%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL644+1.015 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n026.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 03:00:21 PM UTC 2026
% Result : Theorem 0.23s 0.47s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL644+1.015 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 23:07:13 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.23/0.47 % SZS status Theorem
% 0.23/0.47 % SZS output start Proof
% 0.23/0.47 tff(p1_type, type, (
% 0.23/0.47 p1: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_92_type, type, (
% 0.23/0.47 tptp_fun_X_92: $i > $i)).
% 0.23/0.47 tff(r1_type, type, (
% 0.23/0.47 r1: ( $i * $i ) > $o)).
% 0.23/0.47 tff(p2_type, type, (
% 0.23/0.47 p2: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_0_type, type, (
% 0.23/0.47 tptp_fun_X_0: $i)).
% 0.23/0.47 tff(tptp_fun_Y_91_type, type, (
% 0.23/0.47 tptp_fun_Y_91: $i)).
% 0.23/0.47 tff(tptp_fun_X_90_type, type, (
% 0.23/0.47 tptp_fun_X_90: $i)).
% 0.23/0.47 tff(tptp_fun_Y_89_type, type, (
% 0.23/0.47 tptp_fun_Y_89: $i)).
% 0.23/0.47 tff(tptp_fun_X_88_type, type, (
% 0.23/0.47 tptp_fun_X_88: $i)).
% 0.23/0.47 tff(tptp_fun_Y_87_type, type, (
% 0.23/0.47 tptp_fun_Y_87: $i)).
% 0.23/0.47 tff(tptp_fun_X_86_type, type, (
% 0.23/0.47 tptp_fun_X_86: $i > $i)).
% 0.23/0.47 tff(p3_type, type, (
% 0.23/0.47 p3: $i > $o)).
% 0.23/0.47 tff(tptp_fun_Y_85_type, type, (
% 0.23/0.47 tptp_fun_Y_85: $i)).
% 0.23/0.47 tff(tptp_fun_X_84_type, type, (
% 0.23/0.47 tptp_fun_X_84: $i)).
% 0.23/0.47 tff(tptp_fun_Y_83_type, type, (
% 0.23/0.47 tptp_fun_Y_83: $i)).
% 0.23/0.47 tff(tptp_fun_X_82_type, type, (
% 0.23/0.47 tptp_fun_X_82: $i)).
% 0.23/0.47 tff(tptp_fun_Y_81_type, type, (
% 0.23/0.47 tptp_fun_Y_81: $i)).
% 0.23/0.47 tff(tptp_fun_X_75_type, type, (
% 0.23/0.47 tptp_fun_X_75: $i > $i)).
% 0.23/0.47 tff(tptp_fun_Y_80_type, type, (
% 0.23/0.47 tptp_fun_Y_80: $i)).
% 0.23/0.47 tff(p4_type, type, (
% 0.23/0.47 p4: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_79_type, type, (
% 0.23/0.47 tptp_fun_X_79: $i)).
% 0.23/0.47 tff(tptp_fun_Y_78_type, type, (
% 0.23/0.47 tptp_fun_Y_78: $i)).
% 0.23/0.47 tff(tptp_fun_X_77_type, type, (
% 0.23/0.47 tptp_fun_X_77: $i)).
% 0.23/0.47 tff(tptp_fun_Y_76_type, type, (
% 0.23/0.47 tptp_fun_Y_76: $i)).
% 0.23/0.47 tff(tptp_fun_X_74_type, type, (
% 0.23/0.47 tptp_fun_X_74: $i > $i)).
% 0.23/0.47 tff(p5_type, type, (
% 0.23/0.47 p5: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_63_type, type, (
% 0.23/0.47 tptp_fun_X_63: $i > $i)).
% 0.23/0.47 tff(tptp_fun_Y_73_type, type, (
% 0.23/0.47 tptp_fun_Y_73: $i)).
% 0.23/0.47 tff(tptp_fun_X_72_type, type, (
% 0.23/0.47 tptp_fun_X_72: $i)).
% 0.23/0.47 tff(tptp_fun_Y_71_type, type, (
% 0.23/0.47 tptp_fun_Y_71: $i)).
% 0.23/0.47 tff(tptp_fun_X_70_type, type, (
% 0.23/0.47 tptp_fun_X_70: $i)).
% 0.23/0.47 tff(tptp_fun_Y_69_type, type, (
% 0.23/0.47 tptp_fun_Y_69: $i)).
% 0.23/0.47 tff(p6_type, type, (
% 0.23/0.47 p6: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_62_type, type, (
% 0.23/0.47 tptp_fun_X_62: $i > $i)).
% 0.23/0.47 tff(tptp_fun_Y_68_type, type, (
% 0.23/0.47 tptp_fun_Y_68: $i)).
% 0.23/0.47 tff(tptp_fun_X_67_type, type, (
% 0.23/0.47 tptp_fun_X_67: $i)).
% 0.23/0.47 tff(tptp_fun_Y_66_type, type, (
% 0.23/0.47 tptp_fun_Y_66: $i)).
% 0.23/0.47 tff(tptp_fun_Y_64_type, type, (
% 0.23/0.47 tptp_fun_Y_64: $i)).
% 0.23/0.47 tff(tptp_fun_X_65_type, type, (
% 0.23/0.47 tptp_fun_X_65: $i)).
% 0.23/0.47 tff(p7_type, type, (
% 0.23/0.47 p7: $i > $o)).
% 0.23/0.47 tff(tptp_fun_Y_61_type, type, (
% 0.23/0.47 tptp_fun_Y_61: $i)).
% 0.23/0.47 tff(tptp_fun_X_60_type, type, (
% 0.23/0.47 tptp_fun_X_60: $i)).
% 0.23/0.47 tff(tptp_fun_Y_59_type, type, (
% 0.23/0.47 tptp_fun_Y_59: $i)).
% 0.23/0.47 tff(tptp_fun_X_58_type, type, (
% 0.23/0.47 tptp_fun_X_58: $i)).
% 0.23/0.47 tff(tptp_fun_Y_57_type, type, (
% 0.23/0.47 tptp_fun_Y_57: $i)).
% 0.23/0.47 tff(tptp_fun_X_50_type, type, (
% 0.23/0.47 tptp_fun_X_50: $i > $i)).
% 0.23/0.47 tff(p15_type, type, (
% 0.23/0.47 p15: $i > $o)).
% 0.23/0.47 tff(tptp_fun_Y_56_type, type, (
% 0.23/0.47 tptp_fun_Y_56: $i)).
% 0.23/0.47 tff(tptp_fun_Y_55_type, type, (
% 0.23/0.47 tptp_fun_Y_55: $i)).
% 0.23/0.47 tff(p8_type, type, (
% 0.23/0.47 p8: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_54_type, type, (
% 0.23/0.47 tptp_fun_X_54: $i)).
% 0.23/0.47 tff(tptp_fun_Y_53_type, type, (
% 0.23/0.47 tptp_fun_Y_53: $i)).
% 0.23/0.47 tff(tptp_fun_X_52_type, type, (
% 0.23/0.47 tptp_fun_X_52: $i)).
% 0.23/0.47 tff(tptp_fun_Y_51_type, type, (
% 0.23/0.47 tptp_fun_Y_51: $i)).
% 0.23/0.47 tff(tptp_fun_X_39_type, type, (
% 0.23/0.47 tptp_fun_X_39: $i > $i)).
% 0.23/0.47 tff(p9_type, type, (
% 0.23/0.47 p9: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_38_type, type, (
% 0.23/0.47 tptp_fun_X_38: $i > $i)).
% 0.23/0.47 tff(p10_type, type, (
% 0.23/0.47 p10: $i > $o)).
% 0.23/0.47 tff(tptp_fun_Y_49_type, type, (
% 0.23/0.47 tptp_fun_Y_49: $i)).
% 0.23/0.47 tff(tptp_fun_X_48_type, type, (
% 0.23/0.47 tptp_fun_X_48: $i)).
% 0.23/0.47 tff(tptp_fun_Y_47_type, type, (
% 0.23/0.47 tptp_fun_Y_47: $i)).
% 0.23/0.47 tff(tptp_fun_X_46_type, type, (
% 0.23/0.47 tptp_fun_X_46: $i)).
% 0.23/0.47 tff(tptp_fun_Y_45_type, type, (
% 0.23/0.47 tptp_fun_Y_45: $i)).
% 0.23/0.47 tff(tptp_fun_X_37_type, type, (
% 0.23/0.47 tptp_fun_X_37: $i > $i)).
% 0.23/0.47 tff(tptp_fun_Y_44_type, type, (
% 0.23/0.47 tptp_fun_Y_44: $i)).
% 0.23/0.47 tff(tptp_fun_X_43_type, type, (
% 0.23/0.47 tptp_fun_X_43: $i)).
% 0.23/0.47 tff(tptp_fun_Y_42_type, type, (
% 0.23/0.47 tptp_fun_Y_42: $i)).
% 0.23/0.47 tff(tptp_fun_X_41_type, type, (
% 0.23/0.47 tptp_fun_X_41: $i)).
% 0.23/0.47 tff(tptp_fun_Y_40_type, type, (
% 0.23/0.47 tptp_fun_Y_40: $i)).
% 0.23/0.47 tff(p11_type, type, (
% 0.23/0.47 p11: $i > $o)).
% 0.23/0.47 tff(tptp_fun_Y_36_type, type, (
% 0.23/0.47 tptp_fun_Y_36: $i)).
% 0.23/0.47 tff(tptp_fun_X_35_type, type, (
% 0.23/0.47 tptp_fun_X_35: $i)).
% 0.23/0.47 tff(tptp_fun_Y_34_type, type, (
% 0.23/0.47 tptp_fun_Y_34: $i)).
% 0.23/0.47 tff(tptp_fun_X_33_type, type, (
% 0.23/0.47 tptp_fun_X_33: $i)).
% 0.23/0.47 tff(tptp_fun_Y_32_type, type, (
% 0.23/0.47 tptp_fun_Y_32: $i)).
% 0.23/0.47 tff(tptp_fun_X_26_type, type, (
% 0.23/0.47 tptp_fun_X_26: $i > $i)).
% 0.23/0.47 tff(tptp_fun_Y_31_type, type, (
% 0.23/0.47 tptp_fun_Y_31: $i)).
% 0.23/0.47 tff(p12_type, type, (
% 0.23/0.47 p12: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_30_type, type, (
% 0.23/0.47 tptp_fun_X_30: $i)).
% 0.23/0.47 tff(tptp_fun_Y_29_type, type, (
% 0.23/0.47 tptp_fun_Y_29: $i)).
% 0.23/0.47 tff(tptp_fun_X_28_type, type, (
% 0.23/0.47 tptp_fun_X_28: $i)).
% 0.23/0.47 tff(tptp_fun_Y_27_type, type, (
% 0.23/0.47 tptp_fun_Y_27: $i)).
% 0.23/0.47 tff(tptp_fun_X_25_type, type, (
% 0.23/0.47 tptp_fun_X_25: $i > $i)).
% 0.23/0.47 tff(p13_type, type, (
% 0.23/0.47 p13: $i > $o)).
% 0.23/0.47 tff(tptp_fun_Y_24_type, type, (
% 0.23/0.47 tptp_fun_Y_24: $i)).
% 0.23/0.47 tff(tptp_fun_X_23_type, type, (
% 0.23/0.47 tptp_fun_X_23: $i)).
% 0.23/0.47 tff(tptp_fun_Y_22_type, type, (
% 0.23/0.47 tptp_fun_Y_22: $i)).
% 0.23/0.47 tff(tptp_fun_X_21_type, type, (
% 0.23/0.47 tptp_fun_X_21: $i)).
% 0.23/0.47 tff(tptp_fun_Y_20_type, type, (
% 0.23/0.47 tptp_fun_Y_20: $i)).
% 0.23/0.47 tff(tptp_fun_X_9_type, type, (
% 0.23/0.47 tptp_fun_X_9: $i > $i)).
% 0.23/0.47 tff(tptp_fun_Y_19_type, type, (
% 0.23/0.47 tptp_fun_Y_19: $i)).
% 0.23/0.47 tff(p14_type, type, (
% 0.23/0.47 p14: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_18_type, type, (
% 0.23/0.47 tptp_fun_X_18: $i)).
% 0.23/0.47 tff(tptp_fun_Y_17_type, type, (
% 0.23/0.47 tptp_fun_Y_17: $i)).
% 0.23/0.47 tff(tptp_fun_X_16_type, type, (
% 0.23/0.47 tptp_fun_X_16: $i)).
% 0.23/0.47 tff(tptp_fun_Y_15_type, type, (
% 0.23/0.47 tptp_fun_Y_15: $i)).
% 0.23/0.47 tff(tptp_fun_X_8_type, type, (
% 0.23/0.47 tptp_fun_X_8: $i > $i)).
% 0.23/0.47 tff(tptp_fun_X_2_type, type, (
% 0.23/0.47 tptp_fun_X_2: $i > $i)).
% 0.23/0.47 tff(tptp_fun_Y_14_type, type, (
% 0.23/0.47 tptp_fun_Y_14: $i)).
% 0.23/0.47 tff(tptp_fun_X_13_type, type, (
% 0.23/0.47 tptp_fun_X_13: $i)).
% 0.23/0.47 tff(tptp_fun_Y_12_type, type, (
% 0.23/0.47 tptp_fun_Y_12: $i)).
% 0.23/0.47 tff(tptp_fun_Y_10_type, type, (
% 0.23/0.47 tptp_fun_Y_10: $i)).
% 0.23/0.47 tff(tptp_fun_X_11_type, type, (
% 0.23/0.47 tptp_fun_X_11: $i)).
% 0.23/0.47 tff(tptp_fun_Y_7_type, type, (
% 0.23/0.47 tptp_fun_Y_7: $i)).
% 0.23/0.47 tff(p16_type, type, (
% 0.23/0.47 p16: $i > $o)).
% 0.23/0.47 tff(tptp_fun_X_6_type, type, (
% 0.23/0.47 tptp_fun_X_6: $i)).
% 0.23/0.47 tff(tptp_fun_Y_5_type, type, (
% 0.23/0.47 tptp_fun_Y_5: $i)).
% 0.23/0.47 tff(tptp_fun_X_4_type, type, (
% 0.23/0.47 tptp_fun_X_4: $i)).
% 0.23/0.47 tff(tptp_fun_Y_3_type, type, (
% 0.23/0.47 tptp_fun_Y_3: $i)).
% 0.23/0.47 tff(tptp_fun_X_1_type, type, (
% 0.23/0.47 tptp_fun_X_1: $i > $i)).
% 0.23/0.47 tff(1,plain,
% 0.23/0.47 (((![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) | ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))) & (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y))))) & (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | ((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))) | (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))) & (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))) | (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y))))) & (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))) | (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))) & (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | (r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))) | (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y))))) & (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | (r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))) | (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y)))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))) & (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | (r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))) | (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y))))) & $false & (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | (r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))) | (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y)))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) & (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | (r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) & ((r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))) | (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | (r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))) | (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))) & (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | (r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))) | (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | (r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))) | (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y))))))) <=> $false),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(2,plain,
% 0.23/0.48 ((![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | ((r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))) | (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | (r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))) | (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y))))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(3,plain,
% 0.23/0.48 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))) <=> (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y))))), (((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y))))) <=> ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y))))))), (((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))))), rewrite(((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))), (((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(4,plain,
% 0.23/0.48 (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[3])).
% 0.23/0.48 tff(5,plain,
% 0.23/0.48 (((r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))) | (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y)))) | $false) <=> ((r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))) | (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y)))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(6,plain,
% 0.23/0.48 ((r1(X!0, Y!91) & (~p2(Y!91)) & (p2(Y!91) & ![X: $i] : (p2(X) | (~r1(Y!91, X)))) & (~p1(Y!91)) & (p1(Y!91) & ![X: $i] : (p1(X) | (~r1(Y!91, X))))) <=> $false),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(7,plain,
% 0.23/0.48 ((p1(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p1(X))) <=> (p1(Y!91) & ![X: $i] : (p1(X) | (~r1(Y!91, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(8,plain,
% 0.23/0.48 ((p2(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p2(X))) <=> (p2(Y!91) & ![X: $i] : (p2(X) | (~r1(Y!91, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(9,plain,
% 0.23/0.48 ((r1(X!0, Y!91) & (~p2(Y!91)) & (p2(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p2(X))) & (~p1(Y!91)) & (p1(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p1(X)))) <=> (r1(X!0, Y!91) & (~p2(Y!91)) & (p2(Y!91) & ![X: $i] : (p2(X) | (~r1(Y!91, X)))) & (~p1(Y!91)) & (p1(Y!91) & ![X: $i] : (p1(X) | (~r1(Y!91, X)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[8, 7])).
% 0.23/0.48 tff(10,plain,
% 0.23/0.48 ((r1(X!0, Y!91) & (~p2(Y!91)) & (p2(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p2(X))) & (~p1(Y!91)) & (p1(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p1(X)))) <=> $false),
% 0.23/0.48 inference(transitivity,[status(thm)],[9, 6])).
% 0.23/0.48 tff(11,plain,
% 0.23/0.48 ((r1(X!0, Y!89) & (p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X)))) & (~p1(Y!89)) & (r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y))))) <=> (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(12,plain,
% 0.23/0.48 ((r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y))))) <=> (r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(13,plain,
% 0.23/0.48 ((p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y))) <=> (p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(14,plain,
% 0.23/0.48 ((r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y)))) <=> (r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[13])).
% 0.23/0.48 tff(15,plain,
% 0.23/0.48 ((r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y)))) <=> (r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[14, 12])).
% 0.23/0.48 tff(16,plain,
% 0.23/0.48 ((p2(Y!89) & ![X: $i] : ((~r1(Y!89, X)) | p2(X))) <=> (p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(17,plain,
% 0.23/0.48 ((r1(X!0, Y!89) & (p2(Y!89) & ![X: $i] : ((~r1(Y!89, X)) | p2(X))) & (~p1(Y!89)) & (r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y))))) <=> (r1(X!0, Y!89) & (p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X)))) & (~p1(Y!89)) & (r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[16, 15])).
% 0.23/0.48 tff(18,plain,
% 0.23/0.48 ((r1(X!0, Y!89) & (p2(Y!89) & ![X: $i] : ((~r1(Y!89, X)) | p2(X))) & (~p1(Y!89)) & (r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y))))) <=> (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[17, 11])).
% 0.23/0.49 tff(19,plain,
% 0.23/0.49 ((r1(X!0, Y!87) & (~p2(Y!87)) & (p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X)))) & (r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88)))) <=> (r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(20,plain,
% 0.23/0.49 ((r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y)))) & (~p1(X!88))) <=> (r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(21,plain,
% 0.23/0.49 ((p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) <=> (p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(22,plain,
% 0.23/0.49 ((r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) & (~p1(X!88))) <=> (r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y)))) & (~p1(X!88)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[21])).
% 0.23/0.49 tff(23,plain,
% 0.23/0.49 ((r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) & (~p1(X!88))) <=> (r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[22, 20])).
% 0.23/0.49 tff(24,plain,
% 0.23/0.49 ((p1(Y!87) & ![X: $i] : ((~r1(Y!87, X)) | p1(X))) <=> (p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(25,plain,
% 0.23/0.49 ((r1(X!0, Y!87) & (~p2(Y!87)) & (p1(Y!87) & ![X: $i] : ((~r1(Y!87, X)) | p1(X))) & (r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) & (~p1(X!88)))) <=> (r1(X!0, Y!87) & (~p2(Y!87)) & (p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X)))) & (r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[24, 23])).
% 0.23/0.49 tff(26,plain,
% 0.23/0.49 ((r1(X!0, Y!87) & (~p2(Y!87)) & (p1(Y!87) & ![X: $i] : ((~r1(Y!87, X)) | p1(X))) & (r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) & (~p1(X!88)))) <=> (r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[25, 19])).
% 0.23/0.49 tff(27,plain,
% 0.23/0.49 (((r1(X!0, Y!87) & (~p2(Y!87)) & (p1(Y!87) & ![X: $i] : ((~r1(Y!87, X)) | p1(X))) & (r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) & (~p1(X!88)))) | (r1(X!0, Y!89) & (p2(Y!89) & ![X: $i] : ((~r1(Y!89, X)) | p2(X))) & (~p1(Y!89)) & (r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y))))) | (r1(X!0, Y!91) & (~p2(Y!91)) & (p2(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p2(X))) & (~p1(Y!91)) & (p1(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p1(X))))) <=> ((r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))) | (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y)))) | $false)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[26, 18, 10])).
