TSTP Solution File: LCL644+1.015 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL644+1.015 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 04:56:59 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL644+1.015 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 22:55:10 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(p1_type, type, (
% 0.20/0.43 p1: $i > $o)).
% 0.20/0.43 tff(tptp_fun_X_92_type, type, (
% 0.20/0.43 tptp_fun_X_92: $i > $i)).
% 0.20/0.43 tff(r1_type, type, (
% 0.20/0.43 r1: ( $i * $i ) > $o)).
% 0.20/0.43 tff(p2_type, type, (
% 0.20/0.43 p2: $i > $o)).
% 0.20/0.43 tff(tptp_fun_X_0_type, type, (
% 0.20/0.43 tptp_fun_X_0: $i)).
% 0.20/0.43 tff(tptp_fun_Y_91_type, type, (
% 0.20/0.43 tptp_fun_Y_91: $i)).
% 0.20/0.43 tff(tptp_fun_X_90_type, type, (
% 0.20/0.43 tptp_fun_X_90: $i)).
% 0.20/0.43 tff(tptp_fun_Y_89_type, type, (
% 0.20/0.43 tptp_fun_Y_89: $i)).
% 0.20/0.43 tff(tptp_fun_X_88_type, type, (
% 0.20/0.43 tptp_fun_X_88: $i)).
% 0.20/0.43 tff(tptp_fun_Y_87_type, type, (
% 0.20/0.43 tptp_fun_Y_87: $i)).
% 0.20/0.43 tff(tptp_fun_X_81_type, type, (
% 0.20/0.43 tptp_fun_X_81: $i > $i)).
% 0.20/0.43 tff(tptp_fun_Y_86_type, type, (
% 0.20/0.43 tptp_fun_Y_86: $i)).
% 0.20/0.43 tff(p3_type, type, (
% 0.20/0.43 p3: $i > $o)).
% 0.20/0.43 tff(tptp_fun_X_85_type, type, (
% 0.20/0.43 tptp_fun_X_85: $i)).
% 0.20/0.43 tff(tptp_fun_Y_84_type, type, (
% 0.20/0.43 tptp_fun_Y_84: $i)).
% 0.20/0.43 tff(tptp_fun_X_83_type, type, (
% 0.20/0.43 tptp_fun_X_83: $i)).
% 0.20/0.43 tff(tptp_fun_Y_82_type, type, (
% 0.20/0.43 tptp_fun_Y_82: $i)).
% 0.20/0.43 tff(tptp_fun_X_75_type, type, (
% 0.20/0.43 tptp_fun_X_75: $i > $i)).
% 0.20/0.43 tff(tptp_fun_Y_80_type, type, (
% 0.20/0.43 tptp_fun_Y_80: $i)).
% 0.20/0.43 tff(p4_type, type, (
% 0.20/0.43 p4: $i > $o)).
% 0.20/0.43 tff(tptp_fun_X_79_type, type, (
% 0.20/0.43 tptp_fun_X_79: $i)).
% 0.20/0.43 tff(tptp_fun_Y_78_type, type, (
% 0.20/0.43 tptp_fun_Y_78: $i)).
% 0.20/0.43 tff(tptp_fun_X_77_type, type, (
% 0.20/0.43 tptp_fun_X_77: $i)).
% 0.20/0.43 tff(tptp_fun_Y_76_type, type, (
% 0.20/0.43 tptp_fun_Y_76: $i)).
% 0.20/0.43 tff(tptp_fun_X_74_type, type, (
% 0.20/0.43 tptp_fun_X_74: $i > $i)).
% 0.20/0.43 tff(p5_type, type, (
% 0.20/0.43 p5: $i > $o)).
% 0.20/0.43 tff(tptp_fun_X_63_type, type, (
% 0.20/0.43 tptp_fun_X_63: $i > $i)).
% 0.20/0.43 tff(tptp_fun_Y_73_type, type, (
% 0.20/0.43 tptp_fun_Y_73: $i)).
% 0.20/0.43 tff(tptp_fun_X_72_type, type, (
% 0.20/0.43 tptp_fun_X_72: $i)).
% 0.20/0.43 tff(tptp_fun_Y_71_type, type, (
% 0.20/0.43 tptp_fun_Y_71: $i)).
% 0.20/0.43 tff(tptp_fun_X_70_type, type, (
% 0.20/0.43 tptp_fun_X_70: $i)).
% 0.20/0.43 tff(tptp_fun_Y_69_type, type, (
% 0.20/0.43 tptp_fun_Y_69: $i)).
% 0.20/0.43 tff(p6_type, type, (
% 0.20/0.43 p6: $i > $o)).
% 0.20/0.43 tff(tptp_fun_X_62_type, type, (
% 0.20/0.43 tptp_fun_X_62: $i > $i)).
% 0.20/0.43 tff(tptp_fun_Y_68_type, type, (
% 0.20/0.43 tptp_fun_Y_68: $i)).
% 0.20/0.43 tff(tptp_fun_X_67_type, type, (
% 0.20/0.43 tptp_fun_X_67: $i)).
% 0.20/0.43 tff(tptp_fun_Y_66_type, type, (
% 0.20/0.43 tptp_fun_Y_66: $i)).
% 0.20/0.43 tff(tptp_fun_Y_64_type, type, (
% 0.20/0.43 tptp_fun_Y_64: $i)).
% 0.20/0.43 tff(tptp_fun_X_65_type, type, (
% 0.20/0.43 tptp_fun_X_65: $i)).
% 0.20/0.43 tff(p7_type, type, (
% 0.20/0.43 p7: $i > $o)).
% 0.20/0.43 tff(tptp_fun_Y_61_type, type, (
% 0.20/0.43 tptp_fun_Y_61: $i)).
% 0.20/0.43 tff(tptp_fun_X_60_type, type, (
% 0.20/0.43 tptp_fun_X_60: $i)).
% 0.20/0.43 tff(tptp_fun_Y_59_type, type, (
% 0.20/0.43 tptp_fun_Y_59: $i)).
% 0.20/0.43 tff(tptp_fun_X_58_type, type, (
% 0.20/0.43 tptp_fun_X_58: $i)).
% 0.20/0.43 tff(tptp_fun_Y_57_type, type, (
% 0.20/0.43 tptp_fun_Y_57: $i)).
% 0.20/0.43 tff(tptp_fun_X_55_type, type, (
% 0.20/0.43 tptp_fun_X_55: $i > $i)).
% 0.20/0.43 tff(p15_type, type, (
% 0.20/0.43 p15: $i > $o)).
% 0.20/0.43 tff(tptp_fun_Y_56_type, type, (
% 0.20/0.43 tptp_fun_Y_56: $i)).
% 0.20/0.43 tff(p8_type, type, (
% 0.20/0.43 p8: $i > $o)).
% 0.20/0.43 tff(tptp_fun_Y_54_type, type, (
% 0.20/0.43 tptp_fun_Y_54: $i)).
% 0.20/0.43 tff(tptp_fun_X_53_type, type, (
% 0.20/0.43 tptp_fun_X_53: $i)).
% 0.20/0.43 tff(tptp_fun_Y_52_type, type, (
% 0.20/0.43 tptp_fun_Y_52: $i)).
% 0.20/0.43 tff(tptp_fun_X_51_type, type, (
% 0.20/0.43 tptp_fun_X_51: $i)).
% 0.20/0.43 tff(tptp_fun_Y_50_type, type, (
% 0.20/0.43 tptp_fun_Y_50: $i)).
% 0.20/0.43 tff(tptp_fun_X_44_type, type, (
% 0.20/0.43 tptp_fun_X_44: $i > $i)).
% 0.20/0.43 tff(tptp_fun_Y_49_type, type, (
% 0.20/0.43 tptp_fun_Y_49: $i)).
% 0.20/0.43 tff(p9_type, type, (
% 0.20/0.43 p9: $i > $o)).
% 0.20/0.43 tff(tptp_fun_X_48_type, type, (
% 0.20/0.43 tptp_fun_X_48: $i)).
% 0.20/0.43 tff(tptp_fun_Y_47_type, type, (
% 0.20/0.43 tptp_fun_Y_47: $i)).
% 0.20/0.43 tff(tptp_fun_X_46_type, type, (
% 0.20/0.43 tptp_fun_X_46: $i)).
% 0.20/0.43 tff(tptp_fun_Y_45_type, type, (
% 0.20/0.43 tptp_fun_Y_45: $i)).
% 0.20/0.43 tff(tptp_fun_X_43_type, type, (
% 0.20/0.43 tptp_fun_X_43: $i > $i)).
% 0.20/0.43 tff(p10_type, type, (
% 0.20/0.43 p10: $i > $o)).
% 0.20/0.43 tff(tptp_fun_Y_42_type, type, (
% 0.20/0.43 tptp_fun_Y_42: $i)).
% 0.20/0.43 tff(tptp_fun_X_41_type, type, (
% 0.20/0.43 tptp_fun_X_41: $i)).
% 0.20/0.43 tff(tptp_fun_Y_40_type, type, (
% 0.20/0.43 tptp_fun_Y_40: $i)).
% 0.20/0.43 tff(tptp_fun_X_39_type, type, (
% 0.20/0.43 tptp_fun_X_39: $i)).
% 0.20/0.43 tff(tptp_fun_Y_38_type, type, (
% 0.20/0.43 tptp_fun_Y_38: $i)).
% 0.20/0.43 tff(tptp_fun_X_32_type, type, (
% 0.20/0.43 tptp_fun_X_32: $i > $i)).
% 0.20/0.43 tff(p11_type, type, (
% 0.20/0.43 p11: $i > $o)).
% 0.20/0.43 tff(tptp_fun_X_26_type, type, (
% 0.20/0.43 tptp_fun_X_26: $i > $i)).
% 0.20/0.43 tff(p12_type, type, (
% 0.20/0.43 p12: $i > $o)).
% 0.20/0.43 tff(tptp_fun_Y_37_type, type, (
% 0.20/0.43 tptp_fun_Y_37: $i)).
% 0.20/0.43 tff(tptp_fun_X_36_type, type, (
% 0.20/0.43 tptp_fun_X_36: $i)).
% 0.20/0.43 tff(tptp_fun_Y_35_type, type, (
% 0.20/0.43 tptp_fun_Y_35: $i)).
% 0.20/0.43 tff(tptp_fun_X_34_type, type, (
% 0.20/0.44 tptp_fun_X_34: $i)).
% 0.20/0.44 tff(tptp_fun_Y_33_type, type, (
% 0.20/0.44 tptp_fun_Y_33: $i)).
% 0.20/0.44 tff(tptp_fun_X_20_type, type, (
% 0.20/0.44 tptp_fun_X_20: $i > $i)).
% 0.20/0.44 tff(tptp_fun_Y_31_type, type, (
% 0.20/0.44 tptp_fun_Y_31: $i)).
% 0.20/0.44 tff(tptp_fun_X_30_type, type, (
% 0.20/0.44 tptp_fun_X_30: $i)).
% 0.20/0.44 tff(tptp_fun_Y_29_type, type, (
% 0.20/0.44 tptp_fun_Y_29: $i)).
% 0.20/0.44 tff(tptp_fun_Y_27_type, type, (
% 0.20/0.44 tptp_fun_Y_27: $i)).
% 0.20/0.44 tff(tptp_fun_X_28_type, type, (
% 0.20/0.44 tptp_fun_X_28: $i)).
% 0.20/0.44 tff(tptp_fun_Y_25_type, type, (
% 0.20/0.44 tptp_fun_Y_25: $i)).
% 0.20/0.44 tff(p13_type, type, (
% 0.20/0.44 p13: $i > $o)).
% 0.20/0.44 tff(tptp_fun_X_24_type, type, (
% 0.20/0.44 tptp_fun_X_24: $i)).
