%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL642+1.010 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n016.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 03:00:20 PM UTC 2026
% Result : Theorem 0.66s 0.90s
% Output : Proof 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL642+1.010 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 00:52:45 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.66/0.90 % SZS status Theorem
% 0.66/0.90 % SZS output start Proof
% 0.66/0.90 tff(r1_type, type, (
% 0.66/0.90 r1: ( $i * $i ) > $o)).
% 0.66/0.90 tff(tptp_fun_Y_11_type, type, (
% 0.66/0.90 tptp_fun_Y_11: $i > $i)).
% 0.66/0.90 tff(tptp_fun_X_16_type, type, (
% 0.66/0.90 tptp_fun_X_16: $i)).
% 0.66/0.90 tff(p2_type, type, (
% 0.66/0.90 p2: $i > $o)).
% 0.66/0.90 tff(tptp_fun_X_12_type, type, (
% 0.66/0.90 tptp_fun_X_12: $i > $i)).
% 0.66/0.90 tff(tptp_fun_Y_19_type, type, (
% 0.66/0.90 tptp_fun_Y_19: $i > $i)).
% 0.66/0.90 tff(tptp_fun_X_20_type, type, (
% 0.66/0.90 tptp_fun_X_20: $i > $i)).
% 0.66/0.90 tff(tptp_fun_X_6_type, type, (
% 0.66/0.90 tptp_fun_X_6: $i > $i)).
% 0.66/0.90 tff(tptp_fun_Y_7_type, type, (
% 0.66/0.90 tptp_fun_Y_7: $i > $i)).
% 0.66/0.90 tff(tptp_fun_Y_17_type, type, (
% 0.66/0.90 tptp_fun_Y_17: $i)).
% 0.66/0.90 tff(tptp_fun_Y_15_type, type, (
% 0.66/0.90 tptp_fun_Y_15: $i)).
% 0.66/0.90 tff(tptp_fun_X_18_type, type, (
% 0.66/0.90 tptp_fun_X_18: $i > $i)).
% 0.66/0.90 tff(tptp_fun_X_0_type, type, (
% 0.66/0.90 tptp_fun_X_0: $i)).
% 0.66/0.90 tff(tptp_fun_Y_10_type, type, (
% 0.66/0.90 tptp_fun_Y_10: $i)).
% 0.66/0.90 tff(tptp_fun_X_14_type, type, (
% 0.66/0.90 tptp_fun_X_14: $i)).
% 0.66/0.90 tff(tptp_fun_Y_13_type, type, (
% 0.66/0.90 tptp_fun_Y_13: $i)).
% 0.66/0.90 tff(tptp_fun_Y_44_type, type, (
% 0.66/0.90 tptp_fun_Y_44: $i > $i)).
% 0.66/0.90 tff(p1_type, type, (
% 0.66/0.90 p1: $i > $o)).
% 0.66/0.90 tff(tptp_fun_Y_49_type, type, (
% 0.66/0.90 tptp_fun_Y_49: $i)).
% 0.66/0.90 tff(tptp_fun_X_50_type, type, (
% 0.66/0.90 tptp_fun_X_50: $i)).
% 0.66/0.90 tff(tptp_fun_Y_47_type, type, (
% 0.66/0.90 tptp_fun_Y_47: $i)).
% 0.66/0.90 tff(tptp_fun_X_48_type, type, (
% 0.66/0.90 tptp_fun_X_48: $i)).
% 0.66/0.90 tff(p3_type, type, (
% 0.66/0.90 p3: $i > $o)).
% 0.66/0.90 tff(tptp_fun_Y_45_type, type, (
% 0.66/0.90 tptp_fun_Y_45: $i)).
% 0.66/0.90 tff(tptp_fun_X_46_type, type, (
% 0.66/0.90 tptp_fun_X_46: $i)).
% 0.66/0.90 tff(p4_type, type, (
% 0.66/0.90 p4: $i > $o)).
% 0.66/0.90 tff(tptp_fun_Y_42_type, type, (
% 0.66/0.90 tptp_fun_Y_42: $i)).
% 0.66/0.90 tff(tptp_fun_X_43_type, type, (
% 0.66/0.90 tptp_fun_X_43: $i)).
% 0.66/0.90 tff(tptp_fun_X_32_type, type, (
% 0.66/0.90 tptp_fun_X_32: $i > $i)).
% 0.66/0.90 tff(tptp_fun_Y_31_type, type, (
% 0.66/0.90 tptp_fun_Y_31: $i > $i)).
% 0.66/0.90 tff(tptp_fun_Y_39_type, type, (
% 0.66/0.90 tptp_fun_Y_39: $i)).
% 0.66/0.90 tff(tptp_fun_Y_41_type, type, (
% 0.66/0.90 tptp_fun_Y_41: $i)).
% 0.66/0.90 tff(tptp_fun_X_40_type, type, (
% 0.66/0.90 tptp_fun_X_40: $i)).
% 0.66/0.90 tff(tptp_fun_Y_36_type, type, (
% 0.66/0.90 tptp_fun_Y_36: $i)).
% 0.66/0.90 tff(tptp_fun_Y_38_type, type, (
% 0.66/0.90 tptp_fun_Y_38: $i)).
% 0.66/0.90 tff(tptp_fun_X_37_type, type, (
% 0.66/0.90 tptp_fun_X_37: $i)).
% 0.66/0.90 tff(tptp_fun_Y_33_type, type, (
% 0.66/0.90 tptp_fun_Y_33: $i)).
% 0.66/0.90 tff(tptp_fun_Y_35_type, type, (
% 0.66/0.90 tptp_fun_Y_35: $i)).
% 0.66/0.90 tff(tptp_fun_X_34_type, type, (
% 0.66/0.90 tptp_fun_X_34: $i)).
% 0.66/0.90 tff(tptp_fun_Y_28_type, type, (
% 0.66/0.90 tptp_fun_Y_28: $i)).
% 0.66/0.90 tff(tptp_fun_Y_30_type, type, (
% 0.66/0.90 tptp_fun_Y_30: $i)).
% 0.66/0.90 tff(tptp_fun_X_29_type, type, (
% 0.66/0.90 tptp_fun_X_29: $i)).
% 0.66/0.90 tff(tptp_fun_Y_27_type, type, (
% 0.66/0.90 tptp_fun_Y_27: $i > $i)).
% 0.66/0.90 tff(tptp_fun_X_26_type, type, (
% 0.66/0.90 tptp_fun_X_26: $i > $i)).
% 0.66/0.90 tff(tptp_fun_Y_25_type, type, (
% 0.66/0.90 tptp_fun_Y_25: $i > $i)).
