | p2(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.56/0.80 inference(tautology,[status(thm)],[])).
% 0.56/0.80 tff(295,plain,
% 0.56/0.80 (![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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.56/0.80 inference(unit_resolution,[status(thm)],[294, 178])).
% 0.56/0.80 tff(296,plain,
% 0.56/0.80 (((~r1(Y!11, X!12)) | (~r1(X!12, Y!13)) | p2(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)),
% 0.56/0.80 inference(tautology,[status(thm)],[])).
% 0.56/0.80 tff(297,plain,
% 0.56/0.80 (r1(Y!11, X!12)),
% 0.56/0.80 inference(unit_resolution,[status(thm)],[296, 261])).
% 0.56/0.80 tff(298,plain,
% 0.56/0.80 (((~![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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.56/0.80 inference(rewrite,[status(thm)],[])).
% 0.56/0.80 tff(299,plain,
% 0.56/0.80 (((~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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.56/0.80 inference(rewrite,[status(thm)],[])).
% 0.56/0.80 tff(300,plain,
% 0.56/0.80 (((~![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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))))),
% 0.56/0.81 inference(monotonicity,[status(thm)],[299])).
% 0.56/0.81 tff(301,plain,
% 0.56/0.81 (((~![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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.56/0.81 inference(transitivity,[status(thm)],[300, 298])).
% 0.56/0.81 tff(302,plain,
% 0.56/0.81 ((~![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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y)))))))))))))),
% 0.56/0.81 inference(quant_inst,[status(thm)],[])).
% 0.56/0.81 tff(303,plain,
% 0.56/0.81 ((~![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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.56/0.81 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.56/0.81 tff(304,plain,
% 0.56/0.81 ((~(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))))))))),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[303, 297, 295])).
% 0.56/0.81 tff(305,plain,
% 0.56/0.81 (~((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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))))),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[304, 293, 277])).
% 0.56/0.81 tff(306,plain,
% 0.56/0.81 (((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(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)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.56/0.81 inference(tautology,[status(thm)],[])).
% 0.56/0.81 tff(307,plain,
% 0.56/0.81 (![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[306, 305])).
% 0.56/0.81 tff(308,plain,
% 0.56/0.81 (((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!13) | (~r1(X!12, Y!13)) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.56/0.81 inference(rewrite,[status(thm)],[])).
% 0.56/0.81 tff(309,plain,
% 0.56/0.81 ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | (p2(Y!13) | (~r1(X!12, Y!13)) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))))),
% 0.56/0.81 inference(quant_inst,[status(thm)],[])).
% 0.56/0.81 tff(310,plain,
% 0.56/0.81 ((~![Y: $i] : (p2(Y) | (~r1(X!12, Y)) | (~(p2(tptp_fun_Y_5(Y)) | (~r1(Y, tptp_fun_X_4(Y))) | (~p2(tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) | p2(Y!13) | (~r1(X!12, Y!13)) | (~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13)))))),
% 0.56/0.81 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.56/0.81 tff(311,plain,
% 0.56/0.81 ($false),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[310, 287, 280, 278, 307])).
% 0.56/0.81 tff(312,plain,((~(p2(tptp_fun_Y_5(Y!13)) | (~r1(Y!13, tptp_fun_X_4(Y!13))) | (~p2(tptp_fun_X_4(Y!13))) | (~r1(tptp_fun_X_4(Y!13), tptp_fun_Y_5(Y!13))))) | (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.81 tff(313,plain,
% 0.56/0.81 (~(p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))))),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[312, 276])).
% 0.56/0.81 tff(314,plain,
% 0.56/0.81 ((p2(X!12) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X)))))) | (~p2(X!12))),
% 0.56/0.81 inference(tautology,[status(thm)],[])).
% 0.56/0.81 tff(315,plain,
% 0.56/0.81 (~p2(X!12)),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[314, 313])).
% 0.56/0.81 tff(316,plain,
% 0.56/0.81 (![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))))))),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[254, 261])).