% 0.20/0.44 tff(tptp_fun_Y_23_type, type, (
% 0.20/0.44 tptp_fun_Y_23: $i)).
% 0.20/0.44 tff(tptp_fun_X_22_type, type, (
% 0.20/0.44 tptp_fun_X_22: $i)).
% 0.20/0.44 tff(tptp_fun_Y_21_type, type, (
% 0.20/0.44 tptp_fun_Y_21: $i)).
% 0.20/0.44 tff(tptp_fun_X_14_type, type, (
% 0.20/0.44 tptp_fun_X_14: $i > $i)).
% 0.20/0.44 tff(tptp_fun_Y_19_type, type, (
% 0.20/0.44 tptp_fun_Y_19: $i)).
% 0.20/0.44 tff(p14_type, type, (
% 0.20/0.44 p14: $i > $o)).
% 0.20/0.44 tff(tptp_fun_X_18_type, type, (
% 0.20/0.44 tptp_fun_X_18: $i)).
% 0.20/0.44 tff(tptp_fun_Y_17_type, type, (
% 0.20/0.44 tptp_fun_Y_17: $i)).
% 0.20/0.44 tff(tptp_fun_X_16_type, type, (
% 0.20/0.44 tptp_fun_X_16: $i)).
% 0.20/0.44 tff(tptp_fun_Y_15_type, type, (
% 0.20/0.44 tptp_fun_Y_15: $i)).
% 0.20/0.44 tff(tptp_fun_X_13_type, type, (
% 0.20/0.44 tptp_fun_X_13: $i > $i)).
% 0.20/0.44 tff(tptp_fun_X_7_type, type, (
% 0.20/0.44 tptp_fun_X_7: $i > $i)).
% 0.20/0.44 tff(tptp_fun_Y_12_type, type, (
% 0.20/0.44 tptp_fun_Y_12: $i)).
% 0.20/0.44 tff(tptp_fun_X_11_type, type, (
% 0.20/0.44 tptp_fun_X_11: $i)).
% 0.20/0.44 tff(tptp_fun_Y_10_type, type, (
% 0.20/0.44 tptp_fun_Y_10: $i)).
% 0.20/0.44 tff(tptp_fun_X_9_type, type, (
% 0.20/0.44 tptp_fun_X_9: $i)).
% 0.20/0.44 tff(tptp_fun_Y_8_type, type, (
% 0.20/0.44 tptp_fun_Y_8: $i)).
% 0.20/0.44 tff(p16_type, type, (
% 0.20/0.44 p16: $i > $o)).
% 0.20/0.44 tff(tptp_fun_X_6_type, type, (
% 0.20/0.44 tptp_fun_X_6: $i > $i)).
% 0.20/0.44 tff(tptp_fun_Y_5_type, type, (
% 0.20/0.44 tptp_fun_Y_5: $i)).
% 0.20/0.44 tff(tptp_fun_X_4_type, type, (
% 0.20/0.44 tptp_fun_X_4: $i)).
% 0.20/0.44 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.44 tptp_fun_Y_3: $i)).
% 0.20/0.44 tff(tptp_fun_X_2_type, type, (
% 0.20/0.44 tptp_fun_X_2: $i)).
% 0.20/0.44 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.44 tptp_fun_Y_1: $i)).
% 0.20/0.44 tff(1,plain,
% 0.20/0.44 (((((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) | ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) & (((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))) & (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))) | (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | (r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))) | (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y))))) & (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))) | (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))) & (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | (r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))) | (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | (r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))) | (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | (r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))) | (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y))))) & (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | (r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))) | (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))) & $false & (![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(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] : ((~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] : (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))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | (r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))) | (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y))))) & (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(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),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 ((![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(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_81(Y))) | p2(tptp_fun_X_81(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))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (^[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)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (((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)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 ((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),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 ((p1(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p1(X))) <=> (p1(Y!91) & ![X: $i] : (p1(X) | (~r1(Y!91, X))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 ((p2(Y!91) & ![X: $i] : ((~r1(Y!91, X)) | p2(X))) <=> (p2(Y!91) & ![X: $i] : (p2(X) | (~r1(Y!91, X))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 ((~(~r1(X!0, Y!91))) <=> r1(X!0, Y!91)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (((~(~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)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[9, 8, 7])).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 (((~(~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),
% 0.20/0.45 inference(transitivity,[status(thm)],[10, 6])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 ((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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 ((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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(14,plain,
% 0.20/0.45 ((p1(X!90) & ![Y: $i] : ((~r1(X!90, Y)) | p1(Y))) <=> (p1(X!90) & ![Y: $i] : (p1(Y) | (~r1(X!90, Y))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 ((~(~r1(Y!89, X!90))) <=> r1(Y!89, X!90)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (((~(~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)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[15, 14])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (((~(~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))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[16, 13])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 ((p2(Y!89) & ![X: $i] : ((~r1(Y!89, X)) | p2(X))) <=> (p2(Y!89) & ![X: $i] : (p2(X) | (~r1(Y!89, X))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 ((~(~r1(X!0, Y!89))) <=> r1(X!0, Y!89)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 (((~(~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)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[19, 18, 17])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (((~(~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))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[20, 12])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 ((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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 ((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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 ((p2(X!88) & ![Y: $i] : ((~r1(X!88, Y)) | p2(Y))) <=> (p2(X!88) & ![Y: $i] : (p2(Y) | (~r1(X!88, Y))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 ((~(~r1(Y!87, X!88))) <=> r1(Y!87, X!88)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (((~(~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)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[25, 24])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (((~(~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)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[26, 23])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 ((p1(Y!87) & ![X: $i] : ((~r1(Y!87, X)) | p1(X))) <=> (p1(Y!87) & ![X: $i] : (p1(X) | (~r1(Y!87, X))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 ((~(~r1(X!0, Y!87))) <=> r1(X!0, Y!87)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (((~(~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))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[29, 28, 27])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (((~(~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)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[30, 22])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 ((((~(~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)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[31, 21, 11])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 ((((~(~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)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[32, 5])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))) <=> (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))), (((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) <=> ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))))), (((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | p1(Y)))), rewrite(((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))), (((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | p1(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(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_81(Y))) | p2(tptp_fun_X_81(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))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[35, 33, 4])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(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_81(Y))) | p2(tptp_fun_X_81(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))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[36, 2])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 ((![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | ((r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))) | (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | (r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))) | (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (((r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))) | (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y)))) | $false) <=> ((r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))) | (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 ((r1(X!0, Y!86) & (~p3(Y!86)) & (p3(Y!86) & ![X: $i] : (p3(X) | (~r1(Y!86, X)))) & (~p2(Y!86)) & (p2(Y!86) & ![X: $i] : (p2(X) | (~r1(Y!86, X))))) <=> $false),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 ((p2(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p2(X))) <=> (p2(Y!86) & ![X: $i] : (p2(X) | (~r1(Y!86, X))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 ((p3(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p3(X))) <=> (p3(Y!86) & ![X: $i] : (p3(X) | (~r1(Y!86, X))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 ((~(~r1(X!0, Y!86))) <=> r1(X!0, Y!86)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (((~(~r1(X!0, Y!86))) & (~p3(Y!86)) & (p3(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p3(X))) & (~p2(Y!86)) & (p2(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p2(X)))) <=> (r1(X!0, Y!86) & (~p3(Y!86)) & (p3(Y!86) & ![X: $i] : (p3(X) | (~r1(Y!86, X)))) & (~p2(Y!86)) & (p2(Y!86) & ![X: $i] : (p2(X) | (~r1(Y!86, X)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[43, 42, 41])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (((~(~r1(X!0, Y!86))) & (~p3(Y!86)) & (p3(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p3(X))) & (~p2(Y!86)) & (p2(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p2(X)))) <=> $false),
% 0.20/0.46 inference(transitivity,[status(thm)],[44, 40])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 ((r1(X!0, Y!84) & (p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X)))) & (~p2(Y!84)) & (r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y))))) <=> (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 ((r1(Y!84, X!85) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y))))) <=> (r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 ((p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y))) <=> (p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 ((~(~r1(Y!84, X!85))) <=> r1(Y!84, X!85)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (((~(~r1(Y!84, X!85))) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y)))) <=> (r1(Y!84, X!85) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[49, 48])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (((~(~r1(Y!84, X!85))) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y)))) <=> (r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[50, 47])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 ((p3(Y!84) & ![X: $i] : ((~r1(Y!84, X)) | p3(X))) <=> (p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 ((~(~r1(X!0, Y!84))) <=> r1(X!0, Y!84)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (((~(~r1(X!0, Y!84))) & (p3(Y!84) & ![X: $i] : ((~r1(Y!84, X)) | p3(X))) & (~p2(Y!84)) & ((~(~r1(Y!84, X!85))) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y))))) <=> (r1(X!0, Y!84) & (p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X)))) & (~p2(Y!84)) & (r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[53, 52, 51])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (((~(~r1(X!0, Y!84))) & (p3(Y!84) & ![X: $i] : ((~r1(Y!84, X)) | p3(X))) & (~p2(Y!84)) & ((~(~r1(Y!84, X!85))) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y))))) <=> (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[54, 46])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 ((r1(X!0, Y!82) & (~p3(Y!82)) & (p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X)))) & (r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83)))) <=> (r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 ((r1(Y!82, X!83) & (p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y)))) & (~p2(X!83))) <=> (r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 ((p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) <=> (p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 ((~(~r1(Y!82, X!83))) <=> r1(Y!82, X!83)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 (((~(~r1(Y!82, X!83))) & (p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) & (~p2(X!83))) <=> (r1(Y!82, X!83) & (p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y)))) & (~p2(X!83)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[59, 58])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (((~(~r1(Y!82, X!83))) & (p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) & (~p2(X!83))) <=> (r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[60, 57])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 ((p2(Y!82) & ![X: $i] : ((~r1(Y!82, X)) | p2(X))) <=> (p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 ((~(~r1(X!0, Y!82))) <=> r1(X!0, Y!82)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (((~(~r1(X!0, Y!82))) & (~p3(Y!82)) & (p2(Y!82) & ![X: $i] : ((~r1(Y!82, X)) | p2(X))) & ((~(~r1(Y!82, X!83))) & (p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) & (~p2(X!83)))) <=> (r1(X!0, Y!82) & (~p3(Y!82)) & (p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X)))) & (r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[63, 62, 61])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (((~(~r1(X!0, Y!82))) & (~p3(Y!82)) & (p2(Y!82) & ![X: $i] : ((~r1(Y!82, X)) | p2(X))) & ((~(~r1(Y!82, X!83))) & (p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) & (~p2(X!83)))) <=> (r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[64, 56])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 ((((~(~r1(X!0, Y!82))) & (~p3(Y!82)) & (p2(Y!82) & ![X: $i] : ((~r1(Y!82, X)) | p2(X))) & ((~(~r1(Y!82, X!83))) & (p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) & (~p2(X!83)))) | ((~(~r1(X!0, Y!84))) & (p3(Y!84) & ![X: $i] : ((~r1(Y!84, X)) | p3(X))) & (~p2(Y!84)) & ((~(~r1(Y!84, X!85))) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!86))) & (~p3(Y!86)) & (p3(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p3(X))) & (~p2(Y!86)) & (p2(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p2(X))))) <=> ((r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))) | (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y)))) | $false)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[65, 55, 45])).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 ((((~(~r1(X!0, Y!82))) & (~p3(Y!82)) & (p2(Y!82) & ![X: $i] : ((~r1(Y!82, X)) | p2(X))) & ((~(~r1(Y!82, X!83))) & (p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) & (~p2(X!83)))) | ((~(~r1(X!0, Y!84))) & (p3(Y!84) & ![X: $i] : ((~r1(Y!84, X)) | p3(X))) & (~p2(Y!84)) & ((~(~r1(Y!84, X!85))) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!86))) & (~p3(Y!86)) & (p3(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p3(X))) & (~p2(Y!86)) & (p2(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p2(X))))) <=> ((r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))) | (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[66, 39])).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))) <=> (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))), (((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) <=> ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))))), (((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))))), rewrite(((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))), (((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (^[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)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (![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)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 ((![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)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))) | (((~(~r1(X!0, Y!82))) & (~p3(Y!82)) & (p2(Y!82) & ![X: $i] : ((~r1(Y!82, X)) | p2(X))) & ((~(~r1(Y!82, X!83))) & (p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) & (~p2(X!83)))) | ((~(~r1(X!0, Y!84))) & (p3(Y!84) & ![X: $i] : ((~r1(Y!84, X)) | p3(X))) & (~p2(Y!84)) & ((~(~r1(Y!84, X!85))) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!86))) & (~p3(Y!86)) & (p3(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p3(X))) & (~p2(Y!86)) & (p2(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p2(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | ((r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))) | (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[71, 69, 67])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 ((![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)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))) | (((~(~r1(X!0, Y!82))) & (~p3(Y!82)) & (p2(Y!82) & ![X: $i] : ((~r1(Y!82, X)) | p2(X))) & ((~(~r1(Y!82, X!83))) & (p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) & (~p2(X!83)))) | ((~(~r1(X!0, Y!84))) & (p3(Y!84) & ![X: $i] : ((~r1(Y!84, X)) | p3(X))) & (~p2(Y!84)) & ((~(~r1(Y!84, X!85))) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!86))) & (~p3(Y!86)) & (p3(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p3(X))) & (~p2(Y!86)) & (p2(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p2(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_75(Y))) | p3(tptp_fun_X_75(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | (r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))) | (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[72, 38])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 ((![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)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (((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)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 ((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),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 ((p3(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p3(X))) <=> (p3(Y!80) & ![X: $i] : (p3(X) | (~r1(Y!80, X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 ((p4(Y!80) & ![X: $i] : ((~r1(Y!80, X)) | p4(X))) <=> (p4(Y!80) & ![X: $i] : (p4(X) | (~r1(Y!80, X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 ((~(~r1(X!0, Y!80))) <=> r1(X!0, Y!80)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (((~(~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)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[79, 78, 77])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (((~(~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),