% 0.66/0.90 tff(tptp_fun_Y_21_type, type, (
% 0.66/0.90 tptp_fun_Y_21: $i)).
% 0.66/0.90 tff(tptp_fun_X_24_type, type, (
% 0.66/0.90 tptp_fun_X_24: $i)).
% 0.66/0.90 tff(tptp_fun_Y_23_type, type, (
% 0.66/0.90 tptp_fun_Y_23: $i)).
% 0.66/0.90 tff(tptp_fun_X_22_type, type, (
% 0.66/0.90 tptp_fun_X_22: $i)).
% 0.66/0.90 tff(tptp_fun_Y_9_type, type, (
% 0.66/0.90 tptp_fun_Y_9: $i > $i)).
% 0.66/0.90 tff(tptp_fun_X_8_type, type, (
% 0.66/0.90 tptp_fun_X_8: $i > $i)).
% 0.66/0.90 tff(tptp_fun_Y_5_type, type, (
% 0.66/0.90 tptp_fun_Y_5: $i > $i)).
% 0.66/0.90 tff(tptp_fun_X_4_type, type, (
% 0.66/0.90 tptp_fun_X_4: $i > $i)).
% 0.66/0.90 tff(tptp_fun_Y_3_type, type, (
% 0.66/0.90 tptp_fun_Y_3: $i)).
% 0.66/0.90 tff(tptp_fun_Y_2_type, type, (
% 0.66/0.90 tptp_fun_Y_2: $i)).
% 0.66/0.90 tff(tptp_fun_Y_1_type, type, (
% 0.66/0.90 tptp_fun_Y_1: $i)).
% 0.66/0.90 tff(1,assumption,(~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))), introduced(assumption)).
% 0.66/0.90 tff(2,plain,
% 0.66/0.90 (((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17)))) | (~p2(tptp_fun_Y_7(Y!17)))),
% 0.66/0.90 inference(tautology,[status(thm)],[])).
% 0.66/0.90 tff(3,plain,
% 0.66/0.90 (~p2(tptp_fun_Y_7(Y!17))),
% 0.66/0.90 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.66/0.90 tff(4,plain,
% 0.66/0.90 (((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17)))) | r1(Y!17, tptp_fun_X_6(Y!17))),
% 0.66/0.90 inference(tautology,[status(thm)],[])).
% 0.66/0.90 tff(5,plain,
% 0.66/0.90 (r1(Y!17, tptp_fun_X_6(Y!17))),
% 0.66/0.90 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.66/0.90 tff(6,plain,
% 0.66/0.90 (((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17)))) | p2(tptp_fun_X_6(Y!17))),
% 0.66/0.90 inference(tautology,[status(thm)],[])).
% 0.66/0.90 tff(7,plain,
% 0.66/0.90 (p2(tptp_fun_X_6(Y!17))),
% 0.66/0.90 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.66/0.90 tff(8,assumption,(~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))), introduced(assumption)).
% 0.66/0.90 tff(9,plain,
% 0.66/0.90 (((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!10))),
% 0.66/0.90 inference(tautology,[status(thm)],[])).
% 0.66/0.90 tff(10,plain,
% 0.66/0.90 (~p2(Y!10)),
% 0.66/0.90 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.66/0.90 tff(11,plain,
% 0.66/0.90 (((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(X!0, Y!10)),
% 0.66/0.90 inference(tautology,[status(thm)],[])).
% 0.66/0.90 tff(12,plain,
% 0.66/0.90 (r1(X!0, Y!10)),
% 0.66/0.90 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.66/0.90 tff(13,plain,
% 0.66/0.90 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.66/0.90 inference(bind,[status(th)],[])).
% 0.66/0.90 tff(14,plain,
% 0.66/0.90 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.66/0.90 inference(quant_intro,[status(thm)],[13])).
% 0.66/0.90 tff(15,plain,
% 0.66/0.90 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.66/0.90 inference(bind,[status(th)],[])).
% 0.66/0.90 tff(16,plain,
% 0.66/0.90 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.66/0.90 inference(quant_intro,[status(thm)],[15])).
% 0.66/0.90 tff(17,plain,
% 0.66/0.90 (((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~(p2(X!14) | (~r1(Y!13, X!14))))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))) | (~r1(Y!15, X)))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~(p2(X!14) | (~r1(Y!13, X!14))))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))) | (~r1(Y!15, X)))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))),
% 0.66/0.91 inference(rewrite,[status(thm)],[])).
% 0.66/0.92 tff(18,plain,
% 0.66/0.92 ((((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~r1(Y!10, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & (((r1(Y!15, X!16) & (r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~r1(Y!17, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & (r1(X, tptp_fun_Y_19(X)) & (r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~r1(tptp_fun_X_20(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & ((~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & ((~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24))) & ![X: $i] : ((~r1(Y!21, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & ((~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & ((~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30)) & ![X: $i] : ((~r1(Y!28, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & ((~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35)) & ![X: $i] : ((~r1(Y!33, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & ((~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38)) & ![X: $i] : ((~r1(Y!36, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & ((~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41)) & ![X: $i] : ((~r1(Y!39, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : ((~r1(Y!42, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : ((~r1(Y!45, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : ((~r1(Y!47, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : ((~r1(Y!49, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~(p2(X!14) | (~r1(Y!13, X!14))))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))) | (~r1(Y!15, X)))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))),
% 0.66/0.92 inference(rewrite,[status(thm)],[])).
% 0.66/0.92 tff(19,plain,
% 0.66/0.92 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))) <=> (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))), ((r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))) <=> (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))))), (((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))))), rewrite(((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))))), (((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))))))),
% 0.66/0.92 inference(bind,[status(th)],[])).
% 0.66/0.92 tff(20,plain,
% 0.66/0.92 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))))),
% 0.66/0.92 inference(quant_intro,[status(thm)],[19])).
% 0.66/0.92 tff(21,plain,
% 0.66/0.92 (^[Y: $i] : trans(monotonicity(rewrite((r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))) <=> (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))), (((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))), rewrite(((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))), (((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))))),
% 0.66/0.92 inference(bind,[status(th)],[])).
% 0.66/0.92 tff(22,plain,
% 0.66/0.92 (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))),
% 0.66/0.92 inference(quant_intro,[status(thm)],[21])).
% 0.66/0.92 tff(23,plain,
% 0.66/0.92 ((~((~r1(X!0, Y!3)) | p1(Y!3))) <=> (~((~r1(X!0, Y!3)) | p1(Y!3)))),
% 0.66/0.92 inference(rewrite,[status(thm)],[])).
% 0.66/0.92 tff(24,plain,
% 0.66/0.92 ((~((~r1(X!0, Y!1)) | p2(Y!1))) <=> (~((~r1(X!0, Y!1)) | p2(Y!1)))),
% 0.66/0.93 inference(rewrite,[status(thm)],[])).