% 0.23/0.49 tff(28,plain,
% 0.23/0.49 (((r1(X!0, Y!87) & (~p2(Y!87)) & (p1(Y!87) & ![X: $i] : ((~r1(Y!87, X)) | p1(X))) & (r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) & (~p1(X!88)))) | (r1(X!0, Y!89) & (p2(Y!89) & ![X: $i] : ((~r1(Y!89, X)) | p2(X))) & (~p1(Y!89)) & (r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y))))) | (r1(X!0, Y!91) & (~p2(Y!91)) & (p2(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p2(X))) & (~p1(Y!91)) & (p1(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p1(X))))) <=> ((r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))) | (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y)))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[27, 5])).
% 0.23/0.49 tff(29,plain,
% 0.23/0.49 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))) <=> (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))), (((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) <=> ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))))), (((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | p1(Y)))), rewrite(((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))), (((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(30,plain,
% 0.23/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | p1(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[29])).
% 0.23/0.49 tff(31,plain,
% 0.23/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | p1(Y)) | ((r1(X!0, Y!87) & (~p2(Y!87)) & (p1(Y!87) & ![X: $i] : ((~r1(Y!87, X)) | p1(X))) & (r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) & (~p1(X!88)))) | (r1(X!0, Y!89) & (p2(Y!89) & ![X: $i] : ((~r1(Y!89, X)) | p2(X))) & (~p1(Y!89)) & (r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y))))) | (r1(X!0, Y!91) & (~p2(Y!91)) & (p2(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p2(X))) & (~p1(Y!91)) & (p1(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p1(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | ((r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))) | (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y))))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[30, 28, 4])).
% 0.23/0.49 tff(32,plain,
% 0.23/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | p1(Y)) | ((r1(X!0, Y!87) & (~p2(Y!87)) & (p1(Y!87) & ![X: $i] : ((~r1(Y!87, X)) | p1(X))) & (r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) & (~p1(X!88)))) | (r1(X!0, Y!89) & (p2(Y!89) & ![X: $i] : ((~r1(Y!89, X)) | p2(X))) & (~p1(Y!89)) & (r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y))))) | (r1(X!0, Y!91) & (~p2(Y!91)) & (p2(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p2(X))) & (~p1(Y!91)) & (p1(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p1(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | (r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))) | (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y))))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[31, 2])).
% 0.23/0.49 tff(33,plain,
% 0.23/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ((r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))) | (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | (r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))) | (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(34,plain,
% 0.23/0.49 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))) <=> (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))), (((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) <=> ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))))), (((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))))), rewrite(((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))), (((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(35,plain,
% 0.23/0.49 (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[34])).
% 0.23/0.49 tff(36,plain,
% 0.23/0.49 (((r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))) | (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y)))) | $false) <=> ((r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))) | (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y)))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(37,plain,
% 0.23/0.49 ((r1(X!0, Y!85) & (~p3(Y!85)) & (p3(Y!85) & ![X: $i] : (p3(X) | (~r1(Y!85, X)))) & (~p2(Y!85)) & (p2(Y!85) & ![X: $i] : (p2(X) | (~r1(Y!85, X))))) <=> $false),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(38,plain,
% 0.23/0.49 ((p2(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p2(X))) <=> (p2(Y!85) & ![X: $i] : (p2(X) | (~r1(Y!85, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(39,plain,
% 0.23/0.49 ((p3(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p3(X))) <=> (p3(Y!85) & ![X: $i] : (p3(X) | (~r1(Y!85, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(40,plain,
% 0.23/0.49 ((r1(X!0, Y!85) & (~p3(Y!85)) & (p3(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p3(X))) & (~p2(Y!85)) & (p2(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p2(X)))) <=> (r1(X!0, Y!85) & (~p3(Y!85)) & (p3(Y!85) & ![X: $i] : (p3(X) | (~r1(Y!85, X)))) & (~p2(Y!85)) & (p2(Y!85) & ![X: $i] : (p2(X) | (~r1(Y!85, X)))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[39, 38])).
% 0.23/0.49 tff(41,plain,
% 0.23/0.49 ((r1(X!0, Y!85) & (~p3(Y!85)) & (p3(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p3(X))) & (~p2(Y!85)) & (p2(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p2(X)))) <=> $false),
% 0.23/0.49 inference(transitivity,[status(thm)],[40, 37])).
% 0.23/0.49 tff(42,plain,
% 0.23/0.50 ((r1(X!0, Y!83) & (p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X)))) & (~p2(Y!83)) & (r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y))))) <=> (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(43,plain,
% 0.23/0.50 ((r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y))))) <=> (r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(44,plain,
% 0.23/0.50 ((p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y))) <=> (p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(45,plain,
% 0.23/0.50 ((r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y)))) <=> (r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[44])).
% 0.23/0.50 tff(46,plain,
% 0.23/0.50 ((r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y)))) <=> (r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[45, 43])).
% 0.23/0.50 tff(47,plain,
% 0.23/0.50 ((p3(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p3(X))) <=> (p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(48,plain,
% 0.23/0.50 ((r1(X!0, Y!83) & (p3(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p3(X))) & (~p2(Y!83)) & (r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y))))) <=> (r1(X!0, Y!83) & (p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X)))) & (~p2(Y!83)) & (r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[47, 46])).
% 0.23/0.50 tff(49,plain,
% 0.23/0.50 ((r1(X!0, Y!83) & (p3(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p3(X))) & (~p2(Y!83)) & (r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y))))) <=> (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[48, 42])).
% 0.23/0.50 tff(50,plain,
% 0.23/0.50 ((r1(X!0, Y!81) & (~p3(Y!81)) & (p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X)))) & (r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82)))) <=> (r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(51,plain,
% 0.23/0.50 ((r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y)))) & (~p2(X!82))) <=> (r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(52,plain,
% 0.23/0.50 ((p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) <=> (p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(53,plain,
% 0.23/0.50 ((r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) & (~p2(X!82))) <=> (r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y)))) & (~p2(X!82)))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[52])).
% 0.23/0.50 tff(54,plain,
% 0.23/0.50 ((r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) & (~p2(X!82))) <=> (r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82)))),
% 0.23/0.50 inference(transitivity,[status(thm)],[53, 51])).
% 0.23/0.50 tff(55,plain,
% 0.23/0.50 ((p2(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p2(X))) <=> (p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(56,plain,
% 0.23/0.50 ((r1(X!0, Y!81) & (~p3(Y!81)) & (p2(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p2(X))) & (r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) & (~p2(X!82)))) <=> (r1(X!0, Y!81) & (~p3(Y!81)) & (p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X)))) & (r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[55, 54])).
% 0.23/0.50 tff(57,plain,
% 0.23/0.50 ((r1(X!0, Y!81) & (~p3(Y!81)) & (p2(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p2(X))) & (r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) & (~p2(X!82)))) <=> (r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82)))),
% 0.23/0.50 inference(transitivity,[status(thm)],[56, 50])).
% 0.23/0.50 tff(58,plain,
% 0.23/0.50 (((r1(X!0, Y!81) & (~p3(Y!81)) & (p2(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p2(X))) & (r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) & (~p2(X!82)))) | (r1(X!0, Y!83) & (p3(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p3(X))) & (~p2(Y!83)) & (r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y))))) | (r1(X!0, Y!85) & (~p3(Y!85)) & (p3(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p3(X))) & (~p2(Y!85)) & (p2(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p2(X))))) <=> ((r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))) | (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y)))) | $false)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[57, 49, 41])).
% 0.23/0.50 tff(59,plain,
% 0.23/0.50 (((r1(X!0, Y!81) & (~p3(Y!81)) & (p2(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p2(X))) & (r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) & (~p2(X!82)))) | (r1(X!0, Y!83) & (p3(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p3(X))) & (~p2(Y!83)) & (r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y))))) | (r1(X!0, Y!85) & (~p3(Y!85)) & (p3(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p3(X))) & (~p2(Y!85)) & (p2(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p2(X))))) <=> ((r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))) | (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y)))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[58, 36])).
% 0.23/0.50 tff(60,plain,
% 0.23/0.50 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))) <=> (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))), (((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) <=> ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))))), (((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | p2(Y)))), rewrite(((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))), (((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(61,plain,
% 0.23/0.50 (![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | p2(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[60])).
% 0.23/0.50 tff(62,plain,
% 0.23/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | p2(Y)) | ((r1(X!0, Y!81) & (~p3(Y!81)) & (p2(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p2(X))) & (r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) & (~p2(X!82)))) | (r1(X!0, Y!83) & (p3(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p3(X))) & (~p2(Y!83)) & (r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y))))) | (r1(X!0, Y!85) & (~p3(Y!85)) & (p3(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p3(X))) & (~p2(Y!85)) & (p2(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ((r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))) | (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[61, 59, 35])).
% 0.23/0.50 tff(63,plain,
% 0.23/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | p2(Y)) | ((r1(X!0, Y!81) & (~p3(Y!81)) & (p2(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p2(X))) & (r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) & (~p2(X!82)))) | (r1(X!0, Y!83) & (p3(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p3(X))) & (~p2(Y!83)) & (r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y))))) | (r1(X!0, Y!85) & (~p3(Y!85)) & (p3(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p3(X))) & (~p2(Y!85)) & (p2(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | (r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))) | (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[62, 33])).
% 0.23/0.50 tff(64,plain,
% 0.23/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | ((r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))) | (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | (r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))) | (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y)))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(65,plain,
% 0.23/0.50 (((r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))) | (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y)))) | $false) <=> ((r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))) | (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y)))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(66,plain,
% 0.23/0.50 ((r1(X!0, Y!80) & (~p4(Y!80)) & (p4(Y!80) & ![X: $i] : (p4(X) | (~r1(Y!80, X)))) & (~p3(Y!80)) & (p3(Y!80) & ![X: $i] : (p3(X) | (~r1(Y!80, X))))) <=> $false),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(67,plain,
% 0.23/0.50 ((p3(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p3(X))) <=> (p3(Y!80) & ![X: $i] : (p3(X) | (~r1(Y!80, X))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(68,plain,
% 0.23/0.51 ((p4(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p4(X))) <=> (p4(Y!80) & ![X: $i] : (p4(X) | (~r1(Y!80, X))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(69,plain,
% 0.23/0.51 ((r1(X!0, Y!80) & (~p4(Y!80)) & (p4(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p4(X))) & (~p3(Y!80)) & (p3(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p3(X)))) <=> (r1(X!0, Y!80) & (~p4(Y!80)) & (p4(Y!80) & ![X: $i] : (p4(X) | (~r1(Y!80, X)))) & (~p3(Y!80)) & (p3(Y!80) & ![X: $i] : (p3(X) | (~r1(Y!80, X)))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[68, 67])).
% 0.23/0.51 tff(70,plain,
% 0.23/0.51 ((r1(X!0, Y!80) & (~p4(Y!80)) & (p4(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p4(X))) & (~p3(Y!80)) & (p3(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p3(X)))) <=> $false),
% 0.23/0.51 inference(transitivity,[status(thm)],[69, 66])).
% 0.23/0.51 tff(71,plain,
% 0.23/0.51 ((r1(X!0, Y!78) & (p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X)))) & (~p3(Y!78)) & (r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))) <=> (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(72,plain,
% 0.23/0.51 ((r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))) <=> (r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(73,plain,
% 0.23/0.51 ((p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y))) <=> (p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(74,plain,
% 0.23/0.51 ((r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y)))) <=> (r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y)))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[73])).
% 0.23/0.51 tff(75,plain,
% 0.23/0.51 ((r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y)))) <=> (r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[74, 72])).
% 0.23/0.51 tff(76,plain,
% 0.23/0.51 ((p4(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p4(X))) <=> (p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(77,plain,
% 0.23/0.51 ((r1(X!0, Y!78) & (p4(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p4(X))) & (~p3(Y!78)) & (r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y))))) <=> (r1(X!0, Y!78) & (p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X)))) & (~p3(Y!78)) & (r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y)))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[76, 75])).
% 0.23/0.51 tff(78,plain,
% 0.23/0.51 ((r1(X!0, Y!78) & (p4(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p4(X))) & (~p3(Y!78)) & (r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y))))) <=> (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[77, 71])).
% 0.23/0.51 tff(79,plain,
% 0.23/0.51 ((r1(X!0, Y!76) & (~p4(Y!76)) & (p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X)))) & (r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77)))) <=> (r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(80,plain,
% 0.23/0.51 ((r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y)))) & (~p3(X!77))) <=> (r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(81,plain,
% 0.23/0.51 ((p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) <=> (p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(82,plain,
% 0.23/0.51 ((r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) & (~p3(X!77))) <=> (r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y)))) & (~p3(X!77)))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[81])).
% 0.23/0.51 tff(83,plain,
% 0.23/0.51 ((r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) & (~p3(X!77))) <=> (r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[82, 80])).
% 0.23/0.51 tff(84,plain,
% 0.23/0.51 ((p3(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p3(X))) <=> (p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(85,plain,
% 0.23/0.51 ((r1(X!0, Y!76) & (~p4(Y!76)) & (p3(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p3(X))) & (r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) & (~p3(X!77)))) <=> (r1(X!0, Y!76) & (~p4(Y!76)) & (p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X)))) & (r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[84, 83])).
% 0.23/0.51 tff(86,plain,
% 0.23/0.51 ((r1(X!0, Y!76) & (~p4(Y!76)) & (p3(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p3(X))) & (r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) & (~p3(X!77)))) <=> (r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77)))),
% 0.23/0.51 inference(transitivity,[status(thm)],[85, 79])).
% 0.23/0.51 tff(87,plain,
% 0.23/0.51 (((r1(X!0, Y!76) & (~p4(Y!76)) & (p3(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p3(X))) & (r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) & (~p3(X!77)))) | (r1(X!0, Y!78) & (p4(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p4(X))) & (~p3(Y!78)) & (r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y))))) | (r1(X!0, Y!80) & (~p4(Y!80)) & (p4(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p4(X))) & (~p3(Y!80)) & (p3(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p3(X))))) <=> ((r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))) | (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y)))) | $false)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[86, 78, 70])).
% 0.23/0.51 tff(88,plain,
% 0.23/0.51 (((r1(X!0, Y!76) & (~p4(Y!76)) & (p3(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p3(X))) & (r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) & (~p3(X!77)))) | (r1(X!0, Y!78) & (p4(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p4(X))) & (~p3(Y!78)) & (r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y))))) | (r1(X!0, Y!80) & (~p4(Y!80)) & (p4(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p4(X))) & (~p3(Y!80)) & (p3(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p3(X))))) <=> ((r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))) | (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y)))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[87, 65])).
% 0.23/0.51 tff(89,plain,
% 0.23/0.51 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))) <=> (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))), (((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) <=> ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))))), (((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | p3(Y)) <=> ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | p3(Y)))), rewrite(((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | p3(Y)) <=> ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))), (((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | p3(Y)) <=> ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(90,plain,
% 0.23/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | p3(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[89])).
% 0.23/0.52 tff(91,plain,
% 0.23/0.52 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))) <=> (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))), (((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) <=> ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))))), (((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))))), rewrite(((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))), (((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(92,plain,
% 0.23/0.52 (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[91])).
% 0.23/0.52 tff(93,plain,
% 0.23/0.52 ((![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | p3(Y)) | ((r1(X!0, Y!76) & (~p4(Y!76)) & (p3(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p3(X))) & (r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) & (~p3(X!77)))) | (r1(X!0, Y!78) & (p4(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p4(X))) & (~p3(Y!78)) & (r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y))))) | (r1(X!0, Y!80) & (~p4(Y!80)) & (p4(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p4(X))) & (~p3(Y!80)) & (p3(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p3(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | ((r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))) | (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[92, 90, 88])).
% 0.23/0.52 tff(94,plain,
% 0.23/0.52 ((![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | p3(Y)) | ((r1(X!0, Y!76) & (~p4(Y!76)) & (p3(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p3(X))) & (r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) & (~p3(X!77)))) | (r1(X!0, Y!78) & (p4(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p4(X))) & (~p3(Y!78)) & (r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y))))) | (r1(X!0, Y!80) & (~p4(Y!80)) & (p4(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p4(X))) & (~p3(Y!80)) & (p3(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p3(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | (r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))) | (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y)))))),
% 0.23/0.52 inference(transitivity,[status(thm)],[93, 64])).
% 0.23/0.52 tff(95,plain,
% 0.23/0.52 ((((r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))) | (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) <=> ((r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))) | (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(96,plain,
% 0.23/0.52 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))) <=> (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))), (((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) <=> ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))))), (((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | p4(Y)) <=> ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | p4(Y)))), rewrite(((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | p4(Y)) <=> ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))), (((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | p4(Y)) <=> ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(97,plain,
% 0.23/0.52 (![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | p4(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[96])).
% 0.23/0.52 tff(98,plain,
% 0.23/0.52 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))) <=> (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))), (((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) <=> ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))))), (((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))))), rewrite(((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))), (((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(99,plain,
% 0.23/0.52 (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[98])).
% 0.23/0.52 tff(100,plain,
% 0.23/0.52 (((r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))) | (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y)))) | $false) <=> ((r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))) | (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y)))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(101,plain,
% 0.23/0.52 ((r1(X!0, Y!73) & (~p5(Y!73)) & (p5(Y!73) & ![X: $i] : (p5(X) | (~r1(Y!73, X)))) & (~p4(Y!73)) & (p4(Y!73) & ![X: $i] : (p4(X) | (~r1(Y!73, X))))) <=> $false),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(102,plain,
% 0.23/0.52 ((p4(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p4(X))) <=> (p4(Y!73) & ![X: $i] : (p4(X) | (~r1(Y!73, X))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(103,plain,
% 0.23/0.52 ((p5(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p5(X))) <=> (p5(Y!73) & ![X: $i] : (p5(X) | (~r1(Y!73, X))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(104,plain,
% 0.23/0.52 ((r1(X!0, Y!73) & (~p5(Y!73)) & (p5(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p5(X))) & (~p4(Y!73)) & (p4(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p4(X)))) <=> (r1(X!0, Y!73) & (~p5(Y!73)) & (p5(Y!73) & ![X: $i] : (p5(X) | (~r1(Y!73, X)))) & (~p4(Y!73)) & (p4(Y!73) & ![X: $i] : (p4(X) | (~r1(Y!73, X)))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[103, 102])).
% 0.23/0.52 tff(105,plain,
% 0.23/0.52 ((r1(X!0, Y!73) & (~p5(Y!73)) & (p5(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p5(X))) & (~p4(Y!73)) & (p4(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p4(X)))) <=> $false),
% 0.23/0.52 inference(transitivity,[status(thm)],[104, 101])).
% 0.23/0.52 tff(106,plain,
% 0.23/0.52 ((r1(X!0, Y!71) & (p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X)))) & (~p4(Y!71)) & (r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y))))) <=> (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(107,plain,
% 0.23/0.52 ((r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y))))) <=> (r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(108,plain,
% 0.23/0.52 ((p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y))) <=> (p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(109,plain,
% 0.23/0.52 ((r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y)))) <=> (r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y)))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[108])).
% 0.23/0.52 tff(110,plain,
% 0.23/0.52 ((r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y)))) <=> (r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y))))),
% 0.23/0.52 inference(transitivity,[status(thm)],[109, 107])).
% 0.23/0.52 tff(111,plain,
% 0.23/0.52 ((p5(Y!71) & ![X: $i] : ((~r1(Y!71, X)) | p5(X))) <=> (p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(112,plain,
% 0.23/0.52 ((r1(X!0, Y!71) & (p5(Y!71) & ![X: $i] : ((~r1(Y!71, X)) | p5(X))) & (~p4(Y!71)) & (r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y))))) <=> (r1(X!0, Y!71) & (p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X)))) & (~p4(Y!71)) & (r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y)))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[111, 110])).
% 0.23/0.52 tff(113,plain,
% 0.23/0.52 ((r1(X!0, Y!71) & (p5(Y!71) & ![X: $i] : ((~r1(Y!71, X)) | p5(X))) & (~p4(Y!71)) & (r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y))))) <=> (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y))))),
% 0.23/0.52 inference(transitivity,[status(thm)],[112, 106])).
% 0.23/0.52 tff(114,plain,
% 0.23/0.52 ((r1(X!0, Y!69) & (~p5(Y!69)) & (p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X)))) & (r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70)))) <=> (r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(115,plain,
% 0.23/0.52 ((r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y)))) & (~p4(X!70))) <=> (r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(116,plain,
% 0.23/0.53 ((p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) <=> (p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(117,plain,
% 0.23/0.53 ((r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) & (~p4(X!70))) <=> (r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y)))) & (~p4(X!70)))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[116])).
% 0.23/0.53 tff(118,plain,
% 0.23/0.53 ((r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) & (~p4(X!70))) <=> (r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70)))),
% 0.23/0.53 inference(transitivity,[status(thm)],[117, 115])).