% 0.20/0.47 inference(transitivity,[status(thm)],[80, 76])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 ((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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 ((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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 ((p3(X!79) & ![Y: $i] : ((~r1(X!79, Y)) | p3(Y))) <=> (p3(X!79) & ![Y: $i] : (p3(Y) | (~r1(X!79, Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 ((~(~r1(Y!78, X!79))) <=> r1(Y!78, X!79)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (((~(~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)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[85, 84])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (((~(~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))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[86, 83])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 ((p4(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p4(X))) <=> (p4(Y!78) & ![X: $i] : (p4(X) | (~r1(Y!78, X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 ((~(~r1(X!0, Y!78))) <=> r1(X!0, Y!78)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (((~(~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)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[89, 88, 87])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (((~(~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))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[90, 82])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 ((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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 ((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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 ((p4(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p4(Y))) <=> (p4(X!77) & ![Y: $i] : (p4(Y) | (~r1(X!77, Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 ((~(~r1(Y!76, X!77))) <=> r1(Y!76, X!77)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (((~(~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)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[95, 94])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (((~(~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)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[96, 93])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 ((p3(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p3(X))) <=> (p3(Y!76) & ![X: $i] : (p3(X) | (~r1(Y!76, X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 ((~(~r1(X!0, Y!76))) <=> r1(X!0, Y!76)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (((~(~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))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[99, 98, 97])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (((~(~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)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[100, 92])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 ((((~(~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)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[101, 91, 81])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 ((((~(~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)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[102, 75])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (^[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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 (^[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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 ((![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))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[107, 105, 103])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 ((![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)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[108, 74])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 ((((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))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (^[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)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (^[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)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (((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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 ((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),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 ((p4(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p4(X))) <=> (p4(Y!73) & ![X: $i] : (p4(X) | (~r1(Y!73, X))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 ((p5(Y!73) & ![X: $i] : ((~r1(Y!73, X)) | p5(X))) <=> (p5(Y!73) & ![X: $i] : (p5(X) | (~r1(Y!73, X))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 ((~(~r1(X!0, Y!73))) <=> r1(X!0, Y!73)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 (((~(~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)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[119, 118, 117])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 (((~(~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),
% 0.20/0.48 inference(transitivity,[status(thm)],[120, 116])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 ((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))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 ((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))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 ((p4(X!72) & ![Y: $i] : ((~r1(X!72, Y)) | p4(Y))) <=> (p4(X!72) & ![Y: $i] : (p4(Y) | (~r1(X!72, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 ((~(~r1(Y!71, X!72))) <=> r1(Y!71, X!72)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (((~(~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)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[125, 124])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (((~(~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))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[126, 123])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 ((p5(Y!71) & ![X: $i] : ((~r1(Y!71, X)) | p5(X))) <=> (p5(Y!71) & ![X: $i] : (p5(X) | (~r1(Y!71, X))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 ((~(~r1(X!0, Y!71))) <=> r1(X!0, Y!71)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (((~(~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)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[129, 128, 127])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (((~(~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))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[130, 122])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 ((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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 ((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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 ((p5(X!70) & ![Y: $i] : ((~r1(X!70, Y)) | p5(Y))) <=> (p5(X!70) & ![Y: $i] : (p5(Y) | (~r1(X!70, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 ((~(~r1(Y!69, X!70))) <=> r1(Y!69, X!70)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (((~(~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)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[135, 134])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (((~(~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)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[136, 133])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 ((p4(Y!69) & ![X: $i] : ((~r1(Y!69, X)) | p4(X))) <=> (p4(Y!69) & ![X: $i] : (p4(X) | (~r1(Y!69, X))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 ((~(~r1(X!0, Y!69))) <=> r1(X!0, Y!69)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (((~(~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))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[139, 138, 137])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 (((~(~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)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[140, 132])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 ((((~(~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)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[141, 131, 121])).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 ((((~(~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)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[142, 115])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (((((~(~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))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[143, 114, 112])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 (((((~(~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))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[144, 110])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 ((![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] : (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] : ((~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] : (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))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 (^[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)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (![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)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 (((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)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 ((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),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 ((p5(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p5(X))) <=> (p5(Y!68) & ![X: $i] : (p5(X) | (~r1(Y!68, X))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(152,plain,
% 0.20/0.49 ((p6(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p6(X))) <=> (p6(Y!68) & ![X: $i] : (p6(X) | (~r1(Y!68, X))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 ((~(~r1(X!0, Y!68))) <=> r1(X!0, Y!68)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 (((~(~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)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[153, 152, 151])).
% 0.20/0.49 tff(155,plain,
% 0.20/0.49 (((~(~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),
% 0.20/0.49 inference(transitivity,[status(thm)],[154, 150])).
% 0.20/0.49 tff(156,plain,
% 0.20/0.49 ((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))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(157,plain,
% 0.20/0.49 ((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))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 ((p5(X!67) & ![Y: $i] : ((~r1(X!67, Y)) | p5(Y))) <=> (p5(X!67) & ![Y: $i] : (p5(Y) | (~r1(X!67, Y))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 ((~(~r1(Y!66, X!67))) <=> r1(Y!66, X!67)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 (((~(~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)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[159, 158])).
% 0.20/0.49 tff(161,plain,
% 0.20/0.49 (((~(~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))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[160, 157])).
% 0.20/0.49 tff(162,plain,
% 0.20/0.49 ((p6(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p6(X))) <=> (p6(Y!66) & ![X: $i] : (p6(X) | (~r1(Y!66, X))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(163,plain,
% 0.20/0.49 ((~(~r1(X!0, Y!66))) <=> r1(X!0, Y!66)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(164,plain,
% 0.20/0.49 (((~(~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)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[163, 162, 161])).
% 0.20/0.49 tff(165,plain,
% 0.20/0.49 (((~(~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))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[164, 156])).
% 0.20/0.49 tff(166,plain,
% 0.20/0.49 ((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))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(167,plain,
% 0.20/0.49 ((p5(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p5(X))) <=> (p5(Y!64) & ![X: $i] : (p5(X) | (~r1(Y!64, X))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(168,plain,
% 0.20/0.49 ((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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(169,plain,
% 0.20/0.49 ((p6(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p6(Y))) <=> (p6(X!65) & ![Y: $i] : (p6(Y) | (~r1(X!65, Y))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 ((~(~r1(Y!64, X!65))) <=> r1(Y!64, X!65)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(171,plain,
% 0.20/0.49 (((~(~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)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[170, 169])).
% 0.20/0.49 tff(172,plain,
% 0.20/0.49 (((~(~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)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[171, 168])).
% 0.20/0.49 tff(173,plain,
% 0.20/0.49 ((~(~r1(X!0, Y!64))) <=> r1(X!0, Y!64)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(174,plain,
% 0.20/0.49 (((~(~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)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[173, 172, 167])).
% 0.20/0.49 tff(175,plain,
% 0.20/0.49 (((~(~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))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[174, 166])).
% 0.20/0.49 tff(176,plain,
% 0.20/0.49 ((((~(~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)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[175, 165, 155])).
% 0.20/0.49 tff(177,plain,
% 0.20/0.49 ((((~(~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)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[176, 149])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 (^[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)))))) <=> ((~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)))))) <=> ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 (![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] : ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_63(Y))) | p5(tptp_fun_X_63(Y)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[178])).
% 0.20/0.49 tff(180,plain,
% 0.20/0.49 ((![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] : ((~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] : (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))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[179, 177, 148])).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 ((![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] : ((~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] : (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))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[180, 146])).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(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] : ((~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) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(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] : ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(183,plain,
% 0.20/0.50 (^[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)))))) <=> ((~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)))))) <=> ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(184,plain,
% 0.20/0.50 (![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)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[183])).
% 0.20/0.50 tff(185,plain,
% 0.20/0.50 (((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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(186,plain,
% 0.20/0.50 ((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),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 ((p6(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p6(X))) <=> (p6(Y!61) & ![X: $i] : (p6(X) | (~r1(Y!61, X))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(188,plain,
% 0.20/0.50 ((p7(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p7(X))) <=> (p7(Y!61) & ![X: $i] : (p7(X) | (~r1(Y!61, X))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 ((~(~r1(X!0, Y!61))) <=> r1(X!0, Y!61)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(190,plain,
% 0.20/0.50 (((~(~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)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[189, 188, 187])).
% 0.20/0.50 tff(191,plain,
% 0.20/0.50 (((~(~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),
% 0.20/0.50 inference(transitivity,[status(thm)],[190, 186])).
% 0.20/0.50 tff(192,plain,
% 0.20/0.50 ((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))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(193,plain,
% 0.20/0.50 ((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))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(194,plain,
% 0.20/0.50 ((p6(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p6(Y))) <=> (p6(X!60) & ![Y: $i] : (p6(Y) | (~r1(X!60, Y))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(195,plain,
% 0.20/0.50 ((~(~r1(Y!59, X!60))) <=> r1(Y!59, X!60)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(196,plain,
% 0.20/0.50 (((~(~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)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[195, 194])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 (((~(~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))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[196, 193])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 ((p7(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p7(X))) <=> (p7(Y!59) & ![X: $i] : (p7(X) | (~r1(Y!59, X))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 ((~(~r1(X!0, Y!59))) <=> r1(X!0, Y!59)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(200,plain,
% 0.20/0.50 (((~(~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)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[199, 198, 197])).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 (((~(~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))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[200, 192])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 ((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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(203,plain,
% 0.20/0.50 ((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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(204,plain,
% 0.20/0.50 ((p7(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p7(Y))) <=> (p7(X!58) & ![Y: $i] : (p7(Y) | (~r1(X!58, Y))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 ((~(~r1(Y!57, X!58))) <=> r1(Y!57, X!58)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(206,plain,
% 0.20/0.50 (((~(~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)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[205, 204])).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 (((~(~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)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[206, 203])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 ((p6(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p6(X))) <=> (p6(Y!57) & ![X: $i] : (p6(X) | (~r1(Y!57, X))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(209,plain,
% 0.20/0.50 ((~(~r1(X!0, Y!57))) <=> r1(X!0, Y!57)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 (((~(~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))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[209, 208, 207])).