% 0.66/0.93 tff(25,plain,
% 0.66/0.93 (((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~r1(Y!10, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & (((r1(Y!15, X!16) & (r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~r1(Y!17, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & (r1(X, tptp_fun_Y_19(X)) & (r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~r1(tptp_fun_X_20(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & ((~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & ((~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24))) & ![X: $i] : ((~r1(Y!21, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & ((~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & ((~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30)) & ![X: $i] : ((~r1(Y!28, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & ((~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35)) & ![X: $i] : ((~r1(Y!33, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & ((~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38)) & ![X: $i] : ((~r1(Y!36, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & ((~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41)) & ![X: $i] : ((~r1(Y!39, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : ((~r1(Y!42, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : ((~r1(Y!45, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : ((~r1(Y!47, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : ((~r1(Y!49, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~(p2(X!14) | (~r1(Y!13, X!14))))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))) | (~r1(Y!15, X)))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.66/0.94 inference(monotonicity,[status(thm)],[24, 23, 22, 20, 18])).
% 0.66/0.94 tff(26,plain,
% 0.66/0.94 (((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~r1(Y!10, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & (((r1(Y!15, X!16) & (r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~r1(Y!17, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & (r1(X, tptp_fun_Y_19(X)) & (r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~r1(tptp_fun_X_20(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & ((~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & ((~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24))) & ![X: $i] : ((~r1(Y!21, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & ((~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & ((~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30)) & ![X: $i] : ((~r1(Y!28, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & ((~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35)) & ![X: $i] : ((~r1(Y!33, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & ((~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38)) & ![X: $i] : ((~r1(Y!36, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & ((~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41)) & ![X: $i] : ((~r1(Y!39, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : ((~r1(Y!42, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : ((~r1(Y!45, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : ((~r1(Y!47, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : ((~r1(Y!49, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~(p2(X!14) | (~r1(Y!13, X!14))))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))) | (~r1(Y!15, X)))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))),
% 0.66/0.94 inference(transitivity,[status(thm)],[25, 17])).
% 0.66/0.94 tff(27,plain,
% 0.66/0.94 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![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)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![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)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.66/0.95 inference(rewrite,[status(thm)],[])).
% 0.66/0.95 tff(28,plain,
% 0.66/0.95 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![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)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![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)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.66/0.96 inference(rewrite,[status(thm)],[])).
% 0.66/0.96 tff(29,plain,
% 0.66/0.96 ((~?[X: $i] : (~((((((![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)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![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)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.66/0.97 inference(rewrite,[status(thm)],[])).
% 0.66/0.97 tff(30,plain,
% 0.66/0.97 ((~(~?[X: $i] : (~((((((![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)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![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)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))))),
% 0.66/0.98 inference(monotonicity,[status(thm)],[29])).
% 0.66/0.98 tff(31,plain,
% 0.66/0.98 ((~(~?[X: $i] : (~((((((![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)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![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)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.66/0.98 inference(transitivity,[status(thm)],[30, 28])).
% 0.66/0.99 tff(32,axiom,(~(~?[X: $i] : (~((((((![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)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.66/0.99 tff(33,plain,
% 0.66/0.99 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![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)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.66/0.99 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.66/0.99 tff(34,plain,
% 0.66/0.99 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![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)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(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] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.66/1.00 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.66/1.00 tff(35,plain,
% 0.66/1.00 ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~(p2(X!14) | (~r1(Y!13, X!14))))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))) | (~r1(Y!15, X)))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))),
% 0.66/1.00 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.66/1.00 tff(36,plain,
% 0.66/1.00 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))),
% 0.66/1.00 inference(and_elim,[status(thm)],[35])).
% 0.66/1.00 tff(37,plain,
% 0.66/1.00 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.66/1.00 inference(modus_ponens,[status(thm)],[36, 16])).
% 0.66/1.00 tff(38,plain,
% 0.66/1.00 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.66/1.00 inference(modus_ponens,[status(thm)],[37, 14])).
% 0.66/1.00 tff(39,plain,
% 0.66/1.00 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))))),
% 0.66/1.00 inference(rewrite,[status(thm)],[])).
% 0.66/1.00 tff(40,plain,
% 0.66/1.00 ((p2(Y!10) | (~r1(X!0, Y!10)) | (~((~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10)))))) <=> (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))))),
% 0.66/1.00 inference(rewrite,[status(thm)],[])).
% 0.66/1.00 tff(41,plain,
% 0.66/1.00 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10)))))))),
% 0.66/1.00 inference(monotonicity,[status(thm)],[40])).
% 0.66/1.00 tff(42,plain,
% 0.66/1.00 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))))),
% 0.66/1.00 inference(transitivity,[status(thm)],[41, 39])).
% 0.66/1.00 tff(43,plain,
% 0.66/1.00 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))))))),
% 0.66/1.00 inference(quant_inst,[status(thm)],[])).
% 0.66/1.00 tff(44,plain,
% 0.66/1.00 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10)))))),
% 0.66/1.00 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.66/1.00 tff(45,plain,
% 0.66/1.00 (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))),
% 0.66/1.00 inference(unit_resolution,[status(thm)],[44, 38, 12, 10])).
% 0.66/1.00 tff(46,plain,
% 0.66/1.00 (((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10)))) | p2(tptp_fun_X_6(Y!10))),
% 0.66/1.00 inference(tautology,[status(thm)],[])).
% 0.66/1.00 tff(47,plain,
% 0.66/1.00 (p2(tptp_fun_X_6(Y!10))),
% 0.66/1.00 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.66/1.00 tff(48,plain,
% 0.66/1.00 (((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10)))) | r1(Y!10, tptp_fun_X_6(Y!10))),
% 0.66/1.00 inference(tautology,[status(thm)],[])).
% 0.66/1.00 tff(49,plain,
% 0.66/1.00 (r1(Y!10, tptp_fun_X_6(Y!10))),
% 0.66/1.00 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.66/1.00 tff(50,plain,
% 0.66/1.00 (((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.66/1.00 inference(tautology,[status(thm)],[])).
% 0.66/1.00 tff(51,plain,
% 0.66/1.00 (![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.66/1.00 inference(unit_resolution,[status(thm)],[50, 8])).
% 0.66/1.00 tff(52,plain,
% 0.66/1.00 (((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y))))),
% 0.66/1.00 inference(rewrite,[status(thm)],[])).
% 0.66/1.00 tff(53,plain,
% 0.66/1.00 (((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!10), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y))))),
% 0.66/1.00 inference(rewrite,[status(thm)],[])).