% 0.23/0.53 tff(119,plain,
% 0.23/0.53 ((p4(Y!69) & ![X: $i] : ((~r1(Y!69, X)) | p4(X))) <=> (p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(120,plain,
% 0.23/0.53 ((r1(X!0, Y!69) & (~p5(Y!69)) & (p4(Y!69) & ![X: $i] : ((~r1(Y!69, X)) | p4(X))) & (r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) & (~p4(X!70)))) <=> (r1(X!0, Y!69) & (~p5(Y!69)) & (p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X)))) & (r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[119, 118])).
% 0.23/0.53 tff(121,plain,
% 0.23/0.53 ((r1(X!0, Y!69) & (~p5(Y!69)) & (p4(Y!69) & ![X: $i] : ((~r1(Y!69, X)) | p4(X))) & (r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) & (~p4(X!70)))) <=> (r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70)))),
% 0.23/0.53 inference(transitivity,[status(thm)],[120, 114])).
% 0.23/0.53 tff(122,plain,
% 0.23/0.53 (((r1(X!0, Y!69) & (~p5(Y!69)) & (p4(Y!69) & ![X: $i] : ((~r1(Y!69, X)) | p4(X))) & (r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) & (~p4(X!70)))) | (r1(X!0, Y!71) & (p5(Y!71) & ![X: $i] : ((~r1(Y!71, X)) | p5(X))) & (~p4(Y!71)) & (r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y))))) | (r1(X!0, Y!73) & (~p5(Y!73)) & (p5(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p5(X))) & (~p4(Y!73)) & (p4(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p4(X))))) <=> ((r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))) | (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y)))) | $false)),
% 0.23/0.53 inference(monotonicity,[status(thm)],[121, 113, 105])).
% 0.23/0.53 tff(123,plain,
% 0.23/0.53 (((r1(X!0, Y!69) & (~p5(Y!69)) & (p4(Y!69) & ![X: $i] : ((~r1(Y!69, X)) | p4(X))) & (r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) & (~p4(X!70)))) | (r1(X!0, Y!71) & (p5(Y!71) & ![X: $i] : ((~r1(Y!71, X)) | p5(X))) & (~p4(Y!71)) & (r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y))))) | (r1(X!0, Y!73) & (~p5(Y!73)) & (p5(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p5(X))) & (~p4(Y!73)) & (p4(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p4(X))))) <=> ((r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))) | (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y)))))),
% 0.23/0.53 inference(transitivity,[status(thm)],[122, 100])).
% 0.23/0.53 tff(124,plain,
% 0.23/0.53 ((((r1(X!0, Y!69) & (~p5(Y!69)) & (p4(Y!69) & ![X: $i] : ((~r1(Y!69, X)) | p4(X))) & (r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) & (~p4(X!70)))) | (r1(X!0, Y!71) & (p5(Y!71) & ![X: $i] : ((~r1(Y!71, X)) | p5(X))) & (~p4(Y!71)) & (r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y))))) | (r1(X!0, Y!73) & (~p5(Y!73)) & (p5(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p5(X))) & (~p4(Y!73)) & (p4(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p4(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | p4(Y))) <=> (((r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))) | (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[123, 99, 97])).
% 0.23/0.53 tff(125,plain,
% 0.23/0.53 ((((r1(X!0, Y!69) & (~p5(Y!69)) & (p4(Y!69) & ![X: $i] : ((~r1(Y!69, X)) | p4(X))) & (r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) & (~p4(X!70)))) | (r1(X!0, Y!71) & (p5(Y!71) & ![X: $i] : ((~r1(Y!71, X)) | p5(X))) & (~p4(Y!71)) & (r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y))))) | (r1(X!0, Y!73) & (~p5(Y!73)) & (p5(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p5(X))) & (~p4(Y!73)) & (p4(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p4(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | p4(Y))) <=> ((r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))) | (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))))),
% 0.23/0.53 inference(transitivity,[status(thm)],[124, 95])).
% 0.23/0.53 tff(126,plain,
% 0.23/0.53 ((![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | ((r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) <=> (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | (r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(127,plain,
% 0.23/0.53 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))) <=> (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))), (((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))) <=> ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))), (((~r1(X!0, Y)) | p5(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))))), rewrite(((~r1(X!0, Y)) | p5(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))), (((~r1(X!0, Y)) | p5(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(128,plain,
% 0.23/0.53 (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[127])).
% 0.23/0.53 tff(129,plain,
% 0.23/0.53 (((r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y)))) | $false) <=> ((r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y)))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(130,plain,
% 0.23/0.53 ((r1(X!0, Y!68) & (~p6(Y!68)) & (~p5(Y!68)) & (p6(Y!68) & ![X: $i] : (p6(X) | (~r1(Y!68, X)))) & (p5(Y!68) & ![X: $i] : (p5(X) | (~r1(Y!68, X))))) <=> $false),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(131,plain,
% 0.23/0.53 ((p5(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p5(X))) <=> (p5(Y!68) & ![X: $i] : (p5(X) | (~r1(Y!68, X))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(132,plain,
% 0.23/0.53 ((p6(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p6(X))) <=> (p6(Y!68) & ![X: $i] : (p6(X) | (~r1(Y!68, X))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(133,plain,
% 0.23/0.53 ((r1(X!0, Y!68) & (~p6(Y!68)) & (~p5(Y!68)) & (p6(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p6(X))) & (p5(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p5(X)))) <=> (r1(X!0, Y!68) & (~p6(Y!68)) & (~p5(Y!68)) & (p6(Y!68) & ![X: $i] : (p6(X) | (~r1(Y!68, X)))) & (p5(Y!68) & ![X: $i] : (p5(X) | (~r1(Y!68, X)))))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[132, 131])).
% 0.23/0.53 tff(134,plain,
% 0.23/0.53 ((r1(X!0, Y!68) & (~p6(Y!68)) & (~p5(Y!68)) & (p6(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p6(X))) & (p5(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p5(X)))) <=> $false),
% 0.23/0.53 inference(transitivity,[status(thm)],[133, 130])).
% 0.23/0.53 tff(135,plain,
% 0.23/0.53 ((r1(X!0, Y!66) & (~p5(Y!66)) & (p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X)))) & (r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y))))) <=> (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(136,plain,
% 0.23/0.53 ((r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y))))) <=> (r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(137,plain,
% 0.23/0.53 ((p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y))) <=> (p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(138,plain,
% 0.23/0.53 ((r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y)))) <=> (r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y)))))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[137])).
% 0.23/0.53 tff(139,plain,
% 0.23/0.53 ((r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y)))) <=> (r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y))))),
% 0.23/0.53 inference(transitivity,[status(thm)],[138, 136])).
% 0.23/0.53 tff(140,plain,
% 0.23/0.53 ((p6(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p6(X))) <=> (p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(141,plain,
% 0.23/0.53 ((r1(X!0, Y!66) & (~p5(Y!66)) & (p6(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p6(X))) & (r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y))))) <=> (r1(X!0, Y!66) & (~p5(Y!66)) & (p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X)))) & (r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y)))))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[140, 139])).
% 0.23/0.53 tff(142,plain,
% 0.23/0.53 ((r1(X!0, Y!66) & (~p5(Y!66)) & (p6(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p6(X))) & (r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y))))) <=> (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y))))),
% 0.23/0.54 inference(transitivity,[status(thm)],[141, 135])).
% 0.23/0.54 tff(143,plain,
% 0.23/0.54 ((r1(X!0, Y!64) & (r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65))) & (~p6(Y!64)) & (p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X))))) <=> (r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(144,plain,
% 0.23/0.54 ((p5(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p5(X))) <=> (p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(145,plain,
% 0.23/0.54 ((r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y)))) & (~p5(X!65))) <=> (r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(146,plain,
% 0.23/0.54 ((p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) <=> (p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(147,plain,
% 0.23/0.54 ((r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) & (~p5(X!65))) <=> (r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y)))) & (~p5(X!65)))),
% 0.23/0.54 inference(monotonicity,[status(thm)],[146])).
% 0.23/0.54 tff(148,plain,
% 0.23/0.54 ((r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) & (~p5(X!65))) <=> (r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)))),
% 0.23/0.54 inference(transitivity,[status(thm)],[147, 145])).
% 0.23/0.54 tff(149,plain,
% 0.23/0.54 ((r1(X!0, Y!64) & (r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) & (~p5(X!65))) & (~p6(Y!64)) & (p5(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p5(X)))) <=> (r1(X!0, Y!64) & (r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65))) & (~p6(Y!64)) & (p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))))),
% 0.23/0.54 inference(monotonicity,[status(thm)],[148, 144])).
% 0.23/0.54 tff(150,plain,
% 0.23/0.54 ((r1(X!0, Y!64) & (r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) & (~p5(X!65))) & (~p6(Y!64)) & (p5(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p5(X)))) <=> (r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X))))),
% 0.23/0.54 inference(transitivity,[status(thm)],[149, 143])).
% 0.23/0.54 tff(151,plain,
% 0.23/0.54 (((r1(X!0, Y!64) & (r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) & (~p5(X!65))) & (~p6(Y!64)) & (p5(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p5(X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & (p6(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p6(X))) & (r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y))))) | (r1(X!0, Y!68) & (~p6(Y!68)) & (~p5(Y!68)) & (p6(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p6(X))) & (p5(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p5(X))))) <=> ((r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y)))) | $false)),
% 0.23/0.54 inference(monotonicity,[status(thm)],[150, 142, 134])).
% 0.23/0.54 tff(152,plain,
% 0.23/0.54 (((r1(X!0, Y!64) & (r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) & (~p5(X!65))) & (~p6(Y!64)) & (p5(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p5(X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & (p6(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p6(X))) & (r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y))))) | (r1(X!0, Y!68) & (~p6(Y!68)) & (~p5(Y!68)) & (p6(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p6(X))) & (p5(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p5(X))))) <=> ((r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y)))))),
% 0.23/0.54 inference(transitivity,[status(thm)],[151, 129])).
% 0.23/0.54 tff(153,plain,
% 0.23/0.54 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))) <=> (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))), (((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) <=> ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))))), (((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) <=> ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))))), rewrite(((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) <=> (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))), (((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) <=> (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))))),
% 0.23/0.54 inference(bind,[status(th)],[])).
% 0.23/0.54 tff(154,plain,
% 0.23/0.54 (![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) <=> ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))),
% 0.23/0.54 inference(quant_intro,[status(thm)],[153])).
% 0.23/0.54 tff(155,plain,
% 0.23/0.54 ((![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) | ((r1(X!0, Y!64) & (r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) & (~p5(X!65))) & (~p6(Y!64)) & (p5(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p5(X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & (p6(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p6(X))) & (r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y))))) | (r1(X!0, Y!68) & (~p6(Y!68)) & (~p5(Y!68)) & (p6(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p6(X))) & (p5(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))) <=> (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | ((r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))),
% 0.23/0.54 inference(monotonicity,[status(thm)],[154, 152, 128])).
% 0.23/0.54 tff(156,plain,
% 0.23/0.54 ((![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) | ((r1(X!0, Y!64) & (r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) & (~p5(X!65))) & (~p6(Y!64)) & (p5(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p5(X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & (p6(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p6(X))) & (r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y))))) | (r1(X!0, Y!68) & (~p6(Y!68)) & (~p5(Y!68)) & (p6(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p6(X))) & (p5(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))) <=> (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | (r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))),
% 0.23/0.54 inference(transitivity,[status(thm)],[155, 126])).
% 0.23/0.54 tff(157,plain,
% 0.23/0.54 ((![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | ((r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))) | (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y))))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) <=> (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | (r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))) | (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y)))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(158,plain,
% 0.23/0.54 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))) <=> (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))), (((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))) <=> ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))), (((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) <=> ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))))), rewrite(((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) <=> (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))), (((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) <=> (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))))),
% 0.23/0.54 inference(bind,[status(th)],[])).
% 0.23/0.54 tff(159,plain,
% 0.23/0.54 (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) <=> ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))),
% 0.23/0.54 inference(quant_intro,[status(thm)],[158])).
% 0.23/0.54 tff(160,plain,
% 0.23/0.54 (((r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))) | (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y)))) | $false) <=> ((r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))) | (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y)))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(161,plain,
% 0.23/0.54 ((r1(X!0, Y!61) & (~p7(Y!61)) & (p7(Y!61) & ![X: $i] : (p7(X) | (~r1(Y!61, X)))) & (~p6(Y!61)) & (p6(Y!61) & ![X: $i] : (p6(X) | (~r1(Y!61, X))))) <=> $false),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(162,plain,
% 0.23/0.54 ((p6(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p6(X))) <=> (p6(Y!61) & ![X: $i] : (p6(X) | (~r1(Y!61, X))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(163,plain,
% 0.23/0.54 ((p7(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p7(X))) <=> (p7(Y!61) & ![X: $i] : (p7(X) | (~r1(Y!61, X))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(164,plain,
% 0.23/0.54 ((r1(X!0, Y!61) & (~p7(Y!61)) & (p7(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p7(X))) & (~p6(Y!61)) & (p6(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p6(X)))) <=> (r1(X!0, Y!61) & (~p7(Y!61)) & (p7(Y!61) & ![X: $i] : (p7(X) | (~r1(Y!61, X)))) & (~p6(Y!61)) & (p6(Y!61) & ![X: $i] : (p6(X) | (~r1(Y!61, X)))))),
% 0.23/0.54 inference(monotonicity,[status(thm)],[163, 162])).
% 0.23/0.54 tff(165,plain,
% 0.23/0.54 ((r1(X!0, Y!61) & (~p7(Y!61)) & (p7(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p7(X))) & (~p6(Y!61)) & (p6(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p6(X)))) <=> $false),
% 0.23/0.55 inference(transitivity,[status(thm)],[164, 161])).
% 0.23/0.55 tff(166,plain,
% 0.23/0.55 ((r1(X!0, Y!59) & (p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X)))) & (~p6(Y!59)) & (r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y))))) <=> (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(167,plain,
% 0.23/0.55 ((r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y))))) <=> (r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(168,plain,
% 0.23/0.55 ((p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y))) <=> (p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(169,plain,
% 0.23/0.55 ((r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y)))) <=> (r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y)))))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[168])).
% 0.23/0.55 tff(170,plain,
% 0.23/0.55 ((r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y)))) <=> (r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y))))),
% 0.23/0.55 inference(transitivity,[status(thm)],[169, 167])).
% 0.23/0.55 tff(171,plain,
% 0.23/0.55 ((p7(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p7(X))) <=> (p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(172,plain,
% 0.23/0.55 ((r1(X!0, Y!59) & (p7(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p7(X))) & (~p6(Y!59)) & (r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y))))) <=> (r1(X!0, Y!59) & (p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X)))) & (~p6(Y!59)) & (r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y)))))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[171, 170])).
% 0.23/0.55 tff(173,plain,
% 0.23/0.55 ((r1(X!0, Y!59) & (p7(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p7(X))) & (~p6(Y!59)) & (r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y))))) <=> (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y))))),
% 0.23/0.55 inference(transitivity,[status(thm)],[172, 166])).
% 0.23/0.55 tff(174,plain,
% 0.23/0.55 ((r1(X!0, Y!57) & (~p7(Y!57)) & (p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X)))) & (r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58)))) <=> (r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58)))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(175,plain,
% 0.23/0.55 ((r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y)))) & (~p6(X!58))) <=> (r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58)))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(176,plain,
% 0.23/0.55 ((p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) <=> (p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(177,plain,
% 0.23/0.55 ((r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) & (~p6(X!58))) <=> (r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y)))) & (~p6(X!58)))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[176])).
% 0.23/0.55 tff(178,plain,
% 0.23/0.55 ((r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) & (~p6(X!58))) <=> (r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58)))),
% 0.23/0.55 inference(transitivity,[status(thm)],[177, 175])).
% 0.23/0.55 tff(179,plain,
% 0.23/0.55 ((p6(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p6(X))) <=> (p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(180,plain,
% 0.23/0.55 ((r1(X!0, Y!57) & (~p7(Y!57)) & (p6(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p6(X))) & (r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) & (~p6(X!58)))) <=> (r1(X!0, Y!57) & (~p7(Y!57)) & (p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X)))) & (r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[179, 178])).
% 0.23/0.55 tff(181,plain,
% 0.23/0.55 ((r1(X!0, Y!57) & (~p7(Y!57)) & (p6(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p6(X))) & (r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) & (~p6(X!58)))) <=> (r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58)))),
% 0.23/0.55 inference(transitivity,[status(thm)],[180, 174])).
% 0.23/0.55 tff(182,plain,
% 0.23/0.55 (((r1(X!0, Y!57) & (~p7(Y!57)) & (p6(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p6(X))) & (r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) & (~p6(X!58)))) | (r1(X!0, Y!59) & (p7(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p7(X))) & (~p6(Y!59)) & (r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y))))) | (r1(X!0, Y!61) & (~p7(Y!61)) & (p7(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p7(X))) & (~p6(Y!61)) & (p6(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p6(X))))) <=> ((r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))) | (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y)))) | $false)),
% 0.23/0.55 inference(monotonicity,[status(thm)],[181, 173, 165])).
% 0.23/0.55 tff(183,plain,
% 0.23/0.55 (((r1(X!0, Y!57) & (~p7(Y!57)) & (p6(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p6(X))) & (r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) & (~p6(X!58)))) | (r1(X!0, Y!59) & (p7(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p7(X))) & (~p6(Y!59)) & (r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y))))) | (r1(X!0, Y!61) & (~p7(Y!61)) & (p7(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p7(X))) & (~p6(Y!61)) & (p6(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p6(X))))) <=> ((r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))) | (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y)))))),
% 0.23/0.55 inference(transitivity,[status(thm)],[182, 160])).
% 0.23/0.55 tff(184,plain,
% 0.23/0.55 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))) <=> (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))), (((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) <=> ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))))), (((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | p6(Y)) <=> ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | p6(Y)))), rewrite(((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | p6(Y)) <=> (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))), (((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | p6(Y)) <=> (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(185,plain,
% 0.23/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | p6(Y)) <=> ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[184])).
% 0.23/0.55 tff(186,plain,
% 0.23/0.55 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | p6(Y)) | ((r1(X!0, Y!57) & (~p7(Y!57)) & (p6(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p6(X))) & (r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) & (~p6(X!58)))) | (r1(X!0, Y!59) & (p7(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p7(X))) & (~p6(Y!59)) & (r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y))))) | (r1(X!0, Y!61) & (~p7(Y!61)) & (p7(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p7(X))) & (~p6(Y!61)) & (p6(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))) <=> (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | ((r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))) | (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y))))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[185, 183, 159])).
% 0.23/0.55 tff(187,plain,
% 0.23/0.55 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | p6(Y)) | ((r1(X!0, Y!57) & (~p7(Y!57)) & (p6(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p6(X))) & (r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) & (~p6(X!58)))) | (r1(X!0, Y!59) & (p7(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p7(X))) & (~p6(Y!59)) & (r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y))))) | (r1(X!0, Y!61) & (~p7(Y!61)) & (p7(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p7(X))) & (~p6(Y!61)) & (p6(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))) <=> (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | (r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))) | (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y)))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))),
% 0.23/0.55 inference(transitivity,[status(thm)],[186, 157])).
% 0.23/0.55 tff(188,plain,
% 0.23/0.55 (((~p15(Y!56)) & r1(X!0, Y!56) & (![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56))) <=> $false),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(189,plain,
% 0.23/0.55 ((![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56)) <=> (![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(190,plain,
% 0.23/0.55 (((~p15(Y!56)) & r1(X!0, Y!56) & (![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56))) <=> ((~p15(Y!56)) & r1(X!0, Y!56) & (![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56)))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[189])).
% 0.23/0.55 tff(191,plain,
% 0.23/0.55 (((~p15(Y!56)) & r1(X!0, Y!56) & (![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56))) <=> $false),
% 0.23/0.55 inference(transitivity,[status(thm)],[190, 188])).
% 0.23/0.55 tff(192,plain,
% 0.23/0.55 ((![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | ((r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))) | (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y)))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | (r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))) | (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y)))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(193,plain,
% 0.23/0.55 (((r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))) | (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y)))) | $false) <=> ((r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))) | (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y)))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(194,plain,
% 0.23/0.56 ((r1(X!0, Y!55) & (~p8(Y!55)) & (p8(Y!55) & ![X: $i] : (p8(X) | (~r1(Y!55, X)))) & (~p7(Y!55)) & (p7(Y!55) & ![X: $i] : (p7(X) | (~r1(Y!55, X))))) <=> $false),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(195,plain,
% 0.23/0.56 ((p7(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p7(X))) <=> (p7(Y!55) & ![X: $i] : (p7(X) | (~r1(Y!55, X))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(196,plain,
% 0.23/0.56 ((p8(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p8(X))) <=> (p8(Y!55) & ![X: $i] : (p8(X) | (~r1(Y!55, X))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(197,plain,
% 0.23/0.56 ((r1(X!0, Y!55) & (~p8(Y!55)) & (p8(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p8(X))) & (~p7(Y!55)) & (p7(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p7(X)))) <=> (r1(X!0, Y!55) & (~p8(Y!55)) & (p8(Y!55) & ![X: $i] : (p8(X) | (~r1(Y!55, X)))) & (~p7(Y!55)) & (p7(Y!55) & ![X: $i] : (p7(X) | (~r1(Y!55, X)))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[196, 195])).