% 0.20/0.50 tff(211,plain,
% 0.20/0.50 (((~(~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)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[210, 202])).
% 0.20/0.50 tff(212,plain,
% 0.20/0.50 ((((~(~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)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[211, 201, 191])).
% 0.20/0.50 tff(213,plain,
% 0.20/0.50 ((((~(~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)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[212, 185])).
% 0.20/0.50 tff(214,plain,
% 0.20/0.50 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))) <=> (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))), (((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))) <=> ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))))), (((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))) | p6(Y)) <=> ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))) | p6(Y)))), rewrite(((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))) | p6(Y)) <=> ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))), (((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))) | p6(Y)) <=> ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(215,plain,
% 0.20/0.50 (![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))) | p6(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[214])).
% 0.20/0.50 tff(216,plain,
% 0.20/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(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) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(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] : ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[215, 213, 184])).
% 0.20/0.50 tff(217,plain,
% 0.20/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(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) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(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] : ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p6(tptp_fun_X_62(Y))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[216, 182])).
% 0.20/0.50 tff(218,plain,
% 0.20/0.50 (((~p15(Y!56)) & r1(X!0, Y!56) & (![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56))) <=> $false),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(219,plain,
% 0.20/0.50 ((![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56)) <=> (![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(220,plain,
% 0.20/0.50 ((~(~r1(X!0, Y!56))) <=> r1(X!0, Y!56)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(221,plain,
% 0.20/0.50 (((~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)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[220, 219])).
% 0.20/0.50 tff(222,plain,
% 0.20/0.50 (((~p15(Y!56)) & (~(~r1(X!0, Y!56))) & (![X: $i] : (p15(X) | (~r1(Y!56, X))) & p15(Y!56))) <=> $false),
% 0.20/0.50 inference(transitivity,[status(thm)],[221, 218])).
% 0.20/0.50 tff(223,plain,
% 0.20/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | ((r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))) | (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | (r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))) | (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(224,plain,
% 0.20/0.51 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))) <=> (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))), (((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))) <=> ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))))), (((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))) <=> ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))))), rewrite(((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))) <=> ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))), (((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))) <=> ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[224])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 (((r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))) | (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y)))) | $false) <=> ((r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))) | (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 ((r1(X!0, Y!54) & (~p8(Y!54)) & (p8(Y!54) & ![X: $i] : (p8(X) | (~r1(Y!54, X)))) & (~p7(Y!54)) & (p7(Y!54) & ![X: $i] : (p7(X) | (~r1(Y!54, X))))) <=> $false),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 ((p7(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p7(X))) <=> (p7(Y!54) & ![X: $i] : (p7(X) | (~r1(Y!54, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 ((p8(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p8(X))) <=> (p8(Y!54) & ![X: $i] : (p8(X) | (~r1(Y!54, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(230,plain,
% 0.20/0.51 ((~(~r1(X!0, Y!54))) <=> r1(X!0, Y!54)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(231,plain,
% 0.20/0.51 (((~(~r1(X!0, Y!54))) & (~p8(Y!54)) & (p8(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p8(X))) & (~p7(Y!54)) & (p7(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p7(X)))) <=> (r1(X!0, Y!54) & (~p8(Y!54)) & (p8(Y!54) & ![X: $i] : (p8(X) | (~r1(Y!54, X)))) & (~p7(Y!54)) & (p7(Y!54) & ![X: $i] : (p7(X) | (~r1(Y!54, X)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[230, 229, 228])).
% 0.20/0.51 tff(232,plain,
% 0.20/0.51 (((~(~r1(X!0, Y!54))) & (~p8(Y!54)) & (p8(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p8(X))) & (~p7(Y!54)) & (p7(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p7(X)))) <=> $false),
% 0.20/0.51 inference(transitivity,[status(thm)],[231, 227])).
% 0.20/0.51 tff(233,plain,
% 0.20/0.51 ((r1(X!0, Y!52) & (p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X)))) & (~p7(Y!52)) & (r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y))))) <=> (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(234,plain,
% 0.20/0.51 ((r1(Y!52, X!53) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y))))) <=> (r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(235,plain,
% 0.20/0.51 ((p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y))) <=> (p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(236,plain,
% 0.20/0.51 ((~(~r1(Y!52, X!53))) <=> r1(Y!52, X!53)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(237,plain,
% 0.20/0.51 (((~(~r1(Y!52, X!53))) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y)))) <=> (r1(Y!52, X!53) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[236, 235])).
% 0.20/0.51 tff(238,plain,
% 0.20/0.51 (((~(~r1(Y!52, X!53))) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y)))) <=> (r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[237, 234])).
% 0.20/0.51 tff(239,plain,
% 0.20/0.51 ((p8(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p8(X))) <=> (p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(240,plain,
% 0.20/0.51 ((~(~r1(X!0, Y!52))) <=> r1(X!0, Y!52)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(241,plain,
% 0.20/0.51 (((~(~r1(X!0, Y!52))) & (p8(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p8(X))) & (~p7(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y))))) <=> (r1(X!0, Y!52) & (p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X)))) & (~p7(Y!52)) & (r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[240, 239, 238])).
% 0.20/0.51 tff(242,plain,
% 0.20/0.51 (((~(~r1(X!0, Y!52))) & (p8(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p8(X))) & (~p7(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y))))) <=> (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[241, 233])).
% 0.20/0.51 tff(243,plain,
% 0.20/0.51 ((r1(X!0, Y!50) & (~p8(Y!50)) & (p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X)))) & (r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51)))) <=> (r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(244,plain,
% 0.20/0.51 ((r1(Y!50, X!51) & (p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y)))) & (~p7(X!51))) <=> (r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(245,plain,
% 0.20/0.51 ((p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) <=> (p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 ((~(~r1(Y!50, X!51))) <=> r1(Y!50, X!51)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(247,plain,
% 0.20/0.51 (((~(~r1(Y!50, X!51))) & (p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) & (~p7(X!51))) <=> (r1(Y!50, X!51) & (p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y)))) & (~p7(X!51)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[246, 245])).
% 0.20/0.51 tff(248,plain,
% 0.20/0.51 (((~(~r1(Y!50, X!51))) & (p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) & (~p7(X!51))) <=> (r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[247, 244])).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 ((p7(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p7(X))) <=> (p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 ((~(~r1(X!0, Y!50))) <=> r1(X!0, Y!50)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(251,plain,
% 0.20/0.51 (((~(~r1(X!0, Y!50))) & (~p8(Y!50)) & (p7(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p7(X))) & ((~(~r1(Y!50, X!51))) & (p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) & (~p7(X!51)))) <=> (r1(X!0, Y!50) & (~p8(Y!50)) & (p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X)))) & (r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[250, 249, 248])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 (((~(~r1(X!0, Y!50))) & (~p8(Y!50)) & (p7(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p7(X))) & ((~(~r1(Y!50, X!51))) & (p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) & (~p7(X!51)))) <=> (r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[251, 243])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 ((((~(~r1(X!0, Y!50))) & (~p8(Y!50)) & (p7(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p7(X))) & ((~(~r1(Y!50, X!51))) & (p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) & (~p7(X!51)))) | ((~(~r1(X!0, Y!52))) & (p8(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p8(X))) & (~p7(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!54))) & (~p8(Y!54)) & (p8(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p8(X))) & (~p7(Y!54)) & (p7(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p7(X))))) <=> ((r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))) | (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y)))) | $false)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[252, 242, 232])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 ((((~(~r1(X!0, Y!50))) & (~p8(Y!50)) & (p7(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p7(X))) & ((~(~r1(Y!50, X!51))) & (p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) & (~p7(X!51)))) | ((~(~r1(X!0, Y!52))) & (p8(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p8(X))) & (~p7(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!54))) & (~p8(Y!54)) & (p8(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p8(X))) & (~p7(Y!54)) & (p7(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p7(X))))) <=> ((r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))) | (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y)))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[253, 226])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))) <=> (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | p7(Y)) <=> ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | p7(Y)))), rewrite(((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | p7(Y)) <=> ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | p7(Y)) <=> ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | p7(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[255])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | p7(Y)) | (((~(~r1(X!0, Y!50))) & (~p8(Y!50)) & (p7(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p7(X))) & ((~(~r1(Y!50, X!51))) & (p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) & (~p7(X!51)))) | ((~(~r1(X!0, Y!52))) & (p8(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p8(X))) & (~p7(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!54))) & (~p8(Y!54)) & (p8(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p8(X))) & (~p7(Y!54)) & (p7(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | ((r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))) | (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[256, 254, 225])).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | p7(Y)) | (((~(~r1(X!0, Y!50))) & (~p8(Y!50)) & (p7(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p7(X))) & ((~(~r1(Y!50, X!51))) & (p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) & (~p7(X!51)))) | ((~(~r1(X!0, Y!52))) & (p8(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p8(X))) & (~p7(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!54))) & (~p8(Y!54)) & (p8(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p8(X))) & (~p7(Y!54)) & (p7(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | (r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))) | (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[257, 223])).
% 0.20/0.51 tff(259,plain,
% 0.20/0.51 ((![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | ((r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))) | (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | (r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))) | (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(260,plain,
% 0.20/0.51 (((r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))) | (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y)))) | $false) <=> ((r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))) | (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 ((r1(X!0, Y!49) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : (p9(X) | (~r1(Y!49, X)))) & (~p8(Y!49)) & (p8(Y!49) & ![X: $i] : (p8(X) | (~r1(Y!49, X))))) <=> $false),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(262,plain,
% 0.20/0.52 ((p8(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p8(X))) <=> (p8(Y!49) & ![X: $i] : (p8(X) | (~r1(Y!49, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(263,plain,
% 0.20/0.52 ((p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))) <=> (p9(Y!49) & ![X: $i] : (p9(X) | (~r1(Y!49, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(264,plain,
% 0.20/0.52 ((~(~r1(X!0, Y!49))) <=> r1(X!0, Y!49)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(265,plain,
% 0.20/0.52 (((~(~r1(X!0, Y!49))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))) & (~p8(Y!49)) & (p8(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p8(X)))) <=> (r1(X!0, Y!49) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : (p9(X) | (~r1(Y!49, X)))) & (~p8(Y!49)) & (p8(Y!49) & ![X: $i] : (p8(X) | (~r1(Y!49, X)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[264, 263, 262])).
% 0.20/0.52 tff(266,plain,
% 0.20/0.52 (((~(~r1(X!0, Y!49))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))) & (~p8(Y!49)) & (p8(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p8(X)))) <=> $false),
% 0.20/0.52 inference(transitivity,[status(thm)],[265, 261])).
% 0.20/0.52 tff(267,plain,
% 0.20/0.52 ((r1(X!0, Y!47) & (p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X)))) & (~p8(Y!47)) & (r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y))))) <=> (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(268,plain,
% 0.20/0.52 ((r1(Y!47, X!48) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y))))) <=> (r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(269,plain,
% 0.20/0.52 ((p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y))) <=> (p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(270,plain,
% 0.20/0.52 ((~(~r1(Y!47, X!48))) <=> r1(Y!47, X!48)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(271,plain,
% 0.20/0.52 (((~(~r1(Y!47, X!48))) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y)))) <=> (r1(Y!47, X!48) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[270, 269])).