% 0.66/1.00 tff(54,plain,
% 0.66/1.00 (((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!10), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))))),
% 0.66/1.00 inference(monotonicity,[status(thm)],[53])).
% 0.66/1.00 tff(55,plain,
% 0.66/1.00 (((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!10), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y))))),
% 0.66/1.01 inference(transitivity,[status(thm)],[54, 52])).
% 0.66/1.01 tff(56,plain,
% 0.66/1.01 ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!10), Y)) | p2(Y)))),
% 0.66/1.01 inference(quant_inst,[status(thm)],[])).
% 0.66/1.01 tff(57,plain,
% 0.66/1.01 ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))),
% 0.66/1.01 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.66/1.01 tff(58,plain,
% 0.66/1.01 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[57, 51, 49, 47])).
% 0.66/1.01 tff(59,plain,
% 0.66/1.01 (((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10)))) | r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))),
% 0.66/1.01 inference(tautology,[status(thm)],[])).
% 0.66/1.01 tff(60,plain,
% 0.66/1.01 (r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[59, 45])).
% 0.66/1.01 tff(61,plain,
% 0.66/1.01 (((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10)))) | (~p2(tptp_fun_Y_7(Y!10)))),
% 0.66/1.01 inference(tautology,[status(thm)],[])).
% 0.66/1.01 tff(62,plain,
% 0.66/1.01 (~p2(tptp_fun_Y_7(Y!10))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[61, 45])).
% 0.66/1.01 tff(63,plain,
% 0.66/1.01 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))) | (p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))),
% 0.66/1.01 inference(rewrite,[status(thm)],[])).
% 0.66/1.01 tff(64,plain,
% 0.66/1.01 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))) | (p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))),
% 0.66/1.01 inference(quant_inst,[status(thm)],[])).
% 0.66/1.01 tff(65,plain,
% 0.66/1.01 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10)))),
% 0.66/1.01 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.66/1.01 tff(66,plain,
% 0.66/1.01 ($false),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[65, 62, 60, 58])).
% 0.66/1.01 tff(67,plain,((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.66/1.01 tff(68,assumption,(![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))), introduced(assumption)).
% 0.66/1.01 tff(69,assumption,(~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))), introduced(assumption)).
% 0.66/1.01 tff(70,plain,
% 0.66/1.01 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))),
% 0.66/1.01 inference(tautology,[status(thm)],[])).
% 0.66/1.01 tff(71,plain,
% 0.66/1.01 (r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.66/1.01 tff(72,plain,
% 0.66/1.01 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))),
% 0.66/1.01 inference(tautology,[status(thm)],[])).
% 0.66/1.01 tff(73,plain,
% 0.66/1.01 (p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.66/1.01 tff(74,plain,
% 0.66/1.01 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))),
% 0.66/1.01 inference(bind,[status(th)],[])).
% 0.66/1.01 tff(75,plain,
% 0.66/1.01 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.66/1.01 inference(quant_intro,[status(thm)],[74])).
% 0.66/1.01 tff(76,plain,
% 0.66/1.01 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.66/1.01 inference(bind,[status(th)],[])).
% 0.66/1.01 tff(77,plain,
% 0.66/1.01 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.66/1.01 inference(quant_intro,[status(thm)],[76])).
% 0.66/1.01 tff(78,plain,
% 0.66/1.01 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.66/1.01 inference(bind,[status(th)],[])).
% 0.66/1.01 tff(79,plain,
% 0.66/1.01 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.66/1.01 inference(quant_intro,[status(thm)],[78])).
% 0.66/1.01 tff(80,plain,
% 0.66/1.01 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.66/1.01 inference(transitivity,[status(thm)],[79, 77])).
% 0.66/1.01 tff(81,plain,
% 0.66/1.01 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.66/1.01 inference(bind,[status(th)],[])).
% 0.66/1.01 tff(82,plain,
% 0.66/1.01 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.66/1.01 inference(quant_intro,[status(thm)],[81])).
% 0.66/1.01 tff(83,plain,
% 0.66/1.01 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))),
% 0.66/1.01 inference(and_elim,[status(thm)],[35])).
% 0.66/1.01 tff(84,plain,
% 0.66/1.01 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.66/1.01 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.66/1.01 tff(85,plain,
% 0.66/1.01 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.66/1.01 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.66/1.01 tff(86,plain,
% 0.66/1.01 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.66/1.01 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.66/1.01 tff(87,plain,
% 0.66/1.01 (~((~r1(X!0, Y!1)) | p2(Y!1))),
% 0.66/1.01 inference(and_elim,[status(thm)],[35])).
% 0.66/1.01 tff(88,plain,
% 0.66/1.01 (~p2(Y!1)),
% 0.66/1.01 inference(or_elim,[status(thm)],[87])).
% 0.66/1.01 tff(89,plain,
% 0.66/1.01 (r1(X!0, Y!1)),
% 0.66/1.01 inference(or_elim,[status(thm)],[87])).
% 0.66/1.01 tff(90,plain,
% 0.66/1.01 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.66/1.01 inference(rewrite,[status(thm)],[])).
% 0.66/1.01 tff(91,plain,
% 0.66/1.01 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.66/1.01 inference(quant_inst,[status(thm)],[])).
% 0.66/1.01 tff(92,plain,
% 0.66/1.01 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.66/1.01 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.66/1.01 tff(93,plain,
% 0.66/1.01 (~(p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[92, 89, 88, 86])).
% 0.66/1.01 tff(94,plain,
% 0.66/1.01 ((p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.66/1.01 inference(tautology,[status(thm)],[])).
% 0.66/1.01 tff(95,plain,
% 0.66/1.01 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.66/1.01 tff(96,plain,
% 0.66/1.01 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X))))),
% 0.66/1.01 inference(rewrite,[status(thm)],[])).
% 0.66/1.01 tff(97,plain,
% 0.66/1.01 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)) | p2(X))) <=> ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X))))),
% 0.66/1.01 inference(rewrite,[status(thm)],[])).
% 0.66/1.01 tff(98,plain,
% 0.66/1.01 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))))),
% 0.66/1.01 inference(monotonicity,[status(thm)],[97])).
% 0.66/1.01 tff(99,plain,
% 0.66/1.01 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X))))),
% 0.66/1.01 inference(transitivity,[status(thm)],[98, 96])).
% 0.66/1.01 tff(100,plain,
% 0.66/1.01 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)) | p2(X)))),
% 0.66/1.01 inference(quant_inst,[status(thm)],[])).
% 0.66/1.01 tff(101,plain,
% 0.66/1.01 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))),
% 0.66/1.01 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.66/1.01 tff(102,plain,
% 0.66/1.01 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[101, 95, 73, 71])).