% 0.23/0.56 tff(198,plain,
% 0.23/0.56 ((r1(X!0, Y!55) & (~p8(Y!55)) & (p8(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p8(X))) & (~p7(Y!55)) & (p7(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p7(X)))) <=> $false),
% 0.23/0.56 inference(transitivity,[status(thm)],[197, 194])).
% 0.23/0.56 tff(199,plain,
% 0.23/0.56 ((r1(X!0, Y!53) & (p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X)))) & (~p7(Y!53)) & (r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y))))) <=> (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(200,plain,
% 0.23/0.56 ((r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y))))) <=> (r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(201,plain,
% 0.23/0.56 ((p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y))) <=> (p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(202,plain,
% 0.23/0.56 ((r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y)))) <=> (r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y)))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[201])).
% 0.23/0.56 tff(203,plain,
% 0.23/0.56 ((r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y)))) <=> (r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y))))),
% 0.23/0.56 inference(transitivity,[status(thm)],[202, 200])).
% 0.23/0.56 tff(204,plain,
% 0.23/0.56 ((p8(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p8(X))) <=> (p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(205,plain,
% 0.23/0.56 ((r1(X!0, Y!53) & (p8(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p8(X))) & (~p7(Y!53)) & (r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y))))) <=> (r1(X!0, Y!53) & (p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X)))) & (~p7(Y!53)) & (r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y)))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[204, 203])).
% 0.23/0.56 tff(206,plain,
% 0.23/0.56 ((r1(X!0, Y!53) & (p8(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p8(X))) & (~p7(Y!53)) & (r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y))))) <=> (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y))))),
% 0.23/0.56 inference(transitivity,[status(thm)],[205, 199])).
% 0.23/0.56 tff(207,plain,
% 0.23/0.56 ((r1(X!0, Y!51) & (~p8(Y!51)) & (p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X)))) & (r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52)))) <=> (r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52)))),
% 0.33/0.56 inference(rewrite,[status(thm)],[])).
% 0.33/0.56 tff(208,plain,
% 0.33/0.56 ((r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y)))) & (~p7(X!52))) <=> (r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52)))),
% 0.33/0.56 inference(rewrite,[status(thm)],[])).
% 0.33/0.56 tff(209,plain,
% 0.33/0.56 ((p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) <=> (p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))))),
% 0.33/0.56 inference(rewrite,[status(thm)],[])).
% 0.33/0.56 tff(210,plain,
% 0.33/0.56 ((r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) & (~p7(X!52))) <=> (r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y)))) & (~p7(X!52)))),
% 0.33/0.56 inference(monotonicity,[status(thm)],[209])).
% 0.33/0.56 tff(211,plain,
% 0.33/0.56 ((r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) & (~p7(X!52))) <=> (r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52)))),
% 0.33/0.56 inference(transitivity,[status(thm)],[210, 208])).
% 0.33/0.56 tff(212,plain,
% 0.33/0.56 ((p7(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p7(X))) <=> (p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))))),
% 0.33/0.56 inference(rewrite,[status(thm)],[])).
% 0.33/0.56 tff(213,plain,
% 0.33/0.56 ((r1(X!0, Y!51) & (~p8(Y!51)) & (p7(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p7(X))) & (r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) & (~p7(X!52)))) <=> (r1(X!0, Y!51) & (~p8(Y!51)) & (p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X)))) & (r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))))),
% 0.33/0.56 inference(monotonicity,[status(thm)],[212, 211])).
% 0.33/0.56 tff(214,plain,
% 0.33/0.56 ((r1(X!0, Y!51) & (~p8(Y!51)) & (p7(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p7(X))) & (r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) & (~p7(X!52)))) <=> (r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52)))),
% 0.33/0.56 inference(transitivity,[status(thm)],[213, 207])).
% 0.33/0.56 tff(215,plain,
% 0.33/0.56 (((r1(X!0, Y!51) & (~p8(Y!51)) & (p7(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p7(X))) & (r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) & (~p7(X!52)))) | (r1(X!0, Y!53) & (p8(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p8(X))) & (~p7(Y!53)) & (r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y))))) | (r1(X!0, Y!55) & (~p8(Y!55)) & (p8(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p8(X))) & (~p7(Y!55)) & (p7(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p7(X))))) <=> ((r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))) | (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y)))) | $false)),
% 0.33/0.56 inference(monotonicity,[status(thm)],[214, 206, 198])).
% 0.33/0.56 tff(216,plain,
% 0.33/0.56 (((r1(X!0, Y!51) & (~p8(Y!51)) & (p7(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p7(X))) & (r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) & (~p7(X!52)))) | (r1(X!0, Y!53) & (p8(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p8(X))) & (~p7(Y!53)) & (r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y))))) | (r1(X!0, Y!55) & (~p8(Y!55)) & (p8(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p8(X))) & (~p7(Y!55)) & (p7(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p7(X))))) <=> ((r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))) | (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y)))))),
% 0.33/0.56 inference(transitivity,[status(thm)],[215, 193])).
% 0.33/0.56 tff(217,plain,
% 0.33/0.56 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))) <=> (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))), (((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) <=> ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))))), (((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))) <=> ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))))), rewrite(((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))) <=> (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))), (((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))) <=> (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))))),
% 0.33/0.56 inference(bind,[status(th)],[])).
% 0.33/0.56 tff(218,plain,
% 0.33/0.56 (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))) <=> ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))),
% 0.33/0.56 inference(quant_intro,[status(thm)],[217])).
% 0.33/0.56 tff(219,plain,
% 0.33/0.56 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))) <=> (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | p7(Y)) <=> ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | p7(Y)))), rewrite(((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | p7(Y)) <=> (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | p7(Y)) <=> (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))))),
% 0.33/0.56 inference(bind,[status(th)],[])).
% 0.33/0.56 tff(220,plain,
% 0.33/0.56 (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | p7(Y)) <=> ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))),
% 0.33/0.56 inference(quant_intro,[status(thm)],[219])).
% 0.33/0.56 tff(221,plain,
% 0.33/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | p7(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))) | ((r1(X!0, Y!51) & (~p8(Y!51)) & (p7(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p7(X))) & (r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) & (~p7(X!52)))) | (r1(X!0, Y!53) & (p8(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p8(X))) & (~p7(Y!53)) & (r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y))))) | (r1(X!0, Y!55) & (~p8(Y!55)) & (p8(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p8(X))) & (~p7(Y!55)) & (p7(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p7(X)))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | ((r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))) | (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y))))))),
% 0.33/0.56 inference(monotonicity,[status(thm)],[220, 218, 216])).
% 0.33/0.56 tff(222,plain,
% 0.33/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | p7(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))) | ((r1(X!0, Y!51) & (~p8(Y!51)) & (p7(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p7(X))) & (r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) & (~p7(X!52)))) | (r1(X!0, Y!53) & (p8(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p8(X))) & (~p7(Y!53)) & (r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y))))) | (r1(X!0, Y!55) & (~p8(Y!55)) & (p8(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p8(X))) & (~p7(Y!55)) & (p7(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p7(X)))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | (r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))) | (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y)))))),
% 0.33/0.57 inference(transitivity,[status(thm)],[221, 192])).
% 0.33/0.57 tff(223,plain,
% 0.33/0.57 ((![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | ((r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))) | (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))) <=> (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | (r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))) | (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y)))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(224,plain,
% 0.33/0.57 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))) <=> (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))), (((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) <=> ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))))), (((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))) <=> ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))))), rewrite(((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))) <=> (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))), (((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))) <=> (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))))),
% 0.33/0.57 inference(bind,[status(th)],[])).
% 0.33/0.57 tff(225,plain,
% 0.33/0.57 (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))) <=> ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))),
% 0.33/0.57 inference(quant_intro,[status(thm)],[224])).
% 0.33/0.57 tff(226,plain,
% 0.33/0.57 (((r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))) | (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y)))) | $false) <=> ((r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))) | (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y)))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(227,plain,
% 0.33/0.57 ((r1(X!0, Y!49) & (~p10(Y!49)) & (p10(Y!49) & ![X: $i] : (p10(X) | (~r1(Y!49, X)))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : (p9(X) | (~r1(Y!49, X))))) <=> $false),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(228,plain,
% 0.33/0.57 ((p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))) <=> (p9(Y!49) & ![X: $i] : (p9(X) | (~r1(Y!49, X))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(229,plain,
% 0.33/0.57 ((p10(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p10(X))) <=> (p10(Y!49) & ![X: $i] : (p10(X) | (~r1(Y!49, X))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(230,plain,
% 0.33/0.57 ((r1(X!0, Y!49) & (~p10(Y!49)) & (p10(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p10(X))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X)))) <=> (r1(X!0, Y!49) & (~p10(Y!49)) & (p10(Y!49) & ![X: $i] : (p10(X) | (~r1(Y!49, X)))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : (p9(X) | (~r1(Y!49, X)))))),
% 0.33/0.57 inference(monotonicity,[status(thm)],[229, 228])).
% 0.33/0.57 tff(231,plain,
% 0.33/0.57 ((r1(X!0, Y!49) & (~p10(Y!49)) & (p10(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p10(X))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X)))) <=> $false),
% 0.33/0.57 inference(transitivity,[status(thm)],[230, 227])).
% 0.33/0.57 tff(232,plain,
% 0.33/0.57 ((r1(X!0, Y!47) & (p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X)))) & (~p9(Y!47)) & (r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y))))) <=> (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(233,plain,
% 0.33/0.57 ((r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y))))) <=> (r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(234,plain,
% 0.33/0.57 ((p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y))) <=> (p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(235,plain,
% 0.33/0.57 ((r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y)))) <=> (r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y)))))),
% 0.33/0.57 inference(monotonicity,[status(thm)],[234])).
% 0.33/0.57 tff(236,plain,
% 0.33/0.57 ((r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y)))) <=> (r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y))))),
% 0.33/0.57 inference(transitivity,[status(thm)],[235, 233])).
% 0.33/0.57 tff(237,plain,
% 0.33/0.57 ((p10(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p10(X))) <=> (p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(238,plain,
% 0.33/0.57 ((r1(X!0, Y!47) & (p10(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p10(X))) & (~p9(Y!47)) & (r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y))))) <=> (r1(X!0, Y!47) & (p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X)))) & (~p9(Y!47)) & (r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y)))))),
% 0.33/0.57 inference(monotonicity,[status(thm)],[237, 236])).
% 0.33/0.57 tff(239,plain,
% 0.33/0.57 ((r1(X!0, Y!47) & (p10(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p10(X))) & (~p9(Y!47)) & (r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y))))) <=> (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y))))),
% 0.33/0.57 inference(transitivity,[status(thm)],[238, 232])).
% 0.33/0.57 tff(240,plain,
% 0.33/0.57 ((r1(X!0, Y!45) & (~p10(Y!45)) & (p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X)))) & (r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46)))) <=> (r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46)))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(241,plain,
% 0.33/0.57 ((r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y)))) & (~p9(X!46))) <=> (r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46)))),
% 0.33/0.57 inference(rewrite,[status(thm)],[])).
% 0.33/0.57 tff(242,plain,
% 0.33/0.57 ((p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) <=> (p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))))),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(243,plain,
% 0.33/0.58 ((r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) & (~p9(X!46))) <=> (r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y)))) & (~p9(X!46)))),
% 0.33/0.58 inference(monotonicity,[status(thm)],[242])).
% 0.33/0.58 tff(244,plain,
% 0.33/0.58 ((r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) & (~p9(X!46))) <=> (r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46)))),
% 0.33/0.58 inference(transitivity,[status(thm)],[243, 241])).
% 0.33/0.58 tff(245,plain,
% 0.33/0.58 ((p9(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p9(X))) <=> (p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))))),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(246,plain,
% 0.33/0.58 ((r1(X!0, Y!45) & (~p10(Y!45)) & (p9(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p9(X))) & (r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) & (~p9(X!46)))) <=> (r1(X!0, Y!45) & (~p10(Y!45)) & (p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X)))) & (r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))))),
% 0.33/0.58 inference(monotonicity,[status(thm)],[245, 244])).
% 0.33/0.58 tff(247,plain,
% 0.33/0.58 ((r1(X!0, Y!45) & (~p10(Y!45)) & (p9(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p9(X))) & (r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) & (~p9(X!46)))) <=> (r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46)))),
% 0.33/0.58 inference(transitivity,[status(thm)],[246, 240])).
% 0.33/0.58 tff(248,plain,
% 0.33/0.58 (((r1(X!0, Y!45) & (~p10(Y!45)) & (p9(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p9(X))) & (r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) & (~p9(X!46)))) | (r1(X!0, Y!47) & (p10(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p10(X))) & (~p9(Y!47)) & (r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y))))) | (r1(X!0, Y!49) & (~p10(Y!49)) & (p10(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p10(X))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))))) <=> ((r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))) | (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y)))) | $false)),
% 0.33/0.58 inference(monotonicity,[status(thm)],[247, 239, 231])).
% 0.33/0.58 tff(249,plain,
% 0.33/0.58 (((r1(X!0, Y!45) & (~p10(Y!45)) & (p9(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p9(X))) & (r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) & (~p9(X!46)))) | (r1(X!0, Y!47) & (p10(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p10(X))) & (~p9(Y!47)) & (r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y))))) | (r1(X!0, Y!49) & (~p10(Y!49)) & (p10(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p10(X))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))))) <=> ((r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))) | (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y)))))),
% 0.33/0.58 inference(transitivity,[status(thm)],[248, 226])).
% 0.33/0.58 tff(250,plain,
% 0.33/0.58 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))) <=> (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))), (((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) <=> ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))))), (((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | p9(Y)) <=> ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | p9(Y)))), rewrite(((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | p9(Y)) <=> (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))), (((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | p9(Y)) <=> (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))))),
% 0.33/0.58 inference(bind,[status(th)],[])).
% 0.33/0.58 tff(251,plain,
% 0.33/0.58 (![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | p9(Y)) <=> ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))),
% 0.33/0.58 inference(quant_intro,[status(thm)],[250])).
% 0.33/0.58 tff(252,plain,
% 0.33/0.58 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | p9(Y)) | ((r1(X!0, Y!45) & (~p10(Y!45)) & (p9(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p9(X))) & (r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) & (~p9(X!46)))) | (r1(X!0, Y!47) & (p10(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p10(X))) & (~p9(Y!47)) & (r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y))))) | (r1(X!0, Y!49) & (~p10(Y!49)) & (p10(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p10(X))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))))) <=> (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | ((r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))) | (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))))),
% 0.33/0.58 inference(monotonicity,[status(thm)],[251, 249, 225])).
% 0.33/0.58 tff(253,plain,
% 0.33/0.58 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | p9(Y)) | ((r1(X!0, Y!45) & (~p10(Y!45)) & (p9(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p9(X))) & (r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) & (~p9(X!46)))) | (r1(X!0, Y!47) & (p10(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p10(X))) & (~p9(Y!47)) & (r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y))))) | (r1(X!0, Y!49) & (~p10(Y!49)) & (p10(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p10(X))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))))) <=> (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | (r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))) | (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y)))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))))),
% 0.33/0.58 inference(transitivity,[status(thm)],[252, 223])).
% 0.33/0.58 tff(254,plain,
% 0.33/0.58 ((![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | ((r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))) | (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y)))))) <=> (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | (r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))) | (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y)))))),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(255,plain,
% 0.33/0.58 (((r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))) | (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y)))) | $false) <=> ((r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))) | (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y)))))),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(256,plain,
% 0.33/0.58 ((r1(X!0, Y!44) & (~p9(Y!44)) & (p9(Y!44) & ![X: $i] : (p9(X) | (~r1(Y!44, X)))) & (~p8(Y!44)) & (p8(Y!44) & ![X: $i] : (p8(X) | (~r1(Y!44, X))))) <=> $false),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(257,plain,
% 0.33/0.58 ((p8(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p8(X))) <=> (p8(Y!44) & ![X: $i] : (p8(X) | (~r1(Y!44, X))))),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(258,plain,
% 0.33/0.58 ((p9(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p9(X))) <=> (p9(Y!44) & ![X: $i] : (p9(X) | (~r1(Y!44, X))))),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(259,plain,
% 0.33/0.58 ((r1(X!0, Y!44) & (~p9(Y!44)) & (p9(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p9(X))) & (~p8(Y!44)) & (p8(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p8(X)))) <=> (r1(X!0, Y!44) & (~p9(Y!44)) & (p9(Y!44) & ![X: $i] : (p9(X) | (~r1(Y!44, X)))) & (~p8(Y!44)) & (p8(Y!44) & ![X: $i] : (p8(X) | (~r1(Y!44, X)))))),
% 0.33/0.58 inference(monotonicity,[status(thm)],[258, 257])).
% 0.33/0.58 tff(260,plain,
% 0.33/0.58 ((r1(X!0, Y!44) & (~p9(Y!44)) & (p9(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p9(X))) & (~p8(Y!44)) & (p8(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p8(X)))) <=> $false),
% 0.33/0.58 inference(transitivity,[status(thm)],[259, 256])).
% 0.33/0.58 tff(261,plain,
% 0.33/0.58 ((r1(X!0, Y!42) & (p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X)))) & (~p8(Y!42)) & (r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y))))) <=> (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y))))),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(262,plain,
% 0.33/0.58 ((r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y))))) <=> (r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y))))),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(263,plain,
% 0.33/0.58 ((p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y))) <=> (p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y))))),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(264,plain,
% 0.33/0.58 ((r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y)))) <=> (r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y)))))),
% 0.33/0.58 inference(monotonicity,[status(thm)],[263])).
% 0.33/0.58 tff(265,plain,
% 0.33/0.58 ((r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y)))) <=> (r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y))))),
% 0.33/0.58 inference(transitivity,[status(thm)],[264, 262])).
% 0.33/0.58 tff(266,plain,
% 0.33/0.58 ((p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))) <=> (p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))))),
% 0.33/0.58 inference(rewrite,[status(thm)],[])).
% 0.33/0.58 tff(267,plain,
% 0.33/0.58 ((r1(X!0, Y!42) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))) & (~p8(Y!42)) & (r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y))))) <=> (r1(X!0, Y!42) & (p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X)))) & (~p8(Y!42)) & (r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y)))))),
% 0.33/0.58 inference(monotonicity,[status(thm)],[266, 265])).
% 0.33/0.58 tff(268,plain,
% 0.33/0.58 ((r1(X!0, Y!42) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))) & (~p8(Y!42)) & (r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y))))) <=> (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y))))),
% 0.33/0.59 inference(transitivity,[status(thm)],[267, 261])).
% 0.33/0.59 tff(269,plain,
% 0.33/0.59 ((r1(X!0, Y!40) & (~p9(Y!40)) & (p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X)))) & (r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41)))) <=> (r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41)))),
% 0.33/0.59 inference(rewrite,[status(thm)],[])).
% 0.33/0.59 tff(270,plain,
% 0.33/0.59 ((r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))) & (~p8(X!41))) <=> (r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41)))),
% 0.33/0.59 inference(rewrite,[status(thm)],[])).
% 0.33/0.59 tff(271,plain,
% 0.33/0.59 ((p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) <=> (p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))))),
% 0.33/0.59 inference(rewrite,[status(thm)],[])).
% 0.33/0.59 tff(272,plain,
% 0.33/0.59 ((r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) & (~p8(X!41))) <=> (r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))) & (~p8(X!41)))),
% 0.33/0.59 inference(monotonicity,[status(thm)],[271])).
% 0.33/0.59 tff(273,plain,
% 0.33/0.59 ((r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) & (~p8(X!41))) <=> (r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41)))),
% 0.33/0.59 inference(transitivity,[status(thm)],[272, 270])).
% 0.33/0.59 tff(274,plain,
% 0.33/0.59 ((p8(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p8(X))) <=> (p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))))),
% 0.33/0.59 inference(rewrite,[status(thm)],[])).
% 0.33/0.59 tff(275,plain,
% 0.33/0.59 ((r1(X!0, Y!40) & (~p9(Y!40)) & (p8(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p8(X))) & (r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) & (~p8(X!41)))) <=> (r1(X!0, Y!40) & (~p9(Y!40)) & (p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X)))) & (r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))))),
% 0.33/0.59 inference(monotonicity,[status(thm)],[274, 273])).
% 0.33/0.59 tff(276,plain,
% 0.33/0.59 ((r1(X!0, Y!40) & (~p9(Y!40)) & (p8(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p8(X))) & (r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) & (~p8(X!41)))) <=> (r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41)))),
% 0.33/0.59 inference(transitivity,[status(thm)],[275, 269])).