% 0.20/0.52 tff(272,plain,
% 0.20/0.52 (((~(~r1(Y!47, X!48))) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y)))) <=> (r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[271, 268])).
% 0.20/0.52 tff(273,plain,
% 0.20/0.52 ((p9(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p9(X))) <=> (p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(274,plain,
% 0.20/0.52 ((~(~r1(X!0, Y!47))) <=> r1(X!0, Y!47)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(275,plain,
% 0.20/0.52 (((~(~r1(X!0, Y!47))) & (p9(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p9(X))) & (~p8(Y!47)) & ((~(~r1(Y!47, X!48))) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y))))) <=> (r1(X!0, Y!47) & (p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X)))) & (~p8(Y!47)) & (r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[274, 273, 272])).
% 0.20/0.52 tff(276,plain,
% 0.20/0.52 (((~(~r1(X!0, Y!47))) & (p9(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p9(X))) & (~p8(Y!47)) & ((~(~r1(Y!47, X!48))) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y))))) <=> (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[275, 267])).
% 0.20/0.52 tff(277,plain,
% 0.20/0.52 ((r1(X!0, Y!45) & (~p9(Y!45)) & (p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X)))) & (r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46)))) <=> (r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(278,plain,
% 0.20/0.52 ((r1(Y!45, X!46) & (p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y)))) & (~p8(X!46))) <=> (r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(279,plain,
% 0.20/0.52 ((p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) <=> (p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(280,plain,
% 0.20/0.52 ((~(~r1(Y!45, X!46))) <=> r1(Y!45, X!46)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(281,plain,
% 0.20/0.52 (((~(~r1(Y!45, X!46))) & (p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) & (~p8(X!46))) <=> (r1(Y!45, X!46) & (p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y)))) & (~p8(X!46)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[280, 279])).
% 0.20/0.52 tff(282,plain,
% 0.20/0.52 (((~(~r1(Y!45, X!46))) & (p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) & (~p8(X!46))) <=> (r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[281, 278])).
% 0.20/0.52 tff(283,plain,
% 0.20/0.52 ((p8(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p8(X))) <=> (p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(284,plain,
% 0.20/0.52 ((~(~r1(X!0, Y!45))) <=> r1(X!0, Y!45)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(285,plain,
% 0.20/0.52 (((~(~r1(X!0, Y!45))) & (~p9(Y!45)) & (p8(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p8(X))) & ((~(~r1(Y!45, X!46))) & (p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) & (~p8(X!46)))) <=> (r1(X!0, Y!45) & (~p9(Y!45)) & (p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X)))) & (r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[284, 283, 282])).
% 0.20/0.52 tff(286,plain,
% 0.20/0.52 (((~(~r1(X!0, Y!45))) & (~p9(Y!45)) & (p8(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p8(X))) & ((~(~r1(Y!45, X!46))) & (p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) & (~p8(X!46)))) <=> (r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[285, 277])).
% 0.20/0.52 tff(287,plain,
% 0.20/0.52 ((((~(~r1(X!0, Y!45))) & (~p9(Y!45)) & (p8(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p8(X))) & ((~(~r1(Y!45, X!46))) & (p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) & (~p8(X!46)))) | ((~(~r1(X!0, Y!47))) & (p9(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p9(X))) & (~p8(Y!47)) & ((~(~r1(Y!47, X!48))) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!49))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))) & (~p8(Y!49)) & (p8(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p8(X))))) <=> ((r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))) | (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y)))) | $false)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[286, 276, 266])).
% 0.20/0.52 tff(288,plain,
% 0.20/0.52 ((((~(~r1(X!0, Y!45))) & (~p9(Y!45)) & (p8(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p8(X))) & ((~(~r1(Y!45, X!46))) & (p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) & (~p8(X!46)))) | ((~(~r1(X!0, Y!47))) & (p9(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p9(X))) & (~p8(Y!47)) & ((~(~r1(Y!47, X!48))) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!49))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))) & (~p8(Y!49)) & (p8(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p8(X))))) <=> ((r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))) | (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[287, 260])).
% 0.20/0.52 tff(289,plain,
% 0.20/0.52 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))) <=> (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))) <=> ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))))), rewrite(((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))) <=> ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))) <=> ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(290,plain,
% 0.20/0.52 (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[289])).
% 0.20/0.52 tff(291,plain,
% 0.20/0.52 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))) <=> (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))), (((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) <=> ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))))), (((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | p8(Y)) <=> ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | p8(Y)))), rewrite(((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | p8(Y)) <=> ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))), (((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | p8(Y)) <=> ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(292,plain,
% 0.20/0.52 (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | p8(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[291])).
% 0.20/0.52 tff(293,plain,
% 0.20/0.52 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))) | (((~(~r1(X!0, Y!45))) & (~p9(Y!45)) & (p8(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p8(X))) & ((~(~r1(Y!45, X!46))) & (p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) & (~p8(X!46)))) | ((~(~r1(X!0, Y!47))) & (p9(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p9(X))) & (~p8(Y!47)) & ((~(~r1(Y!47, X!48))) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!49))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))) & (~p8(Y!49)) & (p8(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p8(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | ((r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))) | (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[292, 290, 288])).
% 0.20/0.52 tff(294,plain,
% 0.20/0.52 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))) | (((~(~r1(X!0, Y!45))) & (~p9(Y!45)) & (p8(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p8(X))) & ((~(~r1(Y!45, X!46))) & (p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) & (~p8(X!46)))) | ((~(~r1(X!0, Y!47))) & (p9(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p9(X))) & (~p8(Y!47)) & ((~(~r1(Y!47, X!48))) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!49))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))) & (~p8(Y!49)) & (p8(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p8(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | (r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))) | (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[293, 259])).
% 0.20/0.52 tff(295,plain,
% 0.20/0.52 ((![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | ((r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))) | (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | (r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))) | (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(296,plain,
% 0.20/0.52 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))) <=> (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))), (((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) <=> ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))))), (((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))) <=> ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))))), rewrite(((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))) <=> ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))), (((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))) <=> ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(297,plain,
% 0.20/0.52 (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[296])).
% 0.20/0.52 tff(298,plain,
% 0.20/0.52 (((r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))) | (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))) | $false) <=> ((r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))) | (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(299,plain,
% 0.20/0.52 ((r1(X!0, Y!42) & (~p10(Y!42)) & (p10(Y!42) & ![X: $i] : (p10(X) | (~r1(Y!42, X)))) & (~p9(Y!42)) & (p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))))) <=> $false),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(300,plain,
% 0.20/0.53 ((p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))) <=> (p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(301,plain,
% 0.20/0.53 ((p10(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p10(X))) <=> (p10(Y!42) & ![X: $i] : (p10(X) | (~r1(Y!42, X))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(302,plain,
% 0.20/0.53 ((~(~r1(X!0, Y!42))) <=> r1(X!0, Y!42)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(303,plain,
% 0.20/0.53 (((~(~r1(X!0, Y!42))) & (~p10(Y!42)) & (p10(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p10(X))) & (~p9(Y!42)) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X)))) <=> (r1(X!0, Y!42) & (~p10(Y!42)) & (p10(Y!42) & ![X: $i] : (p10(X) | (~r1(Y!42, X)))) & (~p9(Y!42)) & (p9(Y!42) & ![X: $i] : (p9(X) | (~r1(Y!42, X)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[302, 301, 300])).
% 0.20/0.53 tff(304,plain,
% 0.20/0.53 (((~(~r1(X!0, Y!42))) & (~p10(Y!42)) & (p10(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p10(X))) & (~p9(Y!42)) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X)))) <=> $false),
% 0.20/0.53 inference(transitivity,[status(thm)],[303, 299])).
% 0.20/0.53 tff(305,plain,
% 0.20/0.53 ((r1(X!0, Y!40) & (p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X)))) & (~p9(Y!40)) & (r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))))) <=> (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(306,plain,
% 0.20/0.53 ((r1(Y!40, X!41) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))))) <=> (r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(307,plain,
% 0.20/0.53 ((p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))) <=> (p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(308,plain,
% 0.20/0.53 ((~(~r1(Y!40, X!41))) <=> r1(Y!40, X!41)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(309,plain,
% 0.20/0.53 (((~(~r1(Y!40, X!41))) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y)))) <=> (r1(Y!40, X!41) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[308, 307])).
% 0.20/0.53 tff(310,plain,
% 0.20/0.53 (((~(~r1(Y!40, X!41))) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y)))) <=> (r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[309, 306])).
% 0.20/0.53 tff(311,plain,
% 0.20/0.53 ((p10(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p10(X))) <=> (p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(312,plain,
% 0.20/0.53 ((~(~r1(X!0, Y!40))) <=> r1(X!0, Y!40)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(313,plain,
% 0.20/0.53 (((~(~r1(X!0, Y!40))) & (p10(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p10(X))) & (~p9(Y!40)) & ((~(~r1(Y!40, X!41))) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))))) <=> (r1(X!0, Y!40) & (p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X)))) & (~p9(Y!40)) & (r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[312, 311, 310])).
% 0.20/0.53 tff(314,plain,
% 0.20/0.53 (((~(~r1(X!0, Y!40))) & (p10(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p10(X))) & (~p9(Y!40)) & ((~(~r1(Y!40, X!41))) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))))) <=> (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[313, 305])).
% 0.20/0.53 tff(315,plain,
% 0.20/0.53 ((r1(X!0, Y!38) & (~p10(Y!38)) & (p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X)))) & (r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39)))) <=> (r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(316,plain,
% 0.20/0.53 ((r1(Y!38, X!39) & (p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y)))) & (~p9(X!39))) <=> (r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(317,plain,
% 0.20/0.53 ((p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) <=> (p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(318,plain,
% 0.20/0.53 ((~(~r1(Y!38, X!39))) <=> r1(Y!38, X!39)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(319,plain,
% 0.20/0.53 (((~(~r1(Y!38, X!39))) & (p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) & (~p9(X!39))) <=> (r1(Y!38, X!39) & (p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y)))) & (~p9(X!39)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[318, 317])).
% 0.20/0.53 tff(320,plain,
% 0.20/0.53 (((~(~r1(Y!38, X!39))) & (p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) & (~p9(X!39))) <=> (r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[319, 316])).
% 0.20/0.53 tff(321,plain,
% 0.20/0.53 ((p9(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p9(X))) <=> (p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(322,plain,
% 0.20/0.53 ((~(~r1(X!0, Y!38))) <=> r1(X!0, Y!38)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(323,plain,
% 0.20/0.53 (((~(~r1(X!0, Y!38))) & (~p10(Y!38)) & (p9(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p9(X))) & ((~(~r1(Y!38, X!39))) & (p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) & (~p9(X!39)))) <=> (r1(X!0, Y!38) & (~p10(Y!38)) & (p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X)))) & (r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[322, 321, 320])).
% 0.20/0.53 tff(324,plain,
% 0.20/0.53 (((~(~r1(X!0, Y!38))) & (~p10(Y!38)) & (p9(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p9(X))) & ((~(~r1(Y!38, X!39))) & (p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) & (~p9(X!39)))) <=> (r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[323, 315])).
% 0.20/0.53 tff(325,plain,
% 0.20/0.53 ((((~(~r1(X!0, Y!38))) & (~p10(Y!38)) & (p9(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p9(X))) & ((~(~r1(Y!38, X!39))) & (p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) & (~p9(X!39)))) | ((~(~r1(X!0, Y!40))) & (p10(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p10(X))) & (~p9(Y!40)) & ((~(~r1(Y!40, X!41))) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))))) | ((~(~r1(X!0, Y!42))) & (~p10(Y!42)) & (p10(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p10(X))) & (~p9(Y!42)) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))))) <=> ((r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))) | (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))) | $false)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[324, 314, 304])).