% 0.66/1.01 tff(103,plain,
% 0.66/1.01 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | (~p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))),
% 0.66/1.01 inference(tautology,[status(thm)],[])).
% 0.66/1.01 tff(104,plain,
% 0.66/1.01 (~p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[103, 69])).
% 0.66/1.01 tff(105,plain,
% 0.66/1.01 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))),
% 0.66/1.01 inference(tautology,[status(thm)],[])).
% 0.66/1.01 tff(106,plain,
% 0.66/1.01 (r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[105, 69])).
% 0.66/1.01 tff(107,plain,
% 0.66/1.01 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))) | (p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))))),
% 0.66/1.01 inference(rewrite,[status(thm)],[])).
% 0.66/1.01 tff(108,plain,
% 0.66/1.01 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))) | (p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))))),
% 0.66/1.01 inference(quant_inst,[status(thm)],[])).
% 0.66/1.01 tff(109,plain,
% 0.66/1.01 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1))))),
% 0.66/1.01 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.66/1.01 tff(110,plain,
% 0.66/1.01 ($false),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[109, 106, 104, 102])).
% 0.66/1.01 tff(111,plain,((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))), inference(lemma,lemma(discharge,[]))).
% 0.66/1.01 tff(112,plain,
% 0.66/1.01 ((p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | r1(Y!1, tptp_fun_X_18(Y!1))),
% 0.66/1.01 inference(tautology,[status(thm)],[])).
% 0.66/1.01 tff(113,plain,
% 0.66/1.01 (r1(Y!1, tptp_fun_X_18(Y!1))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[112, 93])).
% 0.66/1.01 tff(114,plain,
% 0.66/1.01 ((p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(tptp_fun_X_18(Y!1)))),
% 0.66/1.01 inference(tautology,[status(thm)],[])).
% 0.66/1.01 tff(115,plain,
% 0.66/1.01 (~p2(tptp_fun_X_18(Y!1))),
% 0.66/1.01 inference(unit_resolution,[status(thm)],[114, 93])).
% 0.66/1.01 tff(116,plain,
% 0.66/1.01 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | ((~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))))),
% 0.66/1.01 inference(rewrite,[status(thm)],[])).
% 0.66/1.01 tff(117,plain,
% 0.66/1.01 ((p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1)))) <=> ((~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))))),
% 0.66/1.01 inference(rewrite,[status(thm)],[])).
% 0.66/1.01 tff(118,plain,
% 0.66/1.01 ((~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) <=> (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))))),
% 0.66/1.01 inference(rewrite,[status(thm)],[])).
% 0.66/1.01 tff(119,plain,
% 0.66/1.01 ((p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1)))) <=> (p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1))))),
% 0.66/1.01 inference(monotonicity,[status(thm)],[118])).
% 0.66/1.01 tff(120,plain,
% 0.66/1.01 ((p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1)))) <=> ((~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))))),
% 0.66/1.02 inference(transitivity,[status(thm)],[119, 117])).
% 0.66/1.02 tff(121,plain,
% 0.66/1.02 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | ((~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))))))),
% 0.66/1.02 inference(monotonicity,[status(thm)],[120])).
% 0.66/1.02 tff(122,plain,
% 0.66/1.02 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))))),
% 0.66/1.02 inference(transitivity,[status(thm)],[121, 116])).
% 0.66/1.02 tff(123,plain,
% 0.66/1.02 ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1))))),
% 0.66/1.02 inference(quant_inst,[status(thm)],[])).
% 0.66/1.02 tff(124,plain,
% 0.66/1.02 ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))))),
% 0.66/1.02 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.66/1.02 tff(125,plain,
% 0.66/1.02 ($false),
% 0.66/1.02 inference(unit_resolution,[status(thm)],[124, 115, 113, 111, 68])).
% 0.66/1.02 tff(126,plain,(~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))), inference(lemma,lemma(discharge,[]))).
% 0.66/1.02 tff(127,assumption,(![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))), introduced(assumption)).
% 0.66/1.02 tff(128,plain,
% 0.66/1.02 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | (~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X))))),
% 0.66/1.02 inference(rewrite,[status(thm)],[])).
% 0.66/1.02 tff(129,plain,
% 0.66/1.02 (((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) <=> ((~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X))))),
% 0.66/1.02 inference(rewrite,[status(thm)],[])).
% 0.66/1.02 tff(130,plain,
% 0.66/1.02 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))))),
% 0.66/1.02 inference(monotonicity,[status(thm)],[129])).
% 0.66/1.02 tff(131,plain,
% 0.66/1.02 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | (~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X))))),
% 0.66/1.02 inference(transitivity,[status(thm)],[130, 128])).
% 0.66/1.02 tff(132,plain,
% 0.66/1.02 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))),
% 0.66/1.02 inference(quant_inst,[status(thm)],[])).
% 0.66/1.02 tff(133,plain,
% 0.66/1.02 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | (~r1(X!0, Y!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))),
% 0.66/1.02 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.66/1.02 tff(134,plain,
% 0.66/1.02 ($false),
% 0.66/1.02 inference(unit_resolution,[status(thm)],[133, 89, 127, 126])).
% 0.66/1.02 tff(135,plain,(~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.66/1.02 tff(136,plain,
% 0.66/1.02 ((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))),
% 0.66/1.02 inference(tautology,[status(thm)],[])).
% 0.66/1.02 tff(137,plain,
% 0.66/1.02 ((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))),
% 0.66/1.02 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.66/1.02 tff(138,plain,
% 0.66/1.02 (~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))),
% 0.66/1.02 inference(unit_resolution,[status(thm)],[137, 67])).
% 0.66/1.02 tff(139,plain,
% 0.66/1.02 (((~(p2(X!0) | (~((~p2(Y!13)) | p2(X!14) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)))))) | (~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))))) | ((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))),
% 0.66/1.02 inference(tautology,[status(thm)],[])).
% 0.66/1.02 tff(140,plain,
% 0.66/1.02 ((~(p2(X!0) | (~((~p2(Y!13)) | p2(X!14) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)))))) | (~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))))),
% 0.66/1.02 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.66/1.02 tff(141,plain,
% 0.66/1.02 (((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~p2(Y!13)) | p2(X!14) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))) <=> ((~((~(p2(X!0) | (~((~p2(Y!13)) | p2(X!14) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)))))) | (~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.66/1.02 inference(rewrite,[status(thm)],[])).
% 0.66/1.02 tff(142,plain,
% 0.66/1.02 (((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~p2(Y!13)) | p2(X!14) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))) <=> ((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~p2(Y!13)) | p2(X!14) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))))))))),
% 0.66/1.03 inference(rewrite,[status(thm)],[])).