% 0.33/0.59 tff(277,plain,
% 0.33/0.59 (((r1(X!0, Y!40) & (~p9(Y!40)) & (p8(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p8(X))) & (r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) & (~p8(X!41)))) | (r1(X!0, Y!42) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))) & (~p8(Y!42)) & (r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y))))) | (r1(X!0, Y!44) & (~p9(Y!44)) & (p9(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p9(X))) & (~p8(Y!44)) & (p8(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p8(X))))) <=> ((r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))) | (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y)))) | $false)),
% 0.33/0.59 inference(monotonicity,[status(thm)],[276, 268, 260])).
% 0.33/0.59 tff(278,plain,
% 0.33/0.59 (((r1(X!0, Y!40) & (~p9(Y!40)) & (p8(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p8(X))) & (r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) & (~p8(X!41)))) | (r1(X!0, Y!42) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))) & (~p8(Y!42)) & (r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y))))) | (r1(X!0, Y!44) & (~p9(Y!44)) & (p9(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p9(X))) & (~p8(Y!44)) & (p8(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p8(X))))) <=> ((r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))) | (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y)))))),
% 0.33/0.59 inference(transitivity,[status(thm)],[277, 255])).
% 0.33/0.59 tff(279,plain,
% 0.33/0.59 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))) <=> (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))) <=> ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))))), rewrite(((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))) <=> (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))) <=> (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))))),
% 0.33/0.59 inference(bind,[status(th)],[])).
% 0.33/0.59 tff(280,plain,
% 0.33/0.59 (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))) <=> ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))),
% 0.33/0.59 inference(quant_intro,[status(thm)],[279])).
% 0.33/0.59 tff(281,plain,
% 0.33/0.59 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))) <=> (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))), (((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) <=> ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))))), (((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | p8(Y)) <=> ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | p8(Y)))), rewrite(((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | p8(Y)) <=> (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))), (((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | p8(Y)) <=> (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))))),
% 0.33/0.59 inference(bind,[status(th)],[])).
% 0.33/0.59 tff(282,plain,
% 0.33/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | p8(Y)) <=> ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))),
% 0.33/0.59 inference(quant_intro,[status(thm)],[281])).
% 0.33/0.59 tff(283,plain,
% 0.33/0.59 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))) | ((r1(X!0, Y!40) & (~p9(Y!40)) & (p8(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p8(X))) & (r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) & (~p8(X!41)))) | (r1(X!0, Y!42) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))) & (~p8(Y!42)) & (r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y))))) | (r1(X!0, Y!44) & (~p9(Y!44)) & (p9(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p9(X))) & (~p8(Y!44)) & (p8(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p8(X)))))) <=> (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | ((r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))) | (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y))))))),
% 0.33/0.59 inference(monotonicity,[status(thm)],[282, 280, 278])).
% 0.33/0.59 tff(284,plain,
% 0.33/0.59 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))) | ((r1(X!0, Y!40) & (~p9(Y!40)) & (p8(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p8(X))) & (r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) & (~p8(X!41)))) | (r1(X!0, Y!42) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))) & (~p8(Y!42)) & (r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y))))) | (r1(X!0, Y!44) & (~p9(Y!44)) & (p9(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p9(X))) & (~p8(Y!44)) & (p8(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p8(X)))))) <=> (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | (r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))) | (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y)))))),
% 0.33/0.59 inference(transitivity,[status(thm)],[283, 254])).
% 0.33/0.59 tff(285,plain,
% 0.33/0.59 ((![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | ((r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))) | (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))) <=> (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))) | (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))))),
% 0.33/0.59 inference(rewrite,[status(thm)],[])).
% 0.33/0.59 tff(286,plain,
% 0.33/0.59 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))) <=> (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))), (((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) <=> ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))))), (((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))) <=> ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))))), rewrite(((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))), (((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))))),
% 0.33/0.59 inference(bind,[status(th)],[])).
% 0.33/0.59 tff(287,plain,
% 0.33/0.59 (![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))),
% 0.33/0.59 inference(quant_intro,[status(thm)],[286])).
% 0.33/0.59 tff(288,plain,
% 0.33/0.59 (((r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))) | (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y)))) | $false) <=> ((r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))) | (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y)))))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(289,plain,
% 0.33/0.60 ((r1(X!0, Y!36) & (~p11(Y!36)) & (p11(Y!36) & ![X: $i] : (p11(X) | (~r1(Y!36, X)))) & (~p10(Y!36)) & (p10(Y!36) & ![X: $i] : (p10(X) | (~r1(Y!36, X))))) <=> $false),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(290,plain,
% 0.33/0.60 ((p10(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p10(X))) <=> (p10(Y!36) & ![X: $i] : (p10(X) | (~r1(Y!36, X))))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(291,plain,
% 0.33/0.60 ((p11(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p11(X))) <=> (p11(Y!36) & ![X: $i] : (p11(X) | (~r1(Y!36, X))))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(292,plain,
% 0.33/0.60 ((r1(X!0, Y!36) & (~p11(Y!36)) & (p11(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p11(X))) & (~p10(Y!36)) & (p10(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p10(X)))) <=> (r1(X!0, Y!36) & (~p11(Y!36)) & (p11(Y!36) & ![X: $i] : (p11(X) | (~r1(Y!36, X)))) & (~p10(Y!36)) & (p10(Y!36) & ![X: $i] : (p10(X) | (~r1(Y!36, X)))))),
% 0.33/0.60 inference(monotonicity,[status(thm)],[291, 290])).
% 0.33/0.60 tff(293,plain,
% 0.33/0.60 ((r1(X!0, Y!36) & (~p11(Y!36)) & (p11(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p11(X))) & (~p10(Y!36)) & (p10(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p10(X)))) <=> $false),
% 0.33/0.60 inference(transitivity,[status(thm)],[292, 289])).
% 0.33/0.60 tff(294,plain,
% 0.33/0.60 ((r1(X!0, Y!34) & (p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X)))) & (~p10(Y!34)) & (r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y))))) <=> (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y))))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(295,plain,
% 0.33/0.60 ((r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y))))) <=> (r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y))))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(296,plain,
% 0.33/0.60 ((p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y))) <=> (p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y))))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(297,plain,
% 0.33/0.60 ((r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y)))) <=> (r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y)))))),
% 0.33/0.60 inference(monotonicity,[status(thm)],[296])).
% 0.33/0.60 tff(298,plain,
% 0.33/0.60 ((r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y)))) <=> (r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y))))),
% 0.33/0.60 inference(transitivity,[status(thm)],[297, 295])).
% 0.33/0.60 tff(299,plain,
% 0.33/0.60 ((p11(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p11(X))) <=> (p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(300,plain,
% 0.33/0.60 ((r1(X!0, Y!34) & (p11(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p11(X))) & (~p10(Y!34)) & (r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y))))) <=> (r1(X!0, Y!34) & (p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X)))) & (~p10(Y!34)) & (r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y)))))),
% 0.33/0.60 inference(monotonicity,[status(thm)],[299, 298])).
% 0.33/0.60 tff(301,plain,
% 0.33/0.60 ((r1(X!0, Y!34) & (p11(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p11(X))) & (~p10(Y!34)) & (r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y))))) <=> (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y))))),
% 0.33/0.60 inference(transitivity,[status(thm)],[300, 294])).
% 0.33/0.60 tff(302,plain,
% 0.33/0.60 ((r1(X!0, Y!32) & (~p11(Y!32)) & (p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X)))) & (r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33)))) <=> (r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33)))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(303,plain,
% 0.33/0.60 ((r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y)))) & (~p10(X!33))) <=> (r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33)))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(304,plain,
% 0.33/0.60 ((p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) <=> (p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(305,plain,
% 0.33/0.60 ((r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) & (~p10(X!33))) <=> (r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y)))) & (~p10(X!33)))),
% 0.33/0.60 inference(monotonicity,[status(thm)],[304])).
% 0.33/0.60 tff(306,plain,
% 0.33/0.60 ((r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) & (~p10(X!33))) <=> (r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33)))),
% 0.33/0.60 inference(transitivity,[status(thm)],[305, 303])).
% 0.33/0.60 tff(307,plain,
% 0.33/0.60 ((p10(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p10(X))) <=> (p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))))),
% 0.33/0.60 inference(rewrite,[status(thm)],[])).
% 0.33/0.60 tff(308,plain,
% 0.33/0.60 ((r1(X!0, Y!32) & (~p11(Y!32)) & (p10(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p10(X))) & (r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) & (~p10(X!33)))) <=> (r1(X!0, Y!32) & (~p11(Y!32)) & (p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X)))) & (r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))))),
% 0.33/0.60 inference(monotonicity,[status(thm)],[307, 306])).
% 0.33/0.60 tff(309,plain,
% 0.33/0.60 ((r1(X!0, Y!32) & (~p11(Y!32)) & (p10(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p10(X))) & (r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) & (~p10(X!33)))) <=> (r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33)))),
% 0.33/0.60 inference(transitivity,[status(thm)],[308, 302])).
% 0.33/0.60 tff(310,plain,
% 0.33/0.60 (((r1(X!0, Y!32) & (~p11(Y!32)) & (p10(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p10(X))) & (r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) & (~p10(X!33)))) | (r1(X!0, Y!34) & (p11(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p11(X))) & (~p10(Y!34)) & (r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y))))) | (r1(X!0, Y!36) & (~p11(Y!36)) & (p11(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p11(X))) & (~p10(Y!36)) & (p10(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p10(X))))) <=> ((r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))) | (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y)))) | $false)),
% 0.33/0.60 inference(monotonicity,[status(thm)],[309, 301, 293])).
% 0.33/0.60 tff(311,plain,
% 0.33/0.60 (((r1(X!0, Y!32) & (~p11(Y!32)) & (p10(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p10(X))) & (r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) & (~p10(X!33)))) | (r1(X!0, Y!34) & (p11(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p11(X))) & (~p10(Y!34)) & (r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y))))) | (r1(X!0, Y!36) & (~p11(Y!36)) & (p11(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p11(X))) & (~p10(Y!36)) & (p10(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p10(X))))) <=> ((r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))) | (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y)))))),
% 0.33/0.60 inference(transitivity,[status(thm)],[310, 288])).
% 0.33/0.60 tff(312,plain,
% 0.33/0.60 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))) <=> (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))), (((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) <=> ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))))), (((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | p10(Y)) <=> ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | p10(Y)))), rewrite(((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | p10(Y)) <=> (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))), (((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | p10(Y)) <=> (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))))),
% 0.33/0.60 inference(bind,[status(th)],[])).
% 0.33/0.60 tff(313,plain,
% 0.33/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | p10(Y)) <=> ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))),
% 0.33/0.60 inference(quant_intro,[status(thm)],[312])).
% 0.33/0.60 tff(314,plain,
% 0.33/0.60 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | p10(Y)) | ((r1(X!0, Y!32) & (~p11(Y!32)) & (p10(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p10(X))) & (r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) & (~p10(X!33)))) | (r1(X!0, Y!34) & (p11(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p11(X))) & (~p10(Y!34)) & (r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y))))) | (r1(X!0, Y!36) & (~p11(Y!36)) & (p11(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p11(X))) & (~p10(Y!36)) & (p10(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))))) <=> (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | ((r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))) | (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))))),
% 0.33/0.60 inference(monotonicity,[status(thm)],[313, 311, 287])).
% 0.33/0.60 tff(315,plain,
% 0.33/0.60 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | p10(Y)) | ((r1(X!0, Y!32) & (~p11(Y!32)) & (p10(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p10(X))) & (r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) & (~p10(X!33)))) | (r1(X!0, Y!34) & (p11(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p11(X))) & (~p10(Y!34)) & (r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y))))) | (r1(X!0, Y!36) & (~p11(Y!36)) & (p11(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p11(X))) & (~p10(Y!36)) & (p10(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))))) <=> (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))) | (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))))),
% 0.33/0.60 inference(transitivity,[status(thm)],[314, 285])).
% 0.33/0.60 tff(316,plain,
% 0.33/0.60 ((![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | ((r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))) | (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y)))))) <=> (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))) | (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y)))))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(317,plain,
% 0.33/0.61 (((r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))) | (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y)))) | $false) <=> ((r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))) | (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y)))))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(318,plain,
% 0.33/0.61 ((r1(X!0, Y!31) & (~p12(Y!31)) & (p12(Y!31) & ![X: $i] : (p12(X) | (~r1(Y!31, X)))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : (p11(X) | (~r1(Y!31, X))))) <=> $false),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(319,plain,
% 0.33/0.61 ((p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))) <=> (p11(Y!31) & ![X: $i] : (p11(X) | (~r1(Y!31, X))))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(320,plain,
% 0.33/0.61 ((p12(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p12(X))) <=> (p12(Y!31) & ![X: $i] : (p12(X) | (~r1(Y!31, X))))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(321,plain,
% 0.33/0.61 ((r1(X!0, Y!31) & (~p12(Y!31)) & (p12(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p12(X))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X)))) <=> (r1(X!0, Y!31) & (~p12(Y!31)) & (p12(Y!31) & ![X: $i] : (p12(X) | (~r1(Y!31, X)))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : (p11(X) | (~r1(Y!31, X)))))),
% 0.33/0.61 inference(monotonicity,[status(thm)],[320, 319])).
% 0.33/0.61 tff(322,plain,
% 0.33/0.61 ((r1(X!0, Y!31) & (~p12(Y!31)) & (p12(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p12(X))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X)))) <=> $false),
% 0.33/0.61 inference(transitivity,[status(thm)],[321, 318])).
% 0.33/0.61 tff(323,plain,
% 0.33/0.61 ((r1(X!0, Y!29) & (p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X)))) & (~p11(Y!29)) & (r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y))))) <=> (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y))))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(324,plain,
% 0.33/0.61 ((r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y))))) <=> (r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y))))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(325,plain,
% 0.33/0.61 ((p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y))) <=> (p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y))))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(326,plain,
% 0.33/0.61 ((r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y)))) <=> (r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y)))))),
% 0.33/0.61 inference(monotonicity,[status(thm)],[325])).
% 0.33/0.61 tff(327,plain,
% 0.33/0.61 ((r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y)))) <=> (r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y))))),
% 0.33/0.61 inference(transitivity,[status(thm)],[326, 324])).
% 0.33/0.61 tff(328,plain,
% 0.33/0.61 ((p12(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p12(X))) <=> (p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(329,plain,
% 0.33/0.61 ((r1(X!0, Y!29) & (p12(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p12(X))) & (~p11(Y!29)) & (r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y))))) <=> (r1(X!0, Y!29) & (p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X)))) & (~p11(Y!29)) & (r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y)))))),
% 0.33/0.61 inference(monotonicity,[status(thm)],[328, 327])).
% 0.33/0.61 tff(330,plain,
% 0.33/0.61 ((r1(X!0, Y!29) & (p12(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p12(X))) & (~p11(Y!29)) & (r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y))))) <=> (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y))))),
% 0.33/0.61 inference(transitivity,[status(thm)],[329, 323])).
% 0.33/0.61 tff(331,plain,
% 0.33/0.61 ((r1(X!0, Y!27) & (~p12(Y!27)) & (p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X)))) & (r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28)))) <=> (r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28)))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(332,plain,
% 0.33/0.61 ((r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y)))) & (~p11(X!28))) <=> (r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28)))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(333,plain,
% 0.33/0.61 ((p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) <=> (p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(334,plain,
% 0.33/0.61 ((r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) & (~p11(X!28))) <=> (r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y)))) & (~p11(X!28)))),
% 0.33/0.61 inference(monotonicity,[status(thm)],[333])).
% 0.33/0.61 tff(335,plain,
% 0.33/0.61 ((r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) & (~p11(X!28))) <=> (r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28)))),
% 0.33/0.61 inference(transitivity,[status(thm)],[334, 332])).
% 0.33/0.61 tff(336,plain,
% 0.33/0.61 ((p11(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p11(X))) <=> (p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))))),
% 0.33/0.61 inference(rewrite,[status(thm)],[])).
% 0.33/0.61 tff(337,plain,
% 0.33/0.61 ((r1(X!0, Y!27) & (~p12(Y!27)) & (p11(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p11(X))) & (r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) & (~p11(X!28)))) <=> (r1(X!0, Y!27) & (~p12(Y!27)) & (p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X)))) & (r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))))),
% 0.33/0.61 inference(monotonicity,[status(thm)],[336, 335])).
% 0.33/0.61 tff(338,plain,
% 0.33/0.61 ((r1(X!0, Y!27) & (~p12(Y!27)) & (p11(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p11(X))) & (r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) & (~p11(X!28)))) <=> (r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28)))),
% 0.33/0.61 inference(transitivity,[status(thm)],[337, 331])).
% 0.33/0.61 tff(339,plain,
% 0.33/0.61 (((r1(X!0, Y!27) & (~p12(Y!27)) & (p11(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p11(X))) & (r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) & (~p11(X!28)))) | (r1(X!0, Y!29) & (p12(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p12(X))) & (~p11(Y!29)) & (r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y))))) | (r1(X!0, Y!31) & (~p12(Y!31)) & (p12(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p12(X))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))))) <=> ((r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))) | (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y)))) | $false)),
% 0.33/0.61 inference(monotonicity,[status(thm)],[338, 330, 322])).
% 0.33/0.61 tff(340,plain,
% 0.33/0.61 (((r1(X!0, Y!27) & (~p12(Y!27)) & (p11(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p11(X))) & (r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) & (~p11(X!28)))) | (r1(X!0, Y!29) & (p12(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p12(X))) & (~p11(Y!29)) & (r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y))))) | (r1(X!0, Y!31) & (~p12(Y!31)) & (p12(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p12(X))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))))) <=> ((r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))) | (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y)))))),
% 0.33/0.61 inference(transitivity,[status(thm)],[339, 317])).
% 0.33/0.61 tff(341,plain,
% 0.33/0.61 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))) <=> (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))), (((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) <=> ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))))), (((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) <=> ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))))), rewrite(((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) <=> (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))), (((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) <=> (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))))),
% 0.33/0.61 inference(bind,[status(th)],[])).
% 0.33/0.61 tff(342,plain,
% 0.33/0.61 (![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) <=> ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))),
% 0.33/0.61 inference(quant_intro,[status(thm)],[341])).
% 0.33/0.61 tff(343,plain,
% 0.33/0.61 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))) <=> (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))), (((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) <=> ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))))), (((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | p11(Y)) <=> ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | p11(Y)))), rewrite(((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | p11(Y)) <=> (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))), (((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | p11(Y)) <=> (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))))),
% 0.33/0.61 inference(bind,[status(th)],[])).
% 0.33/0.61 tff(344,plain,
% 0.33/0.61 (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | p11(Y)) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))),
% 0.33/0.61 inference(quant_intro,[status(thm)],[343])).
% 0.33/0.61 tff(345,plain,
% 0.33/0.61 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | p11(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) | ((r1(X!0, Y!27) & (~p12(Y!27)) & (p11(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p11(X))) & (r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) & (~p11(X!28)))) | (r1(X!0, Y!29) & (p12(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p12(X))) & (~p11(Y!29)) & (r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y))))) | (r1(X!0, Y!31) & (~p12(Y!31)) & (p12(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p12(X))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X)))))) <=> (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | ((r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))) | (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y))))))),
% 0.33/0.62 inference(monotonicity,[status(thm)],[344, 342, 340])).
% 0.33/0.62 tff(346,plain,
% 0.33/0.62 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | p11(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) | ((r1(X!0, Y!27) & (~p12(Y!27)) & (p11(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p11(X))) & (r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) & (~p11(X!28)))) | (r1(X!0, Y!29) & (p12(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p12(X))) & (~p11(Y!29)) & (r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y))))) | (r1(X!0, Y!31) & (~p12(Y!31)) & (p12(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p12(X))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X)))))) <=> (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))) | (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y)))))),
% 0.33/0.62 inference(transitivity,[status(thm)],[345, 316])).
% 0.33/0.62 tff(347,plain,
% 0.33/0.62 ((![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))) | (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))) <=> (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))) | (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(348,plain,
% 0.33/0.62 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))) <=> (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))), (((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) <=> ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))))), (((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))) <=> ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))))), rewrite(((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))) <=> (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))), (((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))) <=> (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))))),
% 0.33/0.62 inference(bind,[status(th)],[])).
% 0.33/0.62 tff(349,plain,
% 0.33/0.62 (![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))) <=> ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))),
% 0.33/0.62 inference(quant_intro,[status(thm)],[348])).