% 0.20/0.53 tff(326,plain,
% 0.20/0.53 ((((~(~r1(X!0, Y!38))) & (~p10(Y!38)) & (p9(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p9(X))) & ((~(~r1(Y!38, X!39))) & (p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) & (~p9(X!39)))) | ((~(~r1(X!0, Y!40))) & (p10(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p10(X))) & (~p9(Y!40)) & ((~(~r1(Y!40, X!41))) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))))) | ((~(~r1(X!0, Y!42))) & (~p10(Y!42)) & (p10(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p10(X))) & (~p9(Y!42)) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))))) <=> ((r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))) | (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[325, 298])).
% 0.20/0.53 tff(327,plain,
% 0.20/0.53 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))) <=> (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))), (((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) <=> ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))))), (((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | p9(Y)) <=> ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | p9(Y)))), rewrite(((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | p9(Y)) <=> ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))), (((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | p9(Y)) <=> ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(328,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | p9(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[327])).
% 0.20/0.54 tff(329,plain,
% 0.20/0.54 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | p9(Y)) | (((~(~r1(X!0, Y!38))) & (~p10(Y!38)) & (p9(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p9(X))) & ((~(~r1(Y!38, X!39))) & (p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) & (~p9(X!39)))) | ((~(~r1(X!0, Y!40))) & (p10(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p10(X))) & (~p9(Y!40)) & ((~(~r1(Y!40, X!41))) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))))) | ((~(~r1(X!0, Y!42))) & (~p10(Y!42)) & (p10(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p10(X))) & (~p9(Y!42)) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | ((r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))) | (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[328, 326, 297])).
% 0.20/0.54 tff(330,plain,
% 0.20/0.54 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | p9(Y)) | (((~(~r1(X!0, Y!38))) & (~p10(Y!38)) & (p9(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p9(X))) & ((~(~r1(Y!38, X!39))) & (p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) & (~p9(X!39)))) | ((~(~r1(X!0, Y!40))) & (p10(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p10(X))) & (~p9(Y!40)) & ((~(~r1(Y!40, X!41))) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))))) | ((~(~r1(X!0, Y!42))) & (~p10(Y!42)) & (p10(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p10(X))) & (~p9(Y!42)) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | (r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))) | (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[329, 295])).
% 0.20/0.54 tff(331,plain,
% 0.20/0.54 ((![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | ((r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))) | (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) <=> (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | (r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))) | (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(332,plain,
% 0.20/0.54 (^[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)))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(333,plain,
% 0.20/0.54 (![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)))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[332])).
% 0.20/0.54 tff(334,plain,
% 0.20/0.54 (((r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))) | (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y)))) | $false) <=> ((r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))) | (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(335,plain,
% 0.20/0.54 ((r1(X!0, Y!37) & (~p12(Y!37)) & (p12(Y!37) & ![X: $i] : (p12(X) | (~r1(Y!37, X)))) & (~p11(Y!37)) & (p11(Y!37) & ![X: $i] : (p11(X) | (~r1(Y!37, X))))) <=> $false),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(336,plain,
% 0.20/0.54 ((p11(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p11(X))) <=> (p11(Y!37) & ![X: $i] : (p11(X) | (~r1(Y!37, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(337,plain,
% 0.20/0.54 ((p12(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p12(X))) <=> (p12(Y!37) & ![X: $i] : (p12(X) | (~r1(Y!37, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(338,plain,
% 0.20/0.54 ((~(~r1(X!0, Y!37))) <=> r1(X!0, Y!37)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(339,plain,
% 0.20/0.54 (((~(~r1(X!0, Y!37))) & (~p12(Y!37)) & (p12(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p12(X))) & (~p11(Y!37)) & (p11(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p11(X)))) <=> (r1(X!0, Y!37) & (~p12(Y!37)) & (p12(Y!37) & ![X: $i] : (p12(X) | (~r1(Y!37, X)))) & (~p11(Y!37)) & (p11(Y!37) & ![X: $i] : (p11(X) | (~r1(Y!37, X)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[338, 337, 336])).
% 0.20/0.54 tff(340,plain,
% 0.20/0.54 (((~(~r1(X!0, Y!37))) & (~p12(Y!37)) & (p12(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p12(X))) & (~p11(Y!37)) & (p11(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p11(X)))) <=> $false),
% 0.20/0.54 inference(transitivity,[status(thm)],[339, 335])).
% 0.20/0.54 tff(341,plain,
% 0.20/0.54 ((r1(X!0, Y!35) & (p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X)))) & (~p11(Y!35)) & (r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y))))) <=> (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(342,plain,
% 0.20/0.54 ((r1(Y!35, X!36) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y))))) <=> (r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(343,plain,
% 0.20/0.54 ((p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y))) <=> (p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(344,plain,
% 0.20/0.54 ((~(~r1(Y!35, X!36))) <=> r1(Y!35, X!36)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(345,plain,
% 0.20/0.54 (((~(~r1(Y!35, X!36))) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y)))) <=> (r1(Y!35, X!36) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[344, 343])).
% 0.20/0.54 tff(346,plain,
% 0.20/0.54 (((~(~r1(Y!35, X!36))) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y)))) <=> (r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[345, 342])).
% 0.20/0.54 tff(347,plain,
% 0.20/0.54 ((p12(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p12(X))) <=> (p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(348,plain,
% 0.20/0.54 ((~(~r1(X!0, Y!35))) <=> r1(X!0, Y!35)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(349,plain,
% 0.20/0.54 (((~(~r1(X!0, Y!35))) & (p12(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p12(X))) & (~p11(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y))))) <=> (r1(X!0, Y!35) & (p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X)))) & (~p11(Y!35)) & (r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[348, 347, 346])).
% 0.20/0.54 tff(350,plain,
% 0.20/0.54 (((~(~r1(X!0, Y!35))) & (p12(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p12(X))) & (~p11(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y))))) <=> (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[349, 341])).
% 0.20/0.54 tff(351,plain,
% 0.20/0.54 ((r1(X!0, Y!33) & (~p12(Y!33)) & (p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X)))) & (r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34)))) <=> (r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(352,plain,
% 0.20/0.54 ((r1(Y!33, X!34) & (p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y)))) & (~p11(X!34))) <=> (r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(353,plain,
% 0.20/0.54 ((p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) <=> (p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(354,plain,
% 0.20/0.54 ((~(~r1(Y!33, X!34))) <=> r1(Y!33, X!34)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(355,plain,
% 0.20/0.54 (((~(~r1(Y!33, X!34))) & (p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) & (~p11(X!34))) <=> (r1(Y!33, X!34) & (p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y)))) & (~p11(X!34)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[354, 353])).
% 0.20/0.54 tff(356,plain,
% 0.20/0.54 (((~(~r1(Y!33, X!34))) & (p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) & (~p11(X!34))) <=> (r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[355, 352])).
% 0.20/0.55 tff(357,plain,
% 0.20/0.55 ((p11(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p11(X))) <=> (p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(358,plain,
% 0.20/0.55 ((~(~r1(X!0, Y!33))) <=> r1(X!0, Y!33)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(359,plain,
% 0.20/0.55 (((~(~r1(X!0, Y!33))) & (~p12(Y!33)) & (p11(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p11(X))) & ((~(~r1(Y!33, X!34))) & (p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) & (~p11(X!34)))) <=> (r1(X!0, Y!33) & (~p12(Y!33)) & (p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X)))) & (r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[358, 357, 356])).
% 0.20/0.55 tff(360,plain,
% 0.20/0.55 (((~(~r1(X!0, Y!33))) & (~p12(Y!33)) & (p11(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p11(X))) & ((~(~r1(Y!33, X!34))) & (p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) & (~p11(X!34)))) <=> (r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[359, 351])).
% 0.20/0.55 tff(361,plain,
% 0.20/0.55 ((((~(~r1(X!0, Y!33))) & (~p12(Y!33)) & (p11(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p11(X))) & ((~(~r1(Y!33, X!34))) & (p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) & (~p11(X!34)))) | ((~(~r1(X!0, Y!35))) & (p12(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p12(X))) & (~p11(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!37))) & (~p12(Y!37)) & (p12(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p12(X))) & (~p11(Y!37)) & (p11(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p11(X))))) <=> ((r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))) | (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y)))) | $false)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[360, 350, 340])).
% 0.20/0.55 tff(362,plain,
% 0.20/0.55 ((((~(~r1(X!0, Y!33))) & (~p12(Y!33)) & (p11(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p11(X))) & ((~(~r1(Y!33, X!34))) & (p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) & (~p11(X!34)))) | ((~(~r1(X!0, Y!35))) & (p12(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p12(X))) & (~p11(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!37))) & (~p12(Y!37)) & (p12(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p12(X))) & (~p11(Y!37)) & (p11(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p11(X))))) <=> ((r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))) | (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y)))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[361, 334])).
% 0.20/0.55 tff(363,plain,
% 0.20/0.55 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))) <=> (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))), (((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) <=> ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))))), (((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | p11(Y)) <=> ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | p11(Y)))), rewrite(((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | p11(Y)) <=> (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))), (((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | p11(Y)) <=> (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(364,plain,
% 0.20/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | p11(Y)) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[363])).
% 0.20/0.55 tff(365,plain,
% 0.20/0.55 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | p11(Y)) | (((~(~r1(X!0, Y!33))) & (~p12(Y!33)) & (p11(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p11(X))) & ((~(~r1(Y!33, X!34))) & (p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) & (~p11(X!34)))) | ((~(~r1(X!0, Y!35))) & (p12(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p12(X))) & (~p11(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!37))) & (~p12(Y!37)) & (p12(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p12(X))) & (~p11(Y!37)) & (p11(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p11(X))))) | ![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] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | ((r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))) | (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[364, 362, 333])).
% 0.20/0.55 tff(366,plain,
% 0.20/0.55 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | p11(Y)) | (((~(~r1(X!0, Y!33))) & (~p12(Y!33)) & (p11(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p11(X))) & ((~(~r1(Y!33, X!34))) & (p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) & (~p11(X!34)))) | ((~(~r1(X!0, Y!35))) & (p12(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p12(X))) & (~p11(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!37))) & (~p12(Y!37)) & (p12(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p12(X))) & (~p11(Y!37)) & (p11(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p11(X))))) | ![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] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | (r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))) | (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[365, 331])).
% 0.20/0.55 tff(367,plain,
% 0.20/0.55 ((![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | ((r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))) | (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))) | (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(368,plain,
% 0.20/0.55 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))) <=> (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))), (((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) <=> ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))))), (((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))) <=> ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))))), rewrite(((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))), (((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(369,plain,
% 0.20/0.55 (![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[368])).
% 0.20/0.55 tff(370,plain,
% 0.20/0.55 (((r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))) | (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y)))) | $false) <=> ((r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))) | (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(371,plain,
% 0.20/0.55 ((r1(X!0, Y!31) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : (p11(X) | (~r1(Y!31, X)))) & (~p10(Y!31)) & (p10(Y!31) & ![X: $i] : (p10(X) | (~r1(Y!31, X))))) <=> $false),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(372,plain,
% 0.20/0.55 ((p10(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p10(X))) <=> (p10(Y!31) & ![X: $i] : (p10(X) | (~r1(Y!31, X))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(373,plain,
% 0.20/0.55 ((p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))) <=> (p11(Y!31) & ![X: $i] : (p11(X) | (~r1(Y!31, X))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(374,plain,
% 0.20/0.55 ((~(~r1(X!0, Y!31))) <=> r1(X!0, Y!31)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(375,plain,
% 0.20/0.55 (((~(~r1(X!0, Y!31))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))) & (~p10(Y!31)) & (p10(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p10(X)))) <=> (r1(X!0, Y!31) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : (p11(X) | (~r1(Y!31, X)))) & (~p10(Y!31)) & (p10(Y!31) & ![X: $i] : (p10(X) | (~r1(Y!31, X)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[374, 373, 372])).