% 0.56/0.81 tff(317,plain,
% 0.56/0.81 (((~![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))))))),
% 0.56/0.81 inference(rewrite,[status(thm)],[])).
% 0.56/0.81 tff(318,plain,
% 0.56/0.81 ((~![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))))))),
% 0.56/0.81 inference(quant_inst,[status(thm)],[])).
% 0.56/0.81 tff(319,plain,
% 0.56/0.81 ((~![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)))))),
% 0.56/0.81 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.56/0.81 tff(320,plain,
% 0.56/0.81 (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)))))),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[319, 297, 316])).
% 0.56/0.81 tff(321,plain,
% 0.56/0.81 (~((~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))))),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[320, 315])).
% 0.56/0.81 tff(322,plain,
% 0.56/0.81 (((~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))),
% 0.56/0.81 inference(tautology,[status(thm)],[])).
% 0.56/0.81 tff(323,plain,
% 0.56/0.81 (p2(tptp_fun_Y_14(X!12))),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[322, 321])).
% 0.56/0.81 tff(324,plain,
% 0.56/0.81 (((~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))),
% 0.56/0.81 inference(tautology,[status(thm)],[])).
% 0.56/0.81 tff(325,plain,
% 0.56/0.81 (r1(X!12, tptp_fun_Y_14(X!12))),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[324, 321])).
% 0.56/0.81 tff(326,plain,
% 0.56/0.81 ((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))))),
% 0.56/0.81 inference(tautology,[status(thm)],[])).
% 0.56/0.81 tff(327,plain,
% 0.56/0.81 (![Y: $i] : ((~p2(Y)) | (~r1(X!12, Y)) | ![X: $i] : (p2(X) | (~r1(Y, X))))),
% 0.56/0.81 inference(unit_resolution,[status(thm)],[326, 313])).
% 0.56/0.81 tff(328,plain,
% 0.56/0.81 (((~![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))))),
% 0.56/0.81 inference(rewrite,[status(thm)],[])).
% 0.56/0.81 tff(329,plain,
% 0.56/0.81 ((~![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))))),
% 0.56/0.81 inference(quant_inst,[status(thm)],[])).
% 0.56/0.82 tff(330,plain,
% 0.56/0.82 ((~![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)))),
% 0.56/0.82 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.56/0.82 tff(331,plain,
% 0.56/0.82 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))),
% 0.56/0.82 inference(unit_resolution,[status(thm)],[330, 327, 325, 323])).
% 0.56/0.82 tff(332,plain,
% 0.56/0.82 (((~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))),
% 0.56/0.82 inference(tautology,[status(thm)],[])).
% 0.56/0.82 tff(333,plain,
% 0.56/0.82 (r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12))),
% 0.56/0.82 inference(unit_resolution,[status(thm)],[332, 321])).
% 0.56/0.82 tff(334,plain,
% 0.56/0.82 (((~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)))),
% 0.56/0.82 inference(tautology,[status(thm)],[])).
% 0.56/0.82 tff(335,plain,
% 0.56/0.82 (~p2(tptp_fun_X_15(X!12))),
% 0.56/0.82 inference(unit_resolution,[status(thm)],[334, 321])).
% 0.56/0.82 tff(336,plain,
% 0.56/0.82 (((~![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))))),
% 0.56/0.82 inference(rewrite,[status(thm)],[])).
% 0.56/0.82 tff(337,plain,
% 0.56/0.82 ((~![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))))),
% 0.56/0.82 inference(quant_inst,[status(thm)],[])).
% 0.56/0.82 tff(338,plain,
% 0.56/0.82 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_14(X!12), X)))) | p2(tptp_fun_X_15(X!12)) | (~r1(tptp_fun_Y_14(X!12), tptp_fun_X_15(X!12)))),
% 0.56/0.82 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.56/0.82 tff(339,plain,
% 0.56/0.82 ($false),
% 0.56/0.82 inference(unit_resolution,[status(thm)],[338, 335, 333, 331])).
% 0.56/0.82 % SZS output end Proof
% 0.56/0.82 % E exiting
%------------------------------------------------------------------------------