% 0.66/1.03 tff(143,plain,
% 0.66/1.03 (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~(p2(X!14) | (~r1(Y!13, X!14))))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))) | (~r1(Y!15, X)))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) <=> ((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~p2(Y!13)) | p2(X!14) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))))))))),
% 0.66/1.03 inference(rewrite,[status(thm)],[])).
% 0.66/1.03 tff(144,plain,
% 0.66/1.03 ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~(p2(X!14) | (~r1(Y!13, X!14))))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))) | (~r1(Y!15, X)))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))),
% 0.66/1.03 inference(and_elim,[status(thm)],[35])).
% 0.66/1.03 tff(145,plain,
% 0.66/1.03 ((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~p2(Y!13)) | p2(X!14) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))),
% 0.66/1.03 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.66/1.03 tff(146,plain,
% 0.66/1.03 ((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~p2(Y!13)) | p2(X!14) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))),
% 0.66/1.03 inference(modus_ponens,[status(thm)],[145, 142])).
% 0.66/1.03 tff(147,plain,
% 0.66/1.03 ((~((~(p2(X!0) | (~((~p2(Y!13)) | p2(X!14) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)))))) | (~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))),
% 0.66/1.03 inference(modus_ponens,[status(thm)],[146, 141])).
% 0.66/1.03 tff(148,plain,
% 0.66/1.03 (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))),
% 0.66/1.03 inference(unit_resolution,[status(thm)],[147, 140])).
% 0.66/1.03 tff(149,assumption,((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))), introduced(assumption)).
% 0.66/1.03 tff(150,assumption,(~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))), introduced(assumption)).
% 0.66/1.03 tff(151,plain,
% 0.66/1.03 (((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | ((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))),
% 0.66/1.04 inference(tautology,[status(thm)],[])).
% 0.66/1.04 tff(152,plain,
% 0.66/1.04 ((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.66/1.04 tff(153,plain,
% 0.66/1.04 ((~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))),
% 0.66/1.04 inference(tautology,[status(thm)],[])).
% 0.66/1.04 tff(154,plain,
% 0.66/1.04 (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[153, 152, 149])).
% 0.66/1.04 tff(155,plain,
% 0.66/1.04 ((p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!15))),
% 0.66/1.04 inference(tautology,[status(thm)],[])).
% 0.66/1.04 tff(156,plain,
% 0.66/1.04 (~p2(Y!15)),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.66/1.04 tff(157,plain,
% 0.66/1.04 (((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | r1(X!0, Y!15)),
% 0.66/1.04 inference(tautology,[status(thm)],[])).
% 0.66/1.04 tff(158,plain,
% 0.66/1.04 (r1(X!0, Y!15)),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[157, 150])).
% 0.66/1.04 tff(159,plain,
% 0.66/1.04 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(Y!15) | (~r1(X!0, Y!15)) | (~((~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | p2(Y!15) | (~r1(X!0, Y!15)) | (~((~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))))))),
% 0.66/1.04 inference(rewrite,[status(thm)],[])).
% 0.66/1.04 tff(160,plain,
% 0.66/1.04 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(Y!15) | (~r1(X!0, Y!15)) | (~((~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))))))),
% 0.66/1.04 inference(quant_inst,[status(thm)],[])).
% 0.66/1.04 tff(161,plain,
% 0.66/1.04 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | p2(Y!15) | (~r1(X!0, Y!15)) | (~((~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15)))))),
% 0.66/1.04 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.66/1.04 tff(162,plain,
% 0.66/1.04 (~((~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[161, 38, 158, 156])).
% 0.66/1.04 tff(163,plain,
% 0.66/1.04 (((~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15)))) | r1(Y!15, tptp_fun_X_6(Y!15))),
% 0.66/1.04 inference(tautology,[status(thm)],[])).
% 0.66/1.04 tff(164,plain,
% 0.66/1.04 (r1(Y!15, tptp_fun_X_6(Y!15))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.66/1.04 tff(165,plain,
% 0.66/1.04 (((~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15)))) | p2(tptp_fun_X_6(Y!15))),
% 0.66/1.04 inference(tautology,[status(thm)],[])).
% 0.66/1.04 tff(166,plain,
% 0.66/1.04 (p2(tptp_fun_X_6(Y!15))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[165, 162])).
% 0.66/1.04 tff(167,plain,
% 0.66/1.04 ((p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.66/1.04 inference(tautology,[status(thm)],[])).
% 0.66/1.04 tff(168,plain,
% 0.66/1.04 (![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[167, 154])).
% 0.66/1.04 tff(169,plain,
% 0.66/1.04 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))),
% 0.66/1.04 inference(rewrite,[status(thm)],[])).
% 0.66/1.04 tff(170,plain,
% 0.66/1.04 (((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))),
% 0.66/1.04 inference(rewrite,[status(thm)],[])).
% 0.66/1.04 tff(171,plain,
% 0.66/1.04 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))))),
% 0.66/1.04 inference(monotonicity,[status(thm)],[170])).
% 0.66/1.04 tff(172,plain,
% 0.66/1.04 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))),
% 0.66/1.04 inference(transitivity,[status(thm)],[171, 169])).
% 0.66/1.04 tff(173,plain,
% 0.66/1.04 ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y)))),
% 0.66/1.04 inference(quant_inst,[status(thm)],[])).
% 0.66/1.04 tff(174,plain,
% 0.66/1.04 ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))),
% 0.66/1.04 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.66/1.04 tff(175,plain,
% 0.66/1.04 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[174, 168, 166, 164])).
% 0.66/1.04 tff(176,plain,
% 0.66/1.04 (((~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15)))) | r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))),
% 0.66/1.04 inference(tautology,[status(thm)],[])).
% 0.66/1.04 tff(177,plain,
% 0.66/1.04 (r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[176, 162])).
% 0.66/1.04 tff(178,plain,
% 0.66/1.04 (((~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15)))) | (~p2(tptp_fun_Y_7(Y!15)))),
% 0.66/1.04 inference(tautology,[status(thm)],[])).
% 0.66/1.04 tff(179,plain,
% 0.66/1.04 (~p2(tptp_fun_Y_7(Y!15))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[178, 162])).
% 0.66/1.04 tff(180,plain,
% 0.66/1.04 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | (p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))),
% 0.66/1.04 inference(rewrite,[status(thm)],[])).
% 0.66/1.04 tff(181,plain,
% 0.66/1.04 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | (p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))),
% 0.66/1.04 inference(quant_inst,[status(thm)],[])).
% 0.66/1.04 tff(182,plain,
% 0.66/1.04 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15)))),
% 0.66/1.04 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.66/1.04 tff(183,plain,
% 0.66/1.04 ($false),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[182, 179, 177, 175])).