% 0.20/0.55 tff(376,plain,
% 0.20/0.55 (((~(~r1(X!0, Y!31))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))) & (~p10(Y!31)) & (p10(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p10(X)))) <=> $false),
% 0.20/0.55 inference(transitivity,[status(thm)],[375, 371])).
% 0.20/0.55 tff(377,plain,
% 0.20/0.55 ((r1(X!0, Y!29) & (p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X)))) & (~p10(Y!29)) & (r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y))))) <=> (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(378,plain,
% 0.20/0.55 ((r1(Y!29, X!30) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y))))) <=> (r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(379,plain,
% 0.20/0.55 ((p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y))) <=> (p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(380,plain,
% 0.20/0.55 ((~(~r1(Y!29, X!30))) <=> r1(Y!29, X!30)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(381,plain,
% 0.20/0.55 (((~(~r1(Y!29, X!30))) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y)))) <=> (r1(Y!29, X!30) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[380, 379])).
% 0.20/0.55 tff(382,plain,
% 0.20/0.55 (((~(~r1(Y!29, X!30))) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y)))) <=> (r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[381, 378])).
% 0.20/0.55 tff(383,plain,
% 0.20/0.55 ((p11(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p11(X))) <=> (p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(384,plain,
% 0.20/0.55 ((~(~r1(X!0, Y!29))) <=> r1(X!0, Y!29)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(385,plain,
% 0.20/0.55 (((~(~r1(X!0, Y!29))) & (p11(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p11(X))) & (~p10(Y!29)) & ((~(~r1(Y!29, X!30))) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y))))) <=> (r1(X!0, Y!29) & (p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X)))) & (~p10(Y!29)) & (r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[384, 383, 382])).
% 0.20/0.55 tff(386,plain,
% 0.20/0.55 (((~(~r1(X!0, Y!29))) & (p11(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p11(X))) & (~p10(Y!29)) & ((~(~r1(Y!29, X!30))) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y))))) <=> (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[385, 377])).
% 0.20/0.55 tff(387,plain,
% 0.20/0.55 ((r1(X!0, Y!27) & (r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28))) & (~p11(Y!27)) & (p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X))))) <=> (r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(388,plain,
% 0.20/0.55 ((p10(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p10(X))) <=> (p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(389,plain,
% 0.20/0.55 ((r1(Y!27, X!28) & (p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y)))) & (~p10(X!28))) <=> (r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(390,plain,
% 0.20/0.55 ((p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) <=> (p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(391,plain,
% 0.20/0.55 ((~(~r1(Y!27, X!28))) <=> r1(Y!27, X!28)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(392,plain,
% 0.20/0.55 (((~(~r1(Y!27, X!28))) & (p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) & (~p10(X!28))) <=> (r1(Y!27, X!28) & (p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y)))) & (~p10(X!28)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[391, 390])).
% 0.20/0.55 tff(393,plain,
% 0.20/0.55 (((~(~r1(Y!27, X!28))) & (p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) & (~p10(X!28))) <=> (r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[392, 389])).
% 0.20/0.55 tff(394,plain,
% 0.20/0.55 ((~(~r1(X!0, Y!27))) <=> r1(X!0, Y!27)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(395,plain,
% 0.20/0.55 (((~(~r1(X!0, Y!27))) & ((~(~r1(Y!27, X!28))) & (p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) & (~p10(X!28))) & (~p11(Y!27)) & (p10(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p10(X)))) <=> (r1(X!0, Y!27) & (r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28))) & (~p11(Y!27)) & (p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[394, 393, 388])).
% 0.20/0.56 tff(396,plain,
% 0.20/0.56 (((~(~r1(X!0, Y!27))) & ((~(~r1(Y!27, X!28))) & (p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) & (~p10(X!28))) & (~p11(Y!27)) & (p10(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p10(X)))) <=> (r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[395, 387])).
% 0.20/0.56 tff(397,plain,
% 0.20/0.56 ((((~(~r1(X!0, Y!27))) & ((~(~r1(Y!27, X!28))) & (p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) & (~p10(X!28))) & (~p11(Y!27)) & (p10(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p10(X)))) | ((~(~r1(X!0, Y!29))) & (p11(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p11(X))) & (~p10(Y!29)) & ((~(~r1(Y!29, X!30))) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!31))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))) & (~p10(Y!31)) & (p10(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p10(X))))) <=> ((r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))) | (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y)))) | $false)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[396, 386, 376])).
% 0.20/0.56 tff(398,plain,
% 0.20/0.56 ((((~(~r1(X!0, Y!27))) & ((~(~r1(Y!27, X!28))) & (p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) & (~p10(X!28))) & (~p11(Y!27)) & (p10(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p10(X)))) | ((~(~r1(X!0, Y!29))) & (p11(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p11(X))) & (~p10(Y!29)) & ((~(~r1(Y!29, X!30))) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!31))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))) & (~p10(Y!31)) & (p10(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p10(X))))) <=> ((r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))) | (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y)))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[397, 370])).
% 0.20/0.56 tff(399,plain,
% 0.20/0.56 (^[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)) <=> ((~r1(X!0, Y)) | p10(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)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(400,plain,
% 0.20/0.56 (![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] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[399])).
% 0.20/0.56 tff(401,plain,
% 0.20/0.56 ((![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!27))) & ((~(~r1(Y!27, X!28))) & (p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) & (~p10(X!28))) & (~p11(Y!27)) & (p10(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p10(X)))) | ((~(~r1(X!0, Y!29))) & (p11(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p11(X))) & (~p10(Y!29)) & ((~(~r1(Y!29, X!30))) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!31))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))) & (~p10(Y!31)) & (p10(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | ((r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))) | (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[400, 398, 369])).
% 0.20/0.56 tff(402,plain,
% 0.20/0.56 ((![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!27))) & ((~(~r1(Y!27, X!28))) & (p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) & (~p10(X!28))) & (~p11(Y!27)) & (p10(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p10(X)))) | ((~(~r1(X!0, Y!29))) & (p11(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p11(X))) & (~p10(Y!29)) & ((~(~r1(Y!29, X!30))) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!31))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))) & (~p10(Y!31)) & (p10(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))) | (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[401, 367])).
% 0.20/0.56 tff(403,plain,
% 0.20/0.56 ((![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | ((r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))) | (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y)))))) <=> (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | (r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))) | (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(404,plain,
% 0.20/0.56 (((r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))) | (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y)))) | $false) <=> ((r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))) | (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(405,plain,
% 0.20/0.56 ((r1(X!0, Y!25) & (~p13(Y!25)) & (p13(Y!25) & ![X: $i] : (p13(X) | (~r1(Y!25, X)))) & (~p12(Y!25)) & (p12(Y!25) & ![X: $i] : (p12(X) | (~r1(Y!25, X))))) <=> $false),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(406,plain,
% 0.20/0.56 ((p12(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p12(X))) <=> (p12(Y!25) & ![X: $i] : (p12(X) | (~r1(Y!25, X))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(407,plain,
% 0.20/0.56 ((p13(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p13(X))) <=> (p13(Y!25) & ![X: $i] : (p13(X) | (~r1(Y!25, X))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(408,plain,
% 0.20/0.56 ((~(~r1(X!0, Y!25))) <=> r1(X!0, Y!25)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(409,plain,
% 0.20/0.56 (((~(~r1(X!0, Y!25))) & (~p13(Y!25)) & (p13(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p13(X))) & (~p12(Y!25)) & (p12(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p12(X)))) <=> (r1(X!0, Y!25) & (~p13(Y!25)) & (p13(Y!25) & ![X: $i] : (p13(X) | (~r1(Y!25, X)))) & (~p12(Y!25)) & (p12(Y!25) & ![X: $i] : (p12(X) | (~r1(Y!25, X)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[408, 407, 406])).
% 0.20/0.56 tff(410,plain,
% 0.20/0.56 (((~(~r1(X!0, Y!25))) & (~p13(Y!25)) & (p13(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p13(X))) & (~p12(Y!25)) & (p12(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p12(X)))) <=> $false),
% 0.20/0.56 inference(transitivity,[status(thm)],[409, 405])).
% 0.20/0.56 tff(411,plain,
% 0.20/0.56 ((r1(X!0, Y!23) & (p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X)))) & (~p12(Y!23)) & (r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y))))) <=> (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(412,plain,
% 0.20/0.56 ((r1(Y!23, X!24) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y))))) <=> (r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(413,plain,
% 0.20/0.56 ((p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y))) <=> (p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(414,plain,
% 0.20/0.56 ((~(~r1(Y!23, X!24))) <=> r1(Y!23, X!24)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(415,plain,
% 0.20/0.56 (((~(~r1(Y!23, X!24))) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y)))) <=> (r1(Y!23, X!24) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[414, 413])).
% 0.20/0.56 tff(416,plain,
% 0.20/0.56 (((~(~r1(Y!23, X!24))) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y)))) <=> (r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[415, 412])).
% 0.20/0.56 tff(417,plain,
% 0.20/0.56 ((p13(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p13(X))) <=> (p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(418,plain,
% 0.20/0.56 ((~(~r1(X!0, Y!23))) <=> r1(X!0, Y!23)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(419,plain,
% 0.20/0.56 (((~(~r1(X!0, Y!23))) & (p13(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p13(X))) & (~p12(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y))))) <=> (r1(X!0, Y!23) & (p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X)))) & (~p12(Y!23)) & (r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[418, 417, 416])).
% 0.20/0.56 tff(420,plain,
% 0.20/0.56 (((~(~r1(X!0, Y!23))) & (p13(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p13(X))) & (~p12(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y))))) <=> (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[419, 411])).
% 0.20/0.56 tff(421,plain,
% 0.20/0.56 ((r1(X!0, Y!21) & (~p13(Y!21)) & (p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X)))) & (r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22)))) <=> (r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(422,plain,
% 0.20/0.57 ((r1(Y!21, X!22) & (p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y)))) & (~p12(X!22))) <=> (r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(423,plain,
% 0.20/0.57 ((p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) <=> (p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(424,plain,
% 0.20/0.57 ((~(~r1(Y!21, X!22))) <=> r1(Y!21, X!22)),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(425,plain,
% 0.20/0.57 (((~(~r1(Y!21, X!22))) & (p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) & (~p12(X!22))) <=> (r1(Y!21, X!22) & (p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y)))) & (~p12(X!22)))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[424, 423])).
% 0.20/0.57 tff(426,plain,
% 0.20/0.57 (((~(~r1(Y!21, X!22))) & (p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) & (~p12(X!22))) <=> (r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[425, 422])).
% 0.20/0.57 tff(427,plain,
% 0.20/0.57 ((p12(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p12(X))) <=> (p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(428,plain,
% 0.20/0.57 ((~(~r1(X!0, Y!21))) <=> r1(X!0, Y!21)),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(429,plain,
% 0.20/0.57 (((~(~r1(X!0, Y!21))) & (~p13(Y!21)) & (p12(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p12(X))) & ((~(~r1(Y!21, X!22))) & (p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) & (~p12(X!22)))) <=> (r1(X!0, Y!21) & (~p13(Y!21)) & (p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X)))) & (r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[428, 427, 426])).
% 0.20/0.57 tff(430,plain,
% 0.20/0.57 (((~(~r1(X!0, Y!21))) & (~p13(Y!21)) & (p12(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p12(X))) & ((~(~r1(Y!21, X!22))) & (p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) & (~p12(X!22)))) <=> (r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[429, 421])).