% 0.33/0.62 tff(350,plain,
% 0.33/0.62 (((r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))) | (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y)))) | $false) <=> ((r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))) | (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y)))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(351,plain,
% 0.33/0.62 ((r1(X!0, Y!24) & (~p13(Y!24)) & (p13(Y!24) & ![X: $i] : (p13(X) | (~r1(Y!24, X)))) & (~p12(Y!24)) & (p12(Y!24) & ![X: $i] : (p12(X) | (~r1(Y!24, X))))) <=> $false),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(352,plain,
% 0.33/0.62 ((p12(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p12(X))) <=> (p12(Y!24) & ![X: $i] : (p12(X) | (~r1(Y!24, X))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(353,plain,
% 0.33/0.62 ((p13(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p13(X))) <=> (p13(Y!24) & ![X: $i] : (p13(X) | (~r1(Y!24, X))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(354,plain,
% 0.33/0.62 ((r1(X!0, Y!24) & (~p13(Y!24)) & (p13(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p13(X))) & (~p12(Y!24)) & (p12(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p12(X)))) <=> (r1(X!0, Y!24) & (~p13(Y!24)) & (p13(Y!24) & ![X: $i] : (p13(X) | (~r1(Y!24, X)))) & (~p12(Y!24)) & (p12(Y!24) & ![X: $i] : (p12(X) | (~r1(Y!24, X)))))),
% 0.33/0.62 inference(monotonicity,[status(thm)],[353, 352])).
% 0.33/0.62 tff(355,plain,
% 0.33/0.62 ((r1(X!0, Y!24) & (~p13(Y!24)) & (p13(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p13(X))) & (~p12(Y!24)) & (p12(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p12(X)))) <=> $false),
% 0.33/0.62 inference(transitivity,[status(thm)],[354, 351])).
% 0.33/0.62 tff(356,plain,
% 0.33/0.62 ((r1(X!0, Y!22) & (p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X)))) & (~p12(Y!22)) & (r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y))))) <=> (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(357,plain,
% 0.33/0.62 ((r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y))))) <=> (r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(358,plain,
% 0.33/0.62 ((p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y))) <=> (p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(359,plain,
% 0.33/0.62 ((r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y)))) <=> (r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y)))))),
% 0.33/0.62 inference(monotonicity,[status(thm)],[358])).
% 0.33/0.62 tff(360,plain,
% 0.33/0.62 ((r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y)))) <=> (r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y))))),
% 0.33/0.62 inference(transitivity,[status(thm)],[359, 357])).
% 0.33/0.62 tff(361,plain,
% 0.33/0.62 ((p13(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p13(X))) <=> (p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(362,plain,
% 0.33/0.62 ((r1(X!0, Y!22) & (p13(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p13(X))) & (~p12(Y!22)) & (r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y))))) <=> (r1(X!0, Y!22) & (p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X)))) & (~p12(Y!22)) & (r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y)))))),
% 0.33/0.62 inference(monotonicity,[status(thm)],[361, 360])).
% 0.33/0.62 tff(363,plain,
% 0.33/0.62 ((r1(X!0, Y!22) & (p13(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p13(X))) & (~p12(Y!22)) & (r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y))))) <=> (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y))))),
% 0.33/0.62 inference(transitivity,[status(thm)],[362, 356])).
% 0.33/0.62 tff(364,plain,
% 0.33/0.62 ((r1(X!0, Y!20) & (~p13(Y!20)) & (p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X)))) & (r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21)))) <=> (r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21)))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(365,plain,
% 0.33/0.62 ((r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y)))) & (~p12(X!21))) <=> (r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21)))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(366,plain,
% 0.33/0.62 ((p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) <=> (p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(367,plain,
% 0.33/0.62 ((r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) & (~p12(X!21))) <=> (r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y)))) & (~p12(X!21)))),
% 0.33/0.62 inference(monotonicity,[status(thm)],[366])).
% 0.33/0.62 tff(368,plain,
% 0.33/0.62 ((r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) & (~p12(X!21))) <=> (r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21)))),
% 0.33/0.62 inference(transitivity,[status(thm)],[367, 365])).
% 0.33/0.62 tff(369,plain,
% 0.33/0.62 ((p12(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p12(X))) <=> (p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(370,plain,
% 0.33/0.62 ((r1(X!0, Y!20) & (~p13(Y!20)) & (p12(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p12(X))) & (r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) & (~p12(X!21)))) <=> (r1(X!0, Y!20) & (~p13(Y!20)) & (p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X)))) & (r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))))),
% 0.33/0.62 inference(monotonicity,[status(thm)],[369, 368])).
% 0.33/0.62 tff(371,plain,
% 0.33/0.62 ((r1(X!0, Y!20) & (~p13(Y!20)) & (p12(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p12(X))) & (r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) & (~p12(X!21)))) <=> (r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21)))),
% 0.33/0.62 inference(transitivity,[status(thm)],[370, 364])).
% 0.33/0.62 tff(372,plain,
% 0.33/0.62 (((r1(X!0, Y!20) & (~p13(Y!20)) & (p12(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p12(X))) & (r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) & (~p12(X!21)))) | (r1(X!0, Y!22) & (p13(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p13(X))) & (~p12(Y!22)) & (r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y))))) | (r1(X!0, Y!24) & (~p13(Y!24)) & (p13(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p13(X))) & (~p12(Y!24)) & (p12(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p12(X))))) <=> ((r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))) | (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y)))) | $false)),
% 0.33/0.62 inference(monotonicity,[status(thm)],[371, 363, 355])).
% 0.33/0.62 tff(373,plain,
% 0.33/0.62 (((r1(X!0, Y!20) & (~p13(Y!20)) & (p12(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p12(X))) & (r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) & (~p12(X!21)))) | (r1(X!0, Y!22) & (p13(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p13(X))) & (~p12(Y!22)) & (r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y))))) | (r1(X!0, Y!24) & (~p13(Y!24)) & (p13(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p13(X))) & (~p12(Y!24)) & (p12(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p12(X))))) <=> ((r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))) | (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y)))))),
% 0.33/0.63 inference(transitivity,[status(thm)],[372, 350])).
% 0.33/0.63 tff(374,plain,
% 0.33/0.63 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))) <=> (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))), (((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) <=> ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))))), (((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | p12(Y)) <=> ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | p12(Y)))), rewrite(((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | p12(Y)) <=> (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))), (((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | p12(Y)) <=> (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))))),
% 0.33/0.63 inference(bind,[status(th)],[])).
% 0.33/0.63 tff(375,plain,
% 0.33/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | p12(Y)) <=> ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))),
% 0.33/0.63 inference(quant_intro,[status(thm)],[374])).
% 0.33/0.63 tff(376,plain,
% 0.33/0.63 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | p12(Y)) | ((r1(X!0, Y!20) & (~p13(Y!20)) & (p12(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p12(X))) & (r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) & (~p12(X!21)))) | (r1(X!0, Y!22) & (p13(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p13(X))) & (~p12(Y!22)) & (r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y))))) | (r1(X!0, Y!24) & (~p13(Y!24)) & (p13(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p13(X))) & (~p12(Y!24)) & (p12(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))))) <=> (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))) | (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))))),
% 0.33/0.63 inference(monotonicity,[status(thm)],[375, 373, 349])).
% 0.33/0.63 tff(377,plain,
% 0.33/0.63 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | p12(Y)) | ((r1(X!0, Y!20) & (~p13(Y!20)) & (p12(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p12(X))) & (r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) & (~p12(X!21)))) | (r1(X!0, Y!22) & (p13(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p13(X))) & (~p12(Y!22)) & (r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y))))) | (r1(X!0, Y!24) & (~p13(Y!24)) & (p13(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p13(X))) & (~p12(Y!24)) & (p12(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))))) <=> (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))) | (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))))),
% 0.39/0.63 inference(transitivity,[status(thm)],[376, 347])).
% 0.39/0.63 tff(378,plain,
% 0.39/0.63 ((![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | (((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y)))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | ((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y)))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(379,plain,
% 0.39/0.63 ((((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y)))) | $false) <=> (((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y)))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(380,plain,
% 0.39/0.63 (((~p15(Y!19)) & r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : (p14(X) | (~r1(Y!19, X)))) & (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X))))) <=> $false),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(381,plain,
% 0.39/0.63 ((p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X)))) <=> (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(382,plain,
% 0.39/0.63 ((p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) <=> (p14(Y!19) & ![X: $i] : (p14(X) | (~r1(Y!19, X))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(383,plain,
% 0.39/0.63 (((~p15(Y!19)) & r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X))))) <=> ((~p15(Y!19)) & r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : (p14(X) | (~r1(Y!19, X)))) & (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X)))))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[382, 381])).
% 0.39/0.63 tff(384,plain,
% 0.39/0.63 (((~p15(Y!19)) & r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X))))) <=> $false),
% 0.39/0.63 inference(transitivity,[status(thm)],[383, 380])).
% 0.39/0.63 tff(385,plain,
% 0.39/0.63 ((r1(X!0, Y!17) & (~p14(Y!17)) & (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) & ((~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y))))) <=> (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(386,plain,
% 0.39/0.63 (((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y))))) <=> ((~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(387,plain,
% 0.39/0.63 ((p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y))) <=> (p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(388,plain,
% 0.39/0.63 (((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y)))) <=> ((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y)))))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[387])).
% 0.39/0.63 tff(389,plain,
% 0.39/0.63 (((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y)))) <=> ((~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y))))),
% 0.39/0.63 inference(transitivity,[status(thm)],[388, 386])).
% 0.39/0.63 tff(390,plain,
% 0.39/0.63 ((p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) <=> (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(391,plain,
% 0.39/0.63 ((r1(X!0, Y!17) & (~p14(Y!17)) & (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) & ((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y))))) <=> (r1(X!0, Y!17) & (~p14(Y!17)) & (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) & ((~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y)))))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[390, 389])).
% 0.39/0.63 tff(392,plain,
% 0.39/0.63 ((r1(X!0, Y!17) & (~p14(Y!17)) & (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) & ((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y))))) <=> (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y))))),
% 0.39/0.63 inference(transitivity,[status(thm)],[391, 385])).
% 0.39/0.63 tff(393,plain,
% 0.39/0.63 (((~p15(Y!15)) & r1(X!0, Y!15) & (p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y))))) <=> ((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(394,plain,
% 0.39/0.63 ((r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y))))) <=> (r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(395,plain,
% 0.39/0.63 ((p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) <=> (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(396,plain,
% 0.39/0.63 ((r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y))))) <=> (r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[395])).
% 0.39/0.63 tff(397,plain,
% 0.39/0.63 ((r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y))))) <=> (r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y))))),
% 0.39/0.63 inference(transitivity,[status(thm)],[396, 394])).
% 0.39/0.63 tff(398,plain,
% 0.39/0.63 ((p14(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p14(X))) <=> (p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(399,plain,
% 0.39/0.63 (((~p15(Y!15)) & r1(X!0, Y!15) & (p14(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p14(X))) & (r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))))) <=> ((~p15(Y!15)) & r1(X!0, Y!15) & (p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[398, 397])).
% 0.39/0.63 tff(400,plain,
% 0.39/0.63 (((~p15(Y!15)) & r1(X!0, Y!15) & (p14(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p14(X))) & (r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))))) <=> ((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y))))),
% 0.39/0.64 inference(transitivity,[status(thm)],[399, 393])).
% 0.39/0.64 tff(401,plain,
% 0.39/0.64 ((((~p15(Y!15)) & r1(X!0, Y!15) & (p14(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p14(X))) & (r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p14(Y!17)) & (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) & ((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y))))) | ((~p15(Y!19)) & r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X)))))) <=> (((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y)))) | $false)),
% 0.39/0.64 inference(monotonicity,[status(thm)],[400, 392, 384])).
% 0.39/0.64 tff(402,plain,
% 0.39/0.64 ((((~p15(Y!15)) & r1(X!0, Y!15) & (p14(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p14(X))) & (r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p14(Y!17)) & (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) & ((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y))))) | ((~p15(Y!19)) & r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X)))))) <=> (((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y)))))),
% 0.39/0.64 inference(transitivity,[status(thm)],[401, 379])).
% 0.39/0.64 tff(403,plain,
% 0.39/0.64 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))) <=> (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))), (((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) <=> ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))))), ((p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))))), rewrite((p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))), ((p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))))),
% 0.39/0.64 inference(bind,[status(th)],[])).
% 0.39/0.64 tff(404,plain,
% 0.39/0.64 (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))) <=> ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))),
% 0.39/0.64 inference(quant_intro,[status(thm)],[403])).
% 0.39/0.64 tff(405,plain,
% 0.39/0.64 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))),
% 0.39/0.64 inference(bind,[status(th)],[])).
% 0.39/0.64 tff(406,plain,
% 0.39/0.64 (![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))),
% 0.39/0.64 inference(quant_intro,[status(thm)],[405])).
% 0.39/0.64 tff(407,plain,
% 0.39/0.64 ((![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))) | (((~p15(Y!15)) & r1(X!0, Y!15) & (p14(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p14(X))) & (r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p14(Y!17)) & (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) & ((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y))))) | ((~p15(Y!19)) & r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X))))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | (((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y))))))),
% 0.39/0.64 inference(monotonicity,[status(thm)],[406, 404, 402])).
% 0.39/0.64 tff(408,plain,
% 0.39/0.64 ((![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))) | (((~p15(Y!15)) & r1(X!0, Y!15) & (p14(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p14(X))) & (r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p14(Y!17)) & (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) & ((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y))))) | ((~p15(Y!19)) & r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X))))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | ((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y)))))),
% 0.39/0.64 inference(transitivity,[status(thm)],[407, 378])).
% 0.39/0.64 tff(409,plain,
% 0.39/0.64 ((![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y)))))) <=> (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y)))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(410,plain,
% 0.39/0.64 (((r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y)))) | $false) <=> ((r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y)))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(411,plain,
% 0.39/0.64 ((r1(X!0, Y!14) & (~p14(Y!14)) & (p14(Y!14) & ![X: $i] : (p14(X) | (~r1(Y!14, X)))) & (~p13(Y!14)) & (p13(Y!14) & ![X: $i] : (p13(X) | (~r1(Y!14, X))))) <=> $false),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(412,plain,
% 0.39/0.64 ((p13(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p13(X))) <=> (p13(Y!14) & ![X: $i] : (p13(X) | (~r1(Y!14, X))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(413,plain,
% 0.39/0.64 ((p14(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p14(X))) <=> (p14(Y!14) & ![X: $i] : (p14(X) | (~r1(Y!14, X))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(414,plain,
% 0.39/0.64 ((r1(X!0, Y!14) & (~p14(Y!14)) & (p14(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p14(X))) & (~p13(Y!14)) & (p13(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p13(X)))) <=> (r1(X!0, Y!14) & (~p14(Y!14)) & (p14(Y!14) & ![X: $i] : (p14(X) | (~r1(Y!14, X)))) & (~p13(Y!14)) & (p13(Y!14) & ![X: $i] : (p13(X) | (~r1(Y!14, X)))))),
% 0.39/0.64 inference(monotonicity,[status(thm)],[413, 412])).
% 0.39/0.64 tff(415,plain,
% 0.39/0.64 ((r1(X!0, Y!14) & (~p14(Y!14)) & (p14(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p14(X))) & (~p13(Y!14)) & (p13(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p13(X)))) <=> $false),
% 0.39/0.64 inference(transitivity,[status(thm)],[414, 411])).
% 0.39/0.64 tff(416,plain,
% 0.39/0.64 ((r1(X!0, Y!12) & (p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X)))) & (~p13(Y!12)) & (r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y))))) <=> (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(417,plain,
% 0.39/0.64 ((r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y))))) <=> (r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(418,plain,
% 0.39/0.64 ((p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y))) <=> (p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(419,plain,
% 0.39/0.64 ((r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y)))) <=> (r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y)))))),
% 0.39/0.64 inference(monotonicity,[status(thm)],[418])).
% 0.39/0.64 tff(420,plain,
% 0.39/0.64 ((r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y)))) <=> (r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y))))),
% 0.39/0.64 inference(transitivity,[status(thm)],[419, 417])).
% 0.39/0.64 tff(421,plain,
% 0.39/0.64 ((p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))) <=> (p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(422,plain,
% 0.39/0.64 ((r1(X!0, Y!12) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))) & (~p13(Y!12)) & (r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y))))) <=> (r1(X!0, Y!12) & (p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X)))) & (~p13(Y!12)) & (r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y)))))),
% 0.39/0.64 inference(monotonicity,[status(thm)],[421, 420])).
% 0.39/0.64 tff(423,plain,
% 0.39/0.64 ((r1(X!0, Y!12) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))) & (~p13(Y!12)) & (r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y))))) <=> (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y))))),
% 0.39/0.64 inference(transitivity,[status(thm)],[422, 416])).
% 0.39/0.64 tff(424,plain,
% 0.39/0.64 ((r1(X!0, Y!10) & (~p14(Y!10)) & (r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11))) & (p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X))))) <=> (r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X))))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(425,plain,
% 0.39/0.65 ((p13(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p13(X))) <=> (p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X))))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(426,plain,
% 0.39/0.65 ((r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))) & (~p13(X!11))) <=> (r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(427,plain,
% 0.39/0.65 ((p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) <=> (p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(428,plain,
% 0.39/0.65 ((r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) & (~p13(X!11))) <=> (r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))) & (~p13(X!11)))),
% 0.39/0.65 inference(monotonicity,[status(thm)],[427])).
% 0.39/0.65 tff(429,plain,
% 0.39/0.65 ((r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) & (~p13(X!11))) <=> (r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)))),
% 0.39/0.65 inference(transitivity,[status(thm)],[428, 426])).
% 0.39/0.65 tff(430,plain,
% 0.39/0.65 ((r1(X!0, Y!10) & (~p14(Y!10)) & (r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) & (~p13(X!11))) & (p13(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p13(X)))) <=> (r1(X!0, Y!10) & (~p14(Y!10)) & (r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11))) & (p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))))),
% 0.39/0.65 inference(monotonicity,[status(thm)],[429, 425])).
% 0.39/0.65 tff(431,plain,
% 0.39/0.65 ((r1(X!0, Y!10) & (~p14(Y!10)) & (r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) & (~p13(X!11))) & (p13(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p13(X)))) <=> (r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X))))),
% 0.39/0.65 inference(transitivity,[status(thm)],[430, 424])).
% 0.39/0.65 tff(432,plain,
% 0.39/0.65 (((r1(X!0, Y!10) & (~p14(Y!10)) & (r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) & (~p13(X!11))) & (p13(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p13(X)))) | (r1(X!0, Y!12) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))) & (~p13(Y!12)) & (r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y))))) | (r1(X!0, Y!14) & (~p14(Y!14)) & (p14(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p14(X))) & (~p13(Y!14)) & (p13(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p13(X))))) <=> ((r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y)))) | $false)),
% 0.39/0.65 inference(monotonicity,[status(thm)],[431, 423, 415])).
% 0.39/0.65 tff(433,plain,
% 0.39/0.65 (((r1(X!0, Y!10) & (~p14(Y!10)) & (r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) & (~p13(X!11))) & (p13(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p13(X)))) | (r1(X!0, Y!12) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))) & (~p13(Y!12)) & (r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y))))) | (r1(X!0, Y!14) & (~p14(Y!14)) & (p14(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p14(X))) & (~p13(Y!14)) & (p13(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p13(X))))) <=> ((r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y)))))),
% 0.39/0.65 inference(transitivity,[status(thm)],[432, 410])).
% 0.39/0.65 tff(434,plain,
% 0.39/0.65 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))) <=> (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))), (((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) <=> ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))))), (((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))) <=> ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))))), rewrite(((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))), (((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))))),
% 0.39/0.65 inference(bind,[status(th)],[])).
% 0.39/0.65 tff(435,plain,
% 0.39/0.65 (![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))) <=> ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))),
% 0.39/0.65 inference(quant_intro,[status(thm)],[434])).
% 0.39/0.65 tff(436,plain,
% 0.39/0.65 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))) <=> (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))), (((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) <=> ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))))), (((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | p13(Y)) <=> ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | p13(Y)))), rewrite(((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | p13(Y)) <=> (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))), (((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | p13(Y)) <=> (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))))),
% 0.39/0.65 inference(bind,[status(th)],[])).
% 0.39/0.65 tff(437,plain,
% 0.39/0.65 (![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | p13(Y)) <=> ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))),
% 0.39/0.65 inference(quant_intro,[status(thm)],[436])).
% 0.39/0.65 tff(438,plain,
% 0.39/0.65 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | p13(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p14(Y!10)) & (r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) & (~p13(X!11))) & (p13(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p13(X)))) | (r1(X!0, Y!12) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))) & (~p13(Y!12)) & (r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y))))) | (r1(X!0, Y!14) & (~p14(Y!14)) & (p14(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p14(X))) & (~p13(Y!14)) & (p13(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p13(X)))))) <=> (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y))))))),
% 0.39/0.65 inference(monotonicity,[status(thm)],[437, 435, 433])).