% 0.66/1.04 tff(184,plain,(((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.66/1.04 tff(185,plain,
% 0.66/1.04 (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[184, 148])).
% 0.66/1.04 tff(186,plain,
% 0.66/1.04 (((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.66/1.04 inference(tautology,[status(thm)],[])).
% 0.66/1.04 tff(187,plain,
% 0.66/1.04 (![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.66/1.04 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.66/1.04 tff(188,plain,
% 0.66/1.04 (((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y))))),
% 0.66/1.04 inference(rewrite,[status(thm)],[])).
% 0.66/1.04 tff(189,plain,
% 0.66/1.04 (((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!17), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y))))),
% 0.66/1.04 inference(rewrite,[status(thm)],[])).
% 0.66/1.04 tff(190,plain,
% 0.66/1.04 (((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!17), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))))),
% 0.66/1.04 inference(monotonicity,[status(thm)],[189])).
% 0.66/1.04 tff(191,plain,
% 0.66/1.04 (((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!17), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y))))),
% 0.66/1.04 inference(transitivity,[status(thm)],[190, 188])).
% 0.66/1.04 tff(192,plain,
% 0.66/1.04 ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!17), Y)) | p2(Y)))),
% 0.66/1.05 inference(quant_inst,[status(thm)],[])).
% 0.66/1.05 tff(193,plain,
% 0.66/1.05 ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))),
% 0.66/1.05 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.66/1.05 tff(194,plain,
% 0.66/1.05 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[193, 187, 7, 5])).
% 0.66/1.05 tff(195,plain,
% 0.66/1.05 (((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17)))) | r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))),
% 0.66/1.05 inference(tautology,[status(thm)],[])).
% 0.66/1.05 tff(196,plain,
% 0.66/1.05 (r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[195, 1])).
% 0.66/1.05 tff(197,assumption,(~p2(tptp_fun_Y_7(Y!17))), introduced(assumption)).
% 0.66/1.05 tff(198,plain,
% 0.66/1.05 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))) | (p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))),
% 0.66/1.05 inference(rewrite,[status(thm)],[])).
% 0.66/1.05 tff(199,plain,
% 0.66/1.05 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))) | (p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))),
% 0.66/1.05 inference(quant_inst,[status(thm)],[])).
% 0.66/1.05 tff(200,plain,
% 0.66/1.05 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17)))),
% 0.66/1.05 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.66/1.05 tff(201,plain,
% 0.66/1.05 ($false),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[200, 197, 196, 194])).
% 0.66/1.05 tff(202,plain,(((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17)))) | p2(tptp_fun_Y_7(Y!17))), inference(lemma,lemma(discharge,[]))).
% 0.66/1.05 tff(203,plain,
% 0.66/1.05 ($false),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[202, 3, 1])).
% 0.66/1.05 tff(204,plain,((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17)))), inference(lemma,lemma(discharge,[]))).
% 0.66/1.05 tff(205,assumption,(![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))), introduced(assumption)).
% 0.66/1.05 tff(206,plain,
% 0.66/1.05 (((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(X!16, Y!17)),
% 0.66/1.05 inference(tautology,[status(thm)],[])).
% 0.66/1.05 tff(207,plain,
% 0.66/1.05 (r1(X!16, Y!17)),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[206, 185])).
% 0.66/1.05 tff(208,plain,
% 0.66/1.05 (((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!17))),
% 0.66/1.05 inference(tautology,[status(thm)],[])).
% 0.66/1.05 tff(209,plain,
% 0.66/1.05 (~p2(Y!17)),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[208, 185])).
% 0.66/1.05 tff(210,plain,
% 0.66/1.05 (((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(Y!17) | (~r1(X!16, Y!17)) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | p2(Y!17) | (~r1(X!16, Y!17)) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))),
% 0.66/1.05 inference(rewrite,[status(thm)],[])).
% 0.66/1.05 tff(211,plain,
% 0.66/1.05 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(Y!17) | (~r1(X!16, Y!17)) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))),
% 0.66/1.05 inference(quant_inst,[status(thm)],[])).
% 0.66/1.05 tff(212,plain,
% 0.66/1.05 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | p2(Y!17) | (~r1(X!16, Y!17)) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17)))))),
% 0.66/1.05 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.66/1.05 tff(213,plain,
% 0.66/1.05 ($false),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[212, 209, 207, 205, 204])).
% 0.66/1.05 tff(214,plain,(~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.66/1.05 tff(215,plain,
% 0.66/1.05 (((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16)))) | ![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.66/1.05 inference(tautology,[status(thm)],[])).
% 0.66/1.05 tff(216,plain,
% 0.66/1.05 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16)))),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.66/1.05 tff(217,assumption,((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17)))), introduced(assumption)).
% 0.66/1.05 tff(218,plain,
% 0.66/1.05 ((~(p2(Y!17) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))) | p2(Y!17) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17)))))),
% 0.66/1.05 inference(tautology,[status(thm)],[])).
% 0.66/1.05 tff(219,plain,
% 0.66/1.05 (~(p2(Y!17) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[218, 209, 217])).
% 0.66/1.05 tff(220,plain,
% 0.66/1.05 (((~(p2(Y!17) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, tptp_fun_X_18(Y!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))) | (p2(Y!17) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))),
% 0.66/1.05 inference(tautology,[status(thm)],[])).
% 0.66/1.05 tff(221,plain,
% 0.66/1.05 ((~(p2(Y!17) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, tptp_fun_X_18(Y!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.66/1.05 tff(222,assumption,(![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))), introduced(assumption)).
% 0.66/1.05 tff(223,plain,
% 0.66/1.05 (((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))) | ((~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, tptp_fun_X_18(Y!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))) | (~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, tptp_fun_X_18(Y!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))),
% 0.66/1.05 inference(rewrite,[status(thm)],[])).
% 0.66/1.05 tff(224,plain,
% 0.66/1.05 ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))) | ((~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, tptp_fun_X_18(Y!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))),
% 0.66/1.05 inference(quant_inst,[status(thm)],[])).
% 0.66/1.05 tff(225,plain,
% 0.66/1.05 ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))) | (~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, tptp_fun_X_18(Y!17))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))),
% 0.66/1.05 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.66/1.05 tff(226,plain,
% 0.66/1.05 ($false),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[225, 207, 222, 221])).
% 0.66/1.05 tff(227,plain,((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))) | (~((~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17)))))), inference(lemma,lemma(discharge,[]))).
% 0.66/1.05 tff(228,plain,
% 0.66/1.05 (~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))),
% 0.66/1.05 inference(unit_resolution,[status(thm)],[227, 204])).
% 0.66/1.05 tff(229,plain,
% 0.66/1.05 (((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | ![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.82/1.05 inference(tautology,[status(thm)],[])).