% 0.39/0.65 tff(439,plain,
% 0.39/0.65 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | p13(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p14(Y!10)) & (r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) & (~p13(X!11))) & (p13(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p13(X)))) | (r1(X!0, Y!12) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))) & (~p13(Y!12)) & (r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y))))) | (r1(X!0, Y!14) & (~p14(Y!14)) & (p14(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p14(X))) & (~p13(Y!14)) & (p13(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p13(X)))))) <=> (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y)))))),
% 0.39/0.65 inference(transitivity,[status(thm)],[438, 409])).
% 0.39/0.65 tff(440,plain,
% 0.39/0.65 ((![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) | ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))) <=> (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) | ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(441,plain,
% 0.39/0.65 ((((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) | ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))) | $false) <=> (((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) | ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(442,plain,
% 0.39/0.65 (((~p16(Y!7)) & (~p15(Y!7)) & r1(X!0, Y!7) & (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) & (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X))))) <=> $false),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(443,plain,
% 0.39/0.65 ((p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X)))) <=> (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X))))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(444,plain,
% 0.39/0.65 ((p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) <=> (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X))))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(445,plain,
% 0.39/0.65 (((~p16(Y!7)) & (~p15(Y!7)) & r1(X!0, Y!7) & (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) & (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X))))) <=> ((~p16(Y!7)) & (~p15(Y!7)) & r1(X!0, Y!7) & (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) & (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X)))))),
% 0.39/0.65 inference(monotonicity,[status(thm)],[444, 443])).
% 0.39/0.65 tff(446,plain,
% 0.39/0.65 (((~p16(Y!7)) & (~p15(Y!7)) & r1(X!0, Y!7) & (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) & (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X))))) <=> $false),
% 0.39/0.65 inference(transitivity,[status(thm)],[445, 442])).
% 0.39/0.65 tff(447,plain,
% 0.39/0.65 (((~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & ((~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))) <=> ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(448,plain,
% 0.39/0.66 (((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))) <=> ((~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(449,plain,
% 0.39/0.66 ((p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))) <=> (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(450,plain,
% 0.39/0.66 (((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))) <=> ((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))),
% 0.39/0.66 inference(monotonicity,[status(thm)],[449])).
% 0.39/0.66 tff(451,plain,
% 0.39/0.66 (((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))) <=> ((~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))),
% 0.39/0.66 inference(transitivity,[status(thm)],[450, 448])).
% 0.39/0.66 tff(452,plain,
% 0.39/0.66 ((p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) <=> (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(453,plain,
% 0.39/0.66 (((~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & ((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))) <=> ((~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & ((~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))),
% 0.39/0.66 inference(monotonicity,[status(thm)],[452, 451])).
% 0.39/0.66 tff(454,plain,
% 0.39/0.66 (((~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & ((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))) <=> ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))),
% 0.39/0.66 inference(transitivity,[status(thm)],[453, 447])).
% 0.39/0.66 tff(455,plain,
% 0.39/0.66 (((~p16(Y!3)) & r1(X!0, Y!3) & (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) & ((~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y))))) <=> ((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y))))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(456,plain,
% 0.39/0.66 (((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y))))) <=> ((~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y))))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(457,plain,
% 0.39/0.66 ((p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) <=> (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y))))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(458,plain,
% 0.39/0.66 (((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y))))) <=> ((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))))),
% 0.39/0.66 inference(monotonicity,[status(thm)],[457])).
% 0.39/0.66 tff(459,plain,
% 0.39/0.66 (((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y))))) <=> ((~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y))))),
% 0.39/0.66 inference(transitivity,[status(thm)],[458, 456])).
% 0.39/0.66 tff(460,plain,
% 0.39/0.66 ((p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) <=> (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))))),
% 0.39/0.66 inference(rewrite,[status(thm)],[])).
% 0.39/0.66 tff(461,plain,
% 0.39/0.66 (((~p16(Y!3)) & r1(X!0, Y!3) & (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) & ((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))))) <=> ((~p16(Y!3)) & r1(X!0, Y!3) & (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) & ((~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))))),
% 0.39/0.66 inference(monotonicity,[status(thm)],[460, 459])).
% 0.39/0.66 tff(462,plain,
% 0.39/0.66 (((~p16(Y!3)) & r1(X!0, Y!3) & (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) & ((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))))) <=> ((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y))))),
% 0.39/0.66 inference(transitivity,[status(thm)],[461, 455])).
% 0.39/0.66 tff(463,plain,
% 0.39/0.66 ((((~p16(Y!3)) & r1(X!0, Y!3) & (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) & ((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))))) | ((~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & ((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))) | ((~p16(Y!7)) & (~p15(Y!7)) & r1(X!0, Y!7) & (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) & (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X)))))) <=> (((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) | ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))) | $false)),
% 0.39/0.66 inference(monotonicity,[status(thm)],[462, 454, 446])).
% 0.39/0.66 tff(464,plain,
% 0.39/0.66 ((((~p16(Y!3)) & r1(X!0, Y!3) & (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) & ((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))))) | ((~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & ((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))) | ((~p16(Y!7)) & (~p15(Y!7)) & r1(X!0, Y!7) & (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) & (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X)))))) <=> (((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) | ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))),
% 0.39/0.66 inference(transitivity,[status(thm)],[463, 441])).
% 0.39/0.66 tff(465,plain,
% 0.39/0.66 (^[Y: $i] : rewrite((p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))),
% 0.39/0.66 inference(bind,[status(th)],[])).
% 0.39/0.66 tff(466,plain,
% 0.39/0.66 (![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))),
% 0.39/0.66 inference(quant_intro,[status(thm)],[465])).
% 0.39/0.66 tff(467,plain,
% 0.39/0.66 (^[Y: $i] : rewrite((p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))),
% 0.39/0.66 inference(bind,[status(th)],[])).
% 0.39/0.66 tff(468,plain,
% 0.39/0.66 (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) <=> ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))),
% 0.39/0.66 inference(quant_intro,[status(thm)],[467])).
% 0.39/0.66 tff(469,plain,
% 0.39/0.66 ((![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p16(Y!3)) & r1(X!0, Y!3) & (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) & ((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))))) | ((~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & ((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))) | ((~p16(Y!7)) & (~p15(Y!7)) & r1(X!0, Y!7) & (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) & (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X))))))) <=> (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) | ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))))),
% 0.39/0.67 inference(monotonicity,[status(thm)],[468, 466, 464])).
% 0.39/0.67 tff(470,plain,
% 0.39/0.67 ((![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p16(Y!3)) & r1(X!0, Y!3) & (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) & ((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))))) | ((~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & ((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))) | ((~p16(Y!7)) & (~p15(Y!7)) & r1(X!0, Y!7) & (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) & (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X))))))) <=> (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) | ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))),
% 0.39/0.67 inference(transitivity,[status(thm)],[469, 440])).
% 0.39/0.67 tff(471,plain,
% 0.39/0.67 (((![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p16(Y!3)) & r1(X!0, Y!3) & (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) & ((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))))) | ((~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & ((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))) | ((~p16(Y!7)) & (~p15(Y!7)) & r1(X!0, Y!7) & (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) & (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | p13(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p14(Y!10)) & (r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) & (~p13(X!11))) & (p13(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p13(X)))) | (r1(X!0, Y!12) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))) & (~p13(Y!12)) & (r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y))))) | (r1(X!0, Y!14) & (~p14(Y!14)) & (p14(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p14(X))) & (~p13(Y!14)) & (p13(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p13(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))) | (((~p15(Y!15)) & r1(X!0, Y!15) & (p14(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p14(X))) & (r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p14(Y!17)) & (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) & ((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y))))) | ((~p15(Y!19)) & r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | p12(Y)) | ((r1(X!0, Y!20) & (~p13(Y!20)) & (p12(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p12(X))) & (r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) & (~p12(X!21)))) | (r1(X!0, Y!22) & (p13(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p13(X))) & (~p12(Y!22)) & (r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y))))) | (r1(X!0, Y!24) & (~p13(Y!24)) & (p13(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p13(X))) & (~p12(Y!24)) & (p12(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | p11(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) | ((r1(X!0, Y!27) & (~p12(Y!27)) & (p11(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p11(X))) & (r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) & (~p11(X!28)))) | (r1(X!0, Y!29) & (p12(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p12(X))) & (~p11(Y!29)) & (r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y))))) | (r1(X!0, Y!31) & (~p12(Y!31)) & (p12(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p12(X))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | p10(Y)) | ((r1(X!0, Y!32) & (~p11(Y!32)) & (p10(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p10(X))) & (r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) & (~p10(X!33)))) | (r1(X!0, Y!34) & (p11(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p11(X))) & (~p10(Y!34)) & (r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y))))) | (r1(X!0, Y!36) & (~p11(Y!36)) & (p11(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p11(X))) & (~p10(Y!36)) & (p10(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))) | ((r1(X!0, Y!40) & (~p9(Y!40)) & (p8(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p8(X))) & (r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) & (~p8(X!41)))) | (r1(X!0, Y!42) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))) & (~p8(Y!42)) & (r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y))))) | (r1(X!0, Y!44) & (~p9(Y!44)) & (p9(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p9(X))) & (~p8(Y!44)) & (p8(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p8(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | p9(Y)) | ((r1(X!0, Y!45) & (~p10(Y!45)) & (p9(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p9(X))) & (r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) & (~p9(X!46)))) | (r1(X!0, Y!47) & (p10(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p10(X))) & (~p9(Y!47)) & (r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y))))) | (r1(X!0, Y!49) & (~p10(Y!49)) & (p10(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p10(X))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | p7(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))) | ((r1(X!0, Y!51) & (~p8(Y!51)) & (p7(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p7(X))) & (r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) & (~p7(X!52)))) | (r1(X!0, Y!53) & (p8(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p8(X))) & (~p7(Y!53)) & (r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y))))) | (r1(X!0, Y!55) & (~p8(Y!55)) & (p8(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p8(X))) & (~p7(Y!55)) & (p7(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p7(X)))))) & ((~p15(Y!56)) & r1(X!0, Y!56) & (![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | p6(Y)) | ((r1(X!0, Y!57) & (~p7(Y!57)) & (p6(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p6(X))) & (r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) & (~p6(X!58)))) | (r1(X!0, Y!59) & (p7(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p7(X))) & (~p6(Y!59)) & (r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y))))) | (r1(X!0, Y!61) & (~p7(Y!61)) & (p7(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p7(X))) & (~p6(Y!61)) & (p6(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) | ((r1(X!0, Y!64) & (r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) & (~p5(X!65))) & (~p6(Y!64)) & (p5(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p5(X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & (p6(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p6(X))) & (r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y))))) | (r1(X!0, Y!68) & (~p6(Y!68)) & (~p5(Y!68)) & (p6(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p6(X))) & (p5(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))) & (((r1(X!0, Y!69) & (~p5(Y!69)) & (p4(Y!69) & ![X: $i] : ((~r1(Y!69, X)) | p4(X))) & (r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) & (~p4(X!70)))) | (r1(X!0, Y!71) & (p5(Y!71) & ![X: $i] : ((~r1(Y!71, X)) | p5(X))) & (~p4(Y!71)) & (r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y))))) | (r1(X!0, Y!73) & (~p5(Y!73)) & (p5(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p5(X))) & (~p4(Y!73)) & (p4(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p4(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | p4(Y))) & (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | p3(Y)) | ((r1(X!0, Y!76) & (~p4(Y!76)) & (p3(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p3(X))) & (r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) & (~p3(X!77)))) | (r1(X!0, Y!78) & (p4(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p4(X))) & (~p3(Y!78)) & (r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y))))) | (r1(X!0, Y!80) & (~p4(Y!80)) & (p4(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p4(X))) & (~p3(Y!80)) & (p3(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p3(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | p2(Y)) | ((r1(X!0, Y!81) & (~p3(Y!81)) & (p2(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p2(X))) & (r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) & (~p2(X!82)))) | (r1(X!0, Y!83) & (p3(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p3(X))) & (~p2(Y!83)) & (r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y))))) | (r1(X!0, Y!85) & (~p3(Y!85)) & (p3(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p3(X))) & (~p2(Y!85)) & (p2(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | p1(Y)) | ((r1(X!0, Y!87) & (~p2(Y!87)) & (p1(Y!87) & ![X: $i] : ((~r1(Y!87, X)) | p1(X))) & (r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) & (~p1(X!88)))) | (r1(X!0, Y!89) & (p2(Y!89) & ![X: $i] : ((~r1(Y!89, X)) | p2(X))) & (~p1(Y!89)) & (r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y))))) | (r1(X!0, Y!91) & (~p2(Y!91)) & (p2(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p2(X))) & (~p1(Y!91)) & (p1(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p1(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))))) <=> ((![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ((~p16(Y!3)) & r1(X!0, Y!3) & p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X))) & (~p15(X!4)) & r1(Y!3, X!4) & p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))) | ((~p15(Y!5)) & r1(X!0, Y!5) & p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))) & (~p16(X!6)) & r1(Y!5, X!6) & p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y))))) & (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p14(Y!10)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))) & (~p13(X!11)) & p13(Y!10) & ![X: $i] : (p13(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))) & (~p13(Y!12)) & r1(Y!12, X!13) & (~p14(X!13)) & p13(X!13) & ![Y: $i] : (p13(Y) | (~r1(X!13, Y))))) & (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | ((~p15(Y!15)) & r1(X!0, Y!15) & p14(Y!15) & ![X: $i] : (p14(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p14(X!16)) & p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p14(Y!17)) & p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X))) & (~p15(X!18)) & r1(Y!17, X!18) & p14(X!18) & ![Y: $i] : (p14(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p13(Y!20)) & p12(Y!20) & ![X: $i] : (p12(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p13(X!21) & ![Y: $i] : (p13(Y) | (~r1(X!21, Y))) & (~p12(X!21))) | (r1(X!0, Y!22) & p13(Y!22) & ![X: $i] : (p13(X) | (~r1(Y!22, X))) & (~p12(Y!22)) & r1(Y!22, X!23) & (~p13(X!23)) & p12(X!23) & ![Y: $i] : (p12(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y)))))) & (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & (~p12(Y!27)) & p11(Y!27) & ![X: $i] : (p11(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p12(X!28) & ![Y: $i] : (p12(Y) | (~r1(X!28, Y))) & (~p11(X!28))) | (r1(X!0, Y!29) & p12(Y!29) & ![X: $i] : (p12(X) | (~r1(Y!29, X))) & (~p11(Y!29)) & r1(Y!29, X!30) & (~p12(X!30)) & p11(X!30) & ![Y: $i] : (p11(Y) | (~r1(X!30, Y))))) & (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!32) & (~p11(Y!32)) & p10(Y!32) & ![X: $i] : (p10(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p11(X!33) & ![Y: $i] : (p11(Y) | (~r1(X!33, Y))) & (~p10(X!33))) | (r1(X!0, Y!34) & p11(Y!34) & ![X: $i] : (p11(X) | (~r1(Y!34, X))) & (~p10(Y!34)) & r1(Y!34, X!35) & (~p11(X!35)) & p10(X!35) & ![Y: $i] : (p10(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y)))))) & (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | (r1(X!0, Y!40) & (~p9(Y!40)) & p8(Y!40) & ![X: $i] : (p8(X) | (~r1(Y!40, X))) & r1(Y!40, X!41) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))) & (~p8(X!41))) | (r1(X!0, Y!42) & p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))) & (~p8(Y!42)) & r1(Y!42, X!43) & (~p9(X!43)) & p8(X!43) & ![Y: $i] : (p8(Y) | (~r1(X!43, Y))))) & (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | (r1(X!0, Y!45) & (~p10(Y!45)) & p9(Y!45) & ![X: $i] : (p9(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p10(X!46) & ![Y: $i] : (p10(Y) | (~r1(X!46, Y))) & (~p9(X!46))) | (r1(X!0, Y!47) & p10(Y!47) & ![X: $i] : (p10(X) | (~r1(Y!47, X))) & (~p9(Y!47)) & r1(Y!47, X!48) & (~p10(X!48)) & p9(X!48) & ![Y: $i] : (p9(Y) | (~r1(X!48, Y)))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y)))))) & (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | (r1(X!0, Y!51) & (~p8(Y!51)) & p7(Y!51) & ![X: $i] : (p7(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p8(X!52) & ![Y: $i] : (p8(Y) | (~r1(X!52, Y))) & (~p7(X!52))) | (r1(X!0, Y!53) & p8(Y!53) & ![X: $i] : (p8(X) | (~r1(Y!53, X))) & (~p7(Y!53)) & r1(Y!53, X!54) & (~p8(X!54)) & p7(X!54) & ![Y: $i] : (p7(Y) | (~r1(X!54, Y))))) & $false & (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | (r1(X!0, Y!57) & (~p7(Y!57)) & p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))) & (~p6(X!58))) | (r1(X!0, Y!59) & p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))) & (~p6(Y!59)) & r1(Y!59, X!60) & (~p7(X!60)) & p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y)))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) & (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | (r1(X!0, Y!64) & r1(Y!64, X!65) & p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))) & (~p5(X!65)) & (~p6(Y!64)) & p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))) & r1(Y!66, X!67) & (~p6(X!67)) & p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))) & ((r1(X!0, Y!69) & (~p5(Y!69)) & p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))) & r1(Y!69, X!70) & p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))) & (~p4(X!70))) | (r1(X!0, Y!71) & p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))) & (~p4(Y!71)) & r1(Y!71, X!72) & (~p5(X!72)) & p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | (r1(X!0, Y!76) & (~p4(Y!76)) & p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))) & r1(Y!76, X!77) & p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))) & (~p3(X!77))) | (r1(X!0, Y!78) & p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))) & (~p3(Y!78)) & r1(Y!78, X!79) & (~p4(X!79)) & p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))) & (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | (r1(X!0, Y!81) & (~p3(Y!81)) & p2(Y!81) & ![X: $i] : (p2(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p3(X!82) & ![Y: $i] : (p3(Y) | (~r1(X!82, Y))) & (~p2(X!82))) | (r1(X!0, Y!83) & p3(Y!83) & ![X: $i] : (p3(X) | (~r1(Y!83, X))) & (~p2(Y!83)) & r1(Y!83, X!84) & (~p3(X!84)) & p2(X!84) & ![Y: $i] : (p2(Y) | (~r1(X!84, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | (r1(X!0, Y!87) & (~p2(Y!87)) & p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))) & r1(Y!87, X!88) & p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))) & (~p1(X!88))) | (r1(X!0, Y!89) & p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))) & (~p1(Y!89)) & r1(Y!89, X!90) & (~p2(X!90)) & p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))))),
% 0.39/0.68 inference(monotonicity,[status(thm)],[470, 439, 408, 377, 346, 315, 284, 253, 222, 191, 187, 156, 125, 94, 63, 32])).
% 0.39/0.68 tff(472,plain,
% 0.39/0.68 (((![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p16(Y!3)) & r1(X!0, Y!3) & (p15(Y!3) & ![X: $i] : (p15(X) | (~r1(Y!3, X)))) & ((~p15(X!4)) & r1(Y!3, X!4) & (p16(X!4) & ![Y: $i] : (p16(Y) | (~r1(X!4, Y)))))) | ((~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & ((~p16(X!6)) & r1(Y!5, X!6) & (p15(X!6) & ![Y: $i] : (p15(Y) | (~r1(X!6, Y)))))) | ((~p16(Y!7)) & (~p15(Y!7)) & r1(X!0, Y!7) & (p16(Y!7) & ![X: $i] : (p16(X) | (~r1(Y!7, X)))) & (p15(Y!7) & ![X: $i] : (p15(X) | (~r1(Y!7, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y))))) | p13(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p14(Y!10)) & (r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) & (~p13(X!11))) & (p13(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p13(X)))) | (r1(X!0, Y!12) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))) & (~p13(Y!12)) & (r1(Y!12, X!13) & (~p14(X!13)) & (p13(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p13(Y))))) | (r1(X!0, Y!14) & (~p14(Y!14)) & (p14(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p14(X))) & (~p13(Y!14)) & (p13(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p13(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p14(tptp_fun_X_8(Y)))))) | (((~p15(Y!15)) & r1(X!0, Y!15) & (p14(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p14(X))) & (r1(Y!15, X!16) & (~p14(X!16)) & (p15(X!16) & ![Y: $i] : (p15(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p14(Y!17)) & (p15(Y!17) & ![X: $i] : (p15(X) | (~r1(Y!17, X)))) & ((~p15(X!18)) & r1(Y!17, X!18) & (p14(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p14(Y))))) | ((~p15(Y!19)) & r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (p15(Y!19) & ![X: $i] : (p15(X) | (~r1(Y!19, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p13(tptp_fun_X_9(Y))))) | p12(Y)) | ((r1(X!0, Y!20) & (~p13(Y!20)) & (p12(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p12(X))) & (r1(Y!20, X!21) & (p13(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p13(Y))) & (~p12(X!21)))) | (r1(X!0, Y!22) & (p13(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p13(X))) & (~p12(Y!22)) & (r1(Y!22, X!23) & (~p13(X!23)) & (p12(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p12(Y))))) | (r1(X!0, Y!24) & (~p13(Y!24)) & (p13(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p13(X))) & (~p12(Y!24)) & (p12(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p12(tptp_fun_X_25(Y))))) | p11(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) | ((r1(X!0, Y!27) & (~p12(Y!27)) & (p11(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p11(X))) & (r1(Y!27, X!28) & (p12(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p12(Y))) & (~p11(X!28)))) | (r1(X!0, Y!29) & (p12(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p12(X))) & (~p11(Y!29)) & (r1(Y!29, X!30) & (~p12(X!30)) & (p11(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p11(Y))))) | (r1(X!0, Y!31) & (~p12(Y!31)) & (p12(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p12(X))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | p10(Y)) | ((r1(X!0, Y!32) & (~p11(Y!32)) & (p10(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p10(X))) & (r1(Y!32, X!33) & (p11(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p11(Y))) & (~p10(X!33)))) | (r1(X!0, Y!34) & (p11(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p11(X))) & (~p10(Y!34)) & (r1(Y!34, X!35) & (~p11(X!35)) & (p10(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p10(Y))))) | (r1(X!0, Y!36) & (~p11(Y!36)) & (p11(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p11(X))) & (~p10(Y!36)) & (p10(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y)))))) | ((r1(X!0, Y!40) & (~p9(Y!40)) & (p8(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p8(X))) & (r1(Y!40, X!41) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) & (~p8(X!41)))) | (r1(X!0, Y!42) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))) & (~p8(Y!42)) & (r1(Y!42, X!43) & (~p9(X!43)) & (p8(X!43) & ![Y: $i] : ((~r1(X!43, Y)) | p8(Y))))) | (r1(X!0, Y!44) & (~p9(Y!44)) & (p9(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p9(X))) & (~p8(Y!44)) & (p8(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p8(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p10(tptp_fun_X_37(Y))))) | p9(Y)) | ((r1(X!0, Y!45) & (~p10(Y!45)) & (p9(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p9(X))) & (r1(Y!45, X!46) & (p10(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p10(Y))) & (~p9(X!46)))) | (r1(X!0, Y!47) & (p10(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p10(X))) & (~p9(Y!47)) & (r1(Y!47, X!48) & (~p10(X!48)) & (p9(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p9(Y))))) | (r1(X!0, Y!49) & (~p10(Y!49)) & (p10(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p10(X))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p9(tptp_fun_X_38(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_39(Y))) | p8(tptp_fun_X_39(Y))))) | p7(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y)))))) | ((r1(X!0, Y!51) & (~p8(Y!51)) & (p7(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p7(X))) & (r1(Y!51, X!52) & (p8(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p8(Y))) & (~p7(X!52)))) | (r1(X!0, Y!53) & (p8(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p8(X))) & (~p7(Y!53)) & (r1(Y!53, X!54) & (~p8(X!54)) & (p7(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p7(Y))))) | (r1(X!0, Y!55) & (~p8(Y!55)) & (p8(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p8(X))) & (~p7(Y!55)) & (p7(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p7(X)))))) & ((~p15(Y!56)) & r1(X!0, Y!56) & (![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p7(tptp_fun_X_50(Y))))) | p6(Y)) | ((r1(X!0, Y!57) & (~p7(Y!57)) & (p6(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p6(X))) & (r1(Y!57, X!58) & (p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) & (~p6(X!58)))) | (r1(X!0, Y!59) & (p7(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p7(X))) & (~p6(Y!59)) & (r1(Y!59, X!60) & (~p7(X!60)) & (p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y))))) | (r1(X!0, Y!61) & (~p7(Y!61)) & (p7(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p7(X))) & (~p6(Y!61)) & (p6(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))) | ((r1(X!0, Y!64) & (r1(Y!64, X!65) & (p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) & (~p5(X!65))) & (~p6(Y!64)) & (p5(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p5(X)))) | (r1(X!0, Y!66) & (~p5(Y!66)) & (p6(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p6(X))) & (r1(Y!66, X!67) & (~p6(X!67)) & (p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y))))) | (r1(X!0, Y!68) & (~p6(Y!68)) & (~p5(Y!68)) & (p6(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p6(X))) & (p5(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))) & (((r1(X!0, Y!69) & (~p5(Y!69)) & (p4(Y!69) & ![X: $i] : ((~r1(Y!69, X)) | p4(X))) & (r1(Y!69, X!70) & (p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) & (~p4(X!70)))) | (r1(X!0, Y!71) & (p5(Y!71) & ![X: $i] : ((~r1(Y!71, X)) | p5(X))) & (~p4(Y!71)) & (r1(Y!71, X!72) & (~p5(X!72)) & (p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y))))) | (r1(X!0, Y!73) & (~p5(Y!73)) & (p5(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p5(X))) & (~p4(Y!73)) & (p4(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p4(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y))))) | p4(Y))) & (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p4(tptp_fun_X_74(Y))))) | p3(Y)) | ((r1(X!0, Y!76) & (~p4(Y!76)) & (p3(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p3(X))) & (r1(Y!76, X!77) & (p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) & (~p3(X!77)))) | (r1(X!0, Y!78) & (p4(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p4(X))) & (~p3(Y!78)) & (r1(Y!78, X!79) & (~p4(X!79)) & (p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y))))) | (r1(X!0, Y!80) & (~p4(Y!80)) & (p4(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p4(X))) & (~p3(Y!80)) & (p3(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p3(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | p2(Y)) | ((r1(X!0, Y!81) & (~p3(Y!81)) & (p2(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p2(X))) & (r1(Y!81, X!82) & (p3(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p3(Y))) & (~p2(X!82)))) | (r1(X!0, Y!83) & (p3(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p3(X))) & (~p2(Y!83)) & (r1(Y!83, X!84) & (~p3(X!84)) & (p2(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p2(Y))))) | (r1(X!0, Y!85) & (~p3(Y!85)) & (p3(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p3(X))) & (~p2(Y!85)) & (p2(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p2(tptp_fun_X_86(Y))))) | p1(Y)) | ((r1(X!0, Y!87) & (~p2(Y!87)) & (p1(Y!87) & ![X: $i] : ((~r1(Y!87, X)) | p1(X))) & (r1(Y!87, X!88) & (p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) & (~p1(X!88)))) | (r1(X!0, Y!89) & (p2(Y!89) & ![X: $i] : ((~r1(Y!89, X)) | p2(X))) & (~p1(Y!89)) & (r1(Y!89, X!90) & (~p2(X!90)) & (p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y))))) | (r1(X!0, Y!91) & (~p2(Y!91)) & (p2(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p2(X))) & (~p1(Y!91)) & (p1(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p1(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_92(Y))) | p1(tptp_fun_X_92(Y)))))))) <=> $false),
% 0.39/0.69 inference(transitivity,[status(thm)],[471, 1])).
% 0.39/0.69 tff(473,plain,
% 0.39/0.69 (?[X: $i] : (~((~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X)))))) | ![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p16(X) & ![Y: $i] : (p16(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | ![X: $i] : (p16(X) | (~r1(Y, X)) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p16(Y) | p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | (~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | ![X: $i] : ((~r1(Y, X)) | p11(X) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | p10(X) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(![X: $i] : (p15(X) | (~r1(Y, X))) & p15(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))) <=> ?[X: $i] : (~((~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X)))))) | ![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p16(X) & ![Y: $i] : (p16(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | ![X: $i] : (p16(X) | (~r1(Y, X)) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p16(Y) | p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | (~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | ![X: $i] : ((~r1(Y, X)) | p11(X) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | p10(X) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(![X: $i] : (p15(X) | (~r1(Y, X))) & p15(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(474,plain,
% 0.46/0.71 ((~(~?[X: $i] : (~((~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X)))))) | ![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p16(X) & ![Y: $i] : (p16(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | ![X: $i] : (p16(X) | (~r1(Y, X)) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p16(Y) | p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | (~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | ![X: $i] : ((~r1(Y, X)) | p11(X) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | p10(X) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(![X: $i] : (p15(X) | (~r1(Y, X))) & p15(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) <=> ?[X: $i] : (~((~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X)))))) | ![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p16(X) & ![Y: $i] : (p16(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | ![X: $i] : (p16(X) | (~r1(Y, X)) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p16(Y) | p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | (~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | ![X: $i] : ((~r1(Y, X)) | p11(X) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | p10(X) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(![X: $i] : (p15(X) | (~r1(Y, X))) & p15(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(475,plain,
% 0.46/0.72 ((~?[X: $i] : (~(((((((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![Y: $i] : (((~r1(X, Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))))) | p15(X))) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![X: $i] : (((~r1(Y, X)) | p16(X)) | (~((p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))) & p15(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))))) | p14(X))) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![X: $i] : (((~r1(Y, X)) | p15(X)) | (~((p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))) & p14(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![Y: $i] : (((~r1(X, Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))))) | p13(X))) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![X: $i] : (((~r1(Y, X)) | p14(X)) | (~((p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))) & p13(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![Y: $i] : (((~r1(X, Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))))) | p12(X))) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![X: $i] : (((~r1(Y, X)) | p13(X)) | (~((p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))) & p12(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![Y: $i] : (((~r1(X, Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))))) | p11(X))) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![X: $i] : (((~r1(Y, X)) | p12(X)) | (~((p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))) & p11(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![Y: $i] : (((~r1(X, Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))))) | p10(X))) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![X: $i] : (((~r1(Y, X)) | p11(X)) | (~((p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))) & p10(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))))) | p9(X))) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![X: $i] : (((~r1(Y, X)) | p10(X)) | (~((p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))) & p9(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![Y: $i] : (((~r1(X, Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))))) | p8(X))) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![X: $i] : (((~r1(Y, X)) | p9(X)) | (~((p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))) & p8(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![Y: $i] : (((~r1(X, Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))))) | p7(X))) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![X: $i] : (((~r1(Y, X)) | p8(X)) | (~((p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))) & p7(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![Y: $i] : (((~r1(X, Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))))) | p6(X))) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![X: $i] : (((~r1(Y, X)) | p7(X)) | (~((p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))) & p6(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))))))) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p15(X)) & p15(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p15(X)) & p15(Y))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![Y: $i] : (((~r1(X, Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))))) | p5(X))) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![X: $i] : (((~r1(Y, X)) | p6(X)) | (~((p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))) & p5(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![Y: $i] : (((~r1(X, Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))))) | p4(X))) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![X: $i] : (((~r1(Y, X)) | p5(X)) | (~((p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))) & p4(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | p3(X))) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![X: $i] : (((~r1(Y, X)) | p4(X)) | (~((p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & p3(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))))) | p2(X))) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![X: $i] : (((~r1(Y, X)) | p3(X)) | (~((p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))) & p2(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))))))))) <=> (~?[X: $i] : (~((~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X)))))) | ![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p16(X) & ![Y: $i] : (p16(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | ![X: $i] : (p16(X) | (~r1(Y, X)) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p16(Y) | p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | (~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | ![X: $i] : ((~r1(Y, X)) | p11(X) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | p10(X) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(![X: $i] : (p15(X) | (~r1(Y, X))) & p15(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))),
% 0.46/0.73 inference(rewrite,[status(thm)],[])).
% 0.46/0.73 tff(476,plain,
% 0.46/0.73 ((~(~?[X: $i] : (~(((((((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![Y: $i] : (((~r1(X, Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))))) | p15(X))) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![X: $i] : (((~r1(Y, X)) | p16(X)) | (~((p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))) & p15(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))))) | p14(X))) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![X: $i] : (((~r1(Y, X)) | p15(X)) | (~((p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))) & p14(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![Y: $i] : (((~r1(X, Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))))) | p13(X))) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![X: $i] : (((~r1(Y, X)) | p14(X)) | (~((p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))) & p13(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![Y: $i] : (((~r1(X, Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))))) | p12(X))) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![X: $i] : (((~r1(Y, X)) | p13(X)) | (~((p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))) & p12(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![Y: $i] : (((~r1(X, Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))))) | p11(X))) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![X: $i] : (((~r1(Y, X)) | p12(X)) | (~((p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))) & p11(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![Y: $i] : (((~r1(X, Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))))) | p10(X))) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![X: $i] : (((~r1(Y, X)) | p11(X)) | (~((p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))) & p10(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))))) | p9(X))) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![X: $i] : (((~r1(Y, X)) | p10(X)) | (~((p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))) & p9(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![Y: $i] : (((~r1(X, Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))))) | p8(X))) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![X: $i] : (((~r1(Y, X)) | p9(X)) | (~((p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))) & p8(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![Y: $i] : (((~r1(X, Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))))) | p7(X))) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![X: $i] : (((~r1(Y, X)) | p8(X)) | (~((p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))) & p7(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![Y: $i] : (((~r1(X, Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))))) | p6(X))) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![X: $i] : (((~r1(Y, X)) | p7(X)) | (~((p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))) & p6(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))))))) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p15(X)) & p15(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p15(X)) & p15(Y))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![Y: $i] : (((~r1(X, Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))))) | p5(X))) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![X: $i] : (((~r1(Y, X)) | p6(X)) | (~((p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))) & p5(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![Y: $i] : (((~r1(X, Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))))) | p4(X))) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![X: $i] : (((~r1(Y, X)) | p5(X)) | (~((p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))) & p4(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | p3(X))) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![X: $i] : (((~r1(Y, X)) | p4(X)) | (~((p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & p3(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))))) | p2(X))) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![X: $i] : (((~r1(Y, X)) | p3(X)) | (~((p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))) & p2(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))))))))))) <=> (~(~?[X: $i] : (~((~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X)))))) | ![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p16(X) & ![Y: $i] : (p16(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | ![X: $i] : (p16(X) | (~r1(Y, X)) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p16(Y) | p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | (~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | ![X: $i] : ((~r1(Y, X)) | p11(X) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | p10(X) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(![X: $i] : (p15(X) | (~r1(Y, X))) & p15(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))),
% 0.46/0.75 inference(monotonicity,[status(thm)],[475])).
% 0.46/0.75 tff(477,plain,
% 0.46/0.75 ((~(~?[X: $i] : (~(((((((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![Y: $i] : (((~r1(X, Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))))) | p15(X))) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![X: $i] : (((~r1(Y, X)) | p16(X)) | (~((p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))) & p15(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))))) | p14(X))) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![X: $i] : (((~r1(Y, X)) | p15(X)) | (~((p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))) & p14(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![Y: $i] : (((~r1(X, Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))))) | p13(X))) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![X: $i] : (((~r1(Y, X)) | p14(X)) | (~((p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))) & p13(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![Y: $i] : (((~r1(X, Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))))) | p12(X))) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![X: $i] : (((~r1(Y, X)) | p13(X)) | (~((p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))) & p12(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![Y: $i] : (((~r1(X, Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))))) | p11(X))) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![X: $i] : (((~r1(Y, X)) | p12(X)) | (~((p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))) & p11(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![Y: $i] : (((~r1(X, Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))))) | p10(X))) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![X: $i] : (((~r1(Y, X)) | p11(X)) | (~((p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))) & p10(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))))) | p9(X))) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![X: $i] : (((~r1(Y, X)) | p10(X)) | (~((p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))) & p9(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![Y: $i] : (((~r1(X, Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))))) | p8(X))) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![X: $i] : (((~r1(Y, X)) | p9(X)) | (~((p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))) & p8(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![Y: $i] : (((~r1(X, Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))))) | p7(X))) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![X: $i] : (((~r1(Y, X)) | p8(X)) | (~((p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))) & p7(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![Y: $i] : (((~r1(X, Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))))) | p6(X))) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![X: $i] : (((~r1(Y, X)) | p7(X)) | (~((p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))) & p6(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))))))) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p15(X)) & p15(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p15(X)) & p15(Y))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![Y: $i] : (((~r1(X, Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))))) | p5(X))) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![X: $i] : (((~r1(Y, X)) | p6(X)) | (~((p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))) & p5(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![Y: $i] : (((~r1(X, Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))))) | p4(X))) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![X: $i] : (((~r1(Y, X)) | p5(X)) | (~((p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))) & p4(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | p3(X))) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![X: $i] : (((~r1(Y, X)) | p4(X)) | (~((p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & p3(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))))) | p2(X))) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![X: $i] : (((~r1(Y, X)) | p3(X)) | (~((p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))) & p2(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))))))))))) <=> ?[X: $i] : (~((~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X)))))) | ![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p16(X) & ![Y: $i] : (p16(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | ![X: $i] : (p16(X) | (~r1(Y, X)) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p16(Y) | p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | (~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | ![X: $i] : ((~r1(Y, X)) | p11(X) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | p10(X) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(![X: $i] : (p15(X) | (~r1(Y, X))) & p15(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.46/0.76 inference(transitivity,[status(thm)],[476, 474])).
% 0.46/0.76 tff(478,axiom,(~(~?[X: $i] : (~(((((((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![Y: $i] : (((~r1(X, Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))))) | p15(X))) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![X: $i] : (((~r1(Y, X)) | p16(X)) | (~((p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))) & p15(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))))) | p14(X))) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![X: $i] : (((~r1(Y, X)) | p15(X)) | (~((p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))) & p14(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![Y: $i] : (((~r1(X, Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))))) | p13(X))) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![X: $i] : (((~r1(Y, X)) | p14(X)) | (~((p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))) & p13(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![Y: $i] : (((~r1(X, Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))))) | p12(X))) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![X: $i] : (((~r1(Y, X)) | p13(X)) | (~((p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))) & p12(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![Y: $i] : (((~r1(X, Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))))) | p11(X))) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![X: $i] : (((~r1(Y, X)) | p12(X)) | (~((p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))) & p11(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![Y: $i] : (((~r1(X, Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))))) | p10(X))) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![X: $i] : (((~r1(Y, X)) | p11(X)) | (~((p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))) & p10(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))))) | p9(X))) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![X: $i] : (((~r1(Y, X)) | p10(X)) | (~((p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))) & p9(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![Y: $i] : (((~r1(X, Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))))) | p8(X))) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![X: $i] : (((~r1(Y, X)) | p9(X)) | (~((p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))) & p8(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![Y: $i] : (((~r1(X, Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))))) | p7(X))) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![X: $i] : (((~r1(Y, X)) | p8(X)) | (~((p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))) & p7(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![Y: $i] : (((~r1(X, Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))))) | p6(X))) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![X: $i] : (((~r1(Y, X)) | p7(X)) | (~((p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))) & p6(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))))))) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p15(X)) & p15(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p15(X)) & p15(Y))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![Y: $i] : (((~r1(X, Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))))) | p5(X))) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![X: $i] : (((~r1(Y, X)) | p6(X)) | (~((p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))) & p5(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![Y: $i] : (((~r1(X, Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))))) | p4(X))) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![X: $i] : (((~r1(Y, X)) | p5(X)) | (~((p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))) & p4(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | p3(X))) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![X: $i] : (((~r1(Y, X)) | p4(X)) | (~((p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & p3(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))))) | p2(X))) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![X: $i] : (((~r1(Y, X)) | p3(X)) | (~((p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))) & p2(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.46/0.77 tff(479,plain,
% 0.46/0.77 (?[X: $i] : (~((~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X)))))) | ![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p16(X) & ![Y: $i] : (p16(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | ![X: $i] : (p16(X) | (~r1(Y, X)) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p16(Y) | p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | (~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | ![X: $i] : ((~r1(Y, X)) | p11(X) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | p10(X) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(![X: $i] : (p15(X) | (~r1(Y, X))) & p15(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.46/0.77 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.46/0.77 tff(480,plain,
% 0.46/0.77 (?[X: $i] : (~((~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X)))))) | ![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p16(Y) | (~r1(X, Y)) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p16(X) & ![Y: $i] : (p16(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | ![X: $i] : (p16(X) | (~r1(Y, X)) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p16(Y) | p15(Y) | (~r1(X, Y)) | (~(p16(Y) & ![X: $i] : (p16(X) | (~r1(Y, X))))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | (~(![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p15(X) & ![Y: $i] : (p15(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | ![X: $i] : (p15(X) | (~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : (p15(Y) | (~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | ![X: $i] : ((~r1(Y, X)) | p11(X) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | p10(X) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | ![Y: $i] : (p15(Y) | (~r1(X, Y)) | (~(![X: $i] : (p15(X) | (~r1(Y, X))) & p15(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.46/0.79 inference(modus_ponens,[status(thm)],[479, 473])).
% 0.46/0.79 tff(481,plain,
% 0.46/0.79 ($false),
% 0.46/0.79 inference(modus_ponens,[status(thm)],[480, 472])).
% 0.46/0.79 % SZS output end Proof
% 0.46/0.79 % E exiting
%------------------------------------------------------------------------------