% 0.82/1.05 tff(230,plain,
% 0.82/1.05 (![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[229, 148])).
% 0.82/1.05 tff(231,plain,
% 0.82/1.05 (((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(Y!15, X!16)),
% 0.82/1.05 inference(tautology,[status(thm)],[])).
% 0.82/1.05 tff(232,plain,
% 0.82/1.05 (r1(Y!15, X!16)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[231, 185])).
% 0.82/1.05 tff(233,plain,
% 0.82/1.05 (((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))))),
% 0.82/1.06 inference(rewrite,[status(thm)],[])).
% 0.82/1.06 tff(234,plain,
% 0.82/1.06 (((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16)))))) <=> ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))))),
% 0.82/1.06 inference(rewrite,[status(thm)],[])).
% 0.82/1.06 tff(235,plain,
% 0.82/1.06 ((~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16)))))),
% 0.82/1.06 inference(rewrite,[status(thm)],[])).
% 0.82/1.06 tff(236,plain,
% 0.82/1.06 ((~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.82/1.06 inference(rewrite,[status(thm)],[])).
% 0.82/1.06 tff(237,plain,
% 0.82/1.06 (((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))))),
% 0.82/1.06 inference(monotonicity,[status(thm)],[236, 235])).
% 0.82/1.06 tff(238,plain,
% 0.82/1.06 (((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))))),
% 0.82/1.06 inference(transitivity,[status(thm)],[237, 234])).
% 0.82/1.06 tff(239,plain,
% 0.82/1.06 (((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))))),
% 0.82/1.06 inference(monotonicity,[status(thm)],[238])).
% 0.82/1.06 tff(240,plain,
% 0.82/1.06 (((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))))),
% 0.82/1.06 inference(transitivity,[status(thm)],[239, 233])).
% 0.82/1.06 tff(241,plain,
% 0.82/1.06 ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.82/1.06 inference(quant_inst,[status(thm)],[])).
% 0.82/1.06 tff(242,plain,
% 0.82/1.06 ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))),
% 0.82/1.07 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.82/1.07 tff(243,plain,
% 0.82/1.07 ((~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[242, 232, 230])).
% 0.82/1.07 tff(244,plain,
% 0.82/1.07 ((~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16)))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[243, 228])).
% 0.82/1.07 tff(245,plain,
% 0.82/1.07 (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[244, 216])).
% 0.82/1.07 tff(246,plain,
% 0.82/1.07 ((p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(X!16))),
% 0.82/1.07 inference(tautology,[status(thm)],[])).
% 0.82/1.07 tff(247,plain,
% 0.82/1.07 (~p2(X!16)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.82/1.07 tff(248,plain,
% 0.82/1.07 (((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))),
% 0.82/1.07 inference(tautology,[status(thm)],[])).
% 0.82/1.07 tff(249,plain,
% 0.82/1.07 (![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[248, 185])).
% 0.82/1.07 tff(250,plain,
% 0.82/1.07 (((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(251,plain,
% 0.82/1.07 ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))))),
% 0.82/1.07 inference(quant_inst,[status(thm)],[])).
% 0.82/1.07 tff(252,plain,
% 0.82/1.07 ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))))),
% 0.82/1.07 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.82/1.07 tff(253,plain,
% 0.82/1.07 (p2(X!16) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[252, 232, 249])).
% 0.82/1.07 tff(254,plain,
% 0.82/1.07 (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[253, 247])).
% 0.82/1.07 tff(255,plain,
% 0.82/1.07 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))) | r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))),
% 0.82/1.07 inference(tautology,[status(thm)],[])).
% 0.82/1.07 tff(256,plain,
% 0.82/1.07 (r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.82/1.07 tff(257,plain,
% 0.82/1.07 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))) | (~p2(tptp_fun_X_12(X!16)))),
% 0.82/1.07 inference(tautology,[status(thm)],[])).
% 0.82/1.07 tff(258,plain,
% 0.82/1.07 (~p2(tptp_fun_X_12(X!16))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[257, 254])).
% 0.82/1.07 tff(259,assumption,(![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))), introduced(assumption)).
% 0.82/1.07 tff(260,assumption,(~p2(tptp_fun_X_12(X!16))), introduced(assumption)).
% 0.82/1.07 tff(261,assumption,(r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))), introduced(assumption)).
% 0.82/1.07 tff(262,plain,
% 0.82/1.07 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | (p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(263,plain,
% 0.82/1.07 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | (p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))),
% 0.82/1.07 inference(quant_inst,[status(thm)],[])).
% 0.82/1.07 tff(264,plain,
% 0.82/1.07 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))),
% 0.82/1.07 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.82/1.07 tff(265,plain,
% 0.82/1.07 ($false),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[264, 261, 260, 259])).
% 0.82/1.07 tff(266,plain,((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.07 tff(267,plain,
% 0.82/1.07 (~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[266, 258, 256])).
% 0.82/1.07 tff(268,plain,
% 0.82/1.07 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))) | r1(X!16, tptp_fun_Y_11(X!16))),
% 0.82/1.08 inference(tautology,[status(thm)],[])).
% 0.82/1.08 tff(269,plain,
% 0.82/1.08 (r1(X!16, tptp_fun_Y_11(X!16))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[268, 254])).
% 0.82/1.08 tff(270,plain,
% 0.82/1.08 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))) | p2(tptp_fun_Y_11(X!16))),
% 0.82/1.08 inference(tautology,[status(thm)],[])).
% 0.82/1.08 tff(271,plain,
% 0.82/1.08 (p2(tptp_fun_Y_11(X!16))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[270, 254])).
% 0.82/1.08 tff(272,plain,
% 0.82/1.08 ((p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.82/1.08 inference(tautology,[status(thm)],[])).
% 0.82/1.08 tff(273,plain,
% 0.82/1.08 (![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[272, 245])).
% 0.82/1.08 tff(274,plain,
% 0.82/1.08 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(275,plain,
% 0.82/1.08 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X))) <=> ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(276,plain,
% 0.82/1.08 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[275])).
% 0.82/1.08 tff(277,plain,
% 0.82/1.08 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))),
% 0.82/1.08 inference(transitivity,[status(thm)],[276, 274])).
% 0.82/1.08 tff(278,plain,
% 0.82/1.08 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X)))),
% 0.82/1.08 inference(quant_inst,[status(thm)],[])).
% 0.82/1.08 tff(279,plain,
% 0.82/1.08 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))),
% 0.82/1.08 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.82/1.08 tff(280,plain,
% 0.82/1.08 ($false),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[279, 273, 271, 269, 267])).
% 0.82/1.08 % SZS output end Proof
% 0.82/1.08 % E exiting
%------------------------------------------------------------------------------