% 0.20/0.57 tff(431,plain,
% 0.20/0.57 ((((~(~r1(X!0, Y!21))) & (~p13(Y!21)) & (p12(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p12(X))) & ((~(~r1(Y!21, X!22))) & (p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) & (~p12(X!22)))) | ((~(~r1(X!0, Y!23))) & (p13(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p13(X))) & (~p12(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!25))) & (~p13(Y!25)) & (p13(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p13(X))) & (~p12(Y!25)) & (p12(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p12(X))))) <=> ((r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))) | (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y)))) | $false)),
% 0.20/0.57 inference(monotonicity,[status(thm)],[430, 420, 410])).
% 0.20/0.57 tff(432,plain,
% 0.20/0.57 ((((~(~r1(X!0, Y!21))) & (~p13(Y!21)) & (p12(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p12(X))) & ((~(~r1(Y!21, X!22))) & (p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) & (~p12(X!22)))) | ((~(~r1(X!0, Y!23))) & (p13(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p13(X))) & (~p12(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!25))) & (~p13(Y!25)) & (p13(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p13(X))) & (~p12(Y!25)) & (p12(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p12(X))))) <=> ((r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))) | (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y)))))),
% 0.20/0.57 inference(transitivity,[status(thm)],[431, 404])).
% 0.20/0.57 tff(433,plain,
% 0.20/0.57 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))) <=> (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))), (((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) <=> ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))))), (((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))) <=> ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))))), rewrite(((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))) <=> (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))), (((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))) <=> (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(434,plain,
% 0.20/0.57 (![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))) <=> ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[433])).
% 0.20/0.57 tff(435,plain,
% 0.20/0.57 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))) <=> (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))), (((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) <=> ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))))), (((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | p12(Y)) <=> ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | p12(Y)))), rewrite(((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | p12(Y)) <=> (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))), (((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | p12(Y)) <=> (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(436,plain,
% 0.20/0.57 (![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | p12(Y)) <=> ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[435])).
% 0.20/0.57 tff(437,plain,
% 0.20/0.57 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | p12(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))) | (((~(~r1(X!0, Y!21))) & (~p13(Y!21)) & (p12(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p12(X))) & ((~(~r1(Y!21, X!22))) & (p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) & (~p12(X!22)))) | ((~(~r1(X!0, Y!23))) & (p13(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p13(X))) & (~p12(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!25))) & (~p13(Y!25)) & (p13(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p13(X))) & (~p12(Y!25)) & (p12(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p12(X)))))) <=> (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | ((r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))) | (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y))))))),
% 0.45/0.58 inference(monotonicity,[status(thm)],[436, 434, 432])).
% 0.45/0.58 tff(438,plain,
% 0.45/0.58 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | p12(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))) | (((~(~r1(X!0, Y!21))) & (~p13(Y!21)) & (p12(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p12(X))) & ((~(~r1(Y!21, X!22))) & (p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) & (~p12(X!22)))) | ((~(~r1(X!0, Y!23))) & (p13(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p13(X))) & (~p12(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!25))) & (~p13(Y!25)) & (p13(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p13(X))) & (~p12(Y!25)) & (p12(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p12(X)))))) <=> (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | (r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))) | (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y)))))),
% 0.45/0.58 inference(transitivity,[status(thm)],[437, 403])).
% 0.45/0.58 tff(439,plain,
% 0.45/0.58 ((![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | ((r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))) | (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y)))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))) | (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y)))))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(440,plain,
% 0.45/0.58 (((r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))) | (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y)))) | $false) <=> ((r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))) | (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y)))))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(441,plain,
% 0.45/0.58 ((r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : (p14(X) | (~r1(Y!19, X)))) & (~p13(Y!19)) & (p13(Y!19) & ![X: $i] : (p13(X) | (~r1(Y!19, X))))) <=> $false),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(442,plain,
% 0.45/0.58 ((p13(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p13(X))) <=> (p13(Y!19) & ![X: $i] : (p13(X) | (~r1(Y!19, X))))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(443,plain,
% 0.45/0.58 ((p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) <=> (p14(Y!19) & ![X: $i] : (p14(X) | (~r1(Y!19, X))))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(444,plain,
% 0.45/0.58 ((~(~r1(X!0, Y!19))) <=> r1(X!0, Y!19)),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(445,plain,
% 0.45/0.58 (((~(~r1(X!0, Y!19))) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (~p13(Y!19)) & (p13(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p13(X)))) <=> (r1(X!0, Y!19) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : (p14(X) | (~r1(Y!19, X)))) & (~p13(Y!19)) & (p13(Y!19) & ![X: $i] : (p13(X) | (~r1(Y!19, X)))))),
% 0.45/0.58 inference(monotonicity,[status(thm)],[444, 443, 442])).
% 0.45/0.58 tff(446,plain,
% 0.45/0.58 (((~(~r1(X!0, Y!19))) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (~p13(Y!19)) & (p13(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p13(X)))) <=> $false),
% 0.45/0.58 inference(transitivity,[status(thm)],[445, 441])).
% 0.45/0.58 tff(447,plain,
% 0.45/0.58 ((r1(X!0, Y!17) & (p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X)))) & (~p13(Y!17)) & (r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y))))) <=> (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y))))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(448,plain,
% 0.45/0.58 ((r1(Y!17, X!18) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y))))) <=> (r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y))))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(449,plain,
% 0.45/0.58 ((p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y))) <=> (p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y))))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(450,plain,
% 0.45/0.58 ((~(~r1(Y!17, X!18))) <=> r1(Y!17, X!18)),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(451,plain,
% 0.45/0.58 (((~(~r1(Y!17, X!18))) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y)))) <=> (r1(Y!17, X!18) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y)))))),
% 0.45/0.58 inference(monotonicity,[status(thm)],[450, 449])).
% 0.45/0.58 tff(452,plain,
% 0.45/0.58 (((~(~r1(Y!17, X!18))) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y)))) <=> (r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y))))),
% 0.45/0.58 inference(transitivity,[status(thm)],[451, 448])).
% 0.45/0.58 tff(453,plain,
% 0.45/0.58 ((p14(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p14(X))) <=> (p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(454,plain,
% 0.45/0.58 ((~(~r1(X!0, Y!17))) <=> r1(X!0, Y!17)),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(455,plain,
% 0.45/0.58 (((~(~r1(X!0, Y!17))) & (p14(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p14(X))) & (~p13(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y))))) <=> (r1(X!0, Y!17) & (p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X)))) & (~p13(Y!17)) & (r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y)))))),
% 0.45/0.58 inference(monotonicity,[status(thm)],[454, 453, 452])).
% 0.45/0.58 tff(456,plain,
% 0.45/0.58 (((~(~r1(X!0, Y!17))) & (p14(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p14(X))) & (~p13(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y))))) <=> (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y))))),
% 0.45/0.58 inference(transitivity,[status(thm)],[455, 447])).
% 0.45/0.58 tff(457,plain,
% 0.45/0.58 ((r1(X!0, Y!15) & (~p14(Y!15)) & (p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16)))) <=> (r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16)))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(458,plain,
% 0.45/0.58 ((r1(Y!15, X!16) & (p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y)))) & (~p13(X!16))) <=> (r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16)))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(459,plain,
% 0.45/0.58 ((p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) <=> (p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))))),
% 0.45/0.58 inference(rewrite,[status(thm)],[])).
% 0.45/0.58 tff(460,plain,
% 0.45/0.58 ((~(~r1(Y!15, X!16))) <=> r1(Y!15, X!16)),
% 0.45/0.59 inference(rewrite,[status(thm)],[])).
% 0.45/0.59 tff(461,plain,
% 0.45/0.59 (((~(~r1(Y!15, X!16))) & (p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) & (~p13(X!16))) <=> (r1(Y!15, X!16) & (p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y)))) & (~p13(X!16)))),
% 0.45/0.59 inference(monotonicity,[status(thm)],[460, 459])).
% 0.45/0.59 tff(462,plain,
% 0.45/0.59 (((~(~r1(Y!15, X!16))) & (p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) & (~p13(X!16))) <=> (r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16)))),
% 0.45/0.59 inference(transitivity,[status(thm)],[461, 458])).
% 0.45/0.59 tff(463,plain,
% 0.45/0.59 ((p13(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p13(X))) <=> (p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))))),
% 0.45/0.59 inference(rewrite,[status(thm)],[])).
% 0.45/0.59 tff(464,plain,
% 0.45/0.59 ((~(~r1(X!0, Y!15))) <=> r1(X!0, Y!15)),
% 0.45/0.59 inference(rewrite,[status(thm)],[])).
% 0.45/0.59 tff(465,plain,
% 0.45/0.59 (((~(~r1(X!0, Y!15))) & (~p14(Y!15)) & (p13(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p13(X))) & ((~(~r1(Y!15, X!16))) & (p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) & (~p13(X!16)))) <=> (r1(X!0, Y!15) & (~p14(Y!15)) & (p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))))),
% 0.45/0.59 inference(monotonicity,[status(thm)],[464, 463, 462])).
% 0.45/0.59 tff(466,plain,
% 0.45/0.59 (((~(~r1(X!0, Y!15))) & (~p14(Y!15)) & (p13(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p13(X))) & ((~(~r1(Y!15, X!16))) & (p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) & (~p13(X!16)))) <=> (r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16)))),
% 0.45/0.59 inference(transitivity,[status(thm)],[465, 457])).
% 0.45/0.59 tff(467,plain,
% 0.45/0.59 ((((~(~r1(X!0, Y!15))) & (~p14(Y!15)) & (p13(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p13(X))) & ((~(~r1(Y!15, X!16))) & (p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) & (~p13(X!16)))) | ((~(~r1(X!0, Y!17))) & (p14(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p14(X))) & (~p13(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y))))) | ((~(~r1(X!0, Y!19))) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (~p13(Y!19)) & (p13(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p13(X))))) <=> ((r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))) | (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y)))) | $false)),
% 0.45/0.59 inference(monotonicity,[status(thm)],[466, 456, 446])).
% 0.45/0.59 tff(468,plain,
% 0.45/0.59 ((((~(~r1(X!0, Y!15))) & (~p14(Y!15)) & (p13(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p13(X))) & ((~(~r1(Y!15, X!16))) & (p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) & (~p13(X!16)))) | ((~(~r1(X!0, Y!17))) & (p14(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p14(X))) & (~p13(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y))))) | ((~(~r1(X!0, Y!19))) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (~p13(Y!19)) & (p13(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p13(X))))) <=> ((r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))) | (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y)))))),
% 0.45/0.59 inference(transitivity,[status(thm)],[467, 440])).
% 0.45/0.59 tff(469,plain,
% 0.45/0.59 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))) <=> (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))), (((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) <=> ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))))), (((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | p13(Y)) <=> ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | p13(Y)))), rewrite(((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | p13(Y)) <=> (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))), (((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | p13(Y)) <=> (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))))),
% 0.46/0.59 inference(bind,[status(th)],[])).
% 0.46/0.59 tff(470,plain,
% 0.46/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | p13(Y)) <=> ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))),
% 0.46/0.59 inference(quant_intro,[status(thm)],[469])).
% 0.46/0.59 tff(471,plain,
% 0.46/0.59 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))) <=> (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))), (((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) <=> ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))))), (((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))) <=> ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))))), rewrite(((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))), (((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))))),
% 0.46/0.59 inference(bind,[status(th)],[])).
% 0.46/0.59 tff(472,plain,
% 0.46/0.59 (![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))) <=> ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))),
% 0.46/0.59 inference(quant_intro,[status(thm)],[471])).
% 0.46/0.59 tff(473,plain,
% 0.46/0.59 ((![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | p13(Y)) | (((~(~r1(X!0, Y!15))) & (~p14(Y!15)) & (p13(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p13(X))) & ((~(~r1(Y!15, X!16))) & (p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) & (~p13(X!16)))) | ((~(~r1(X!0, Y!17))) & (p14(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p14(X))) & (~p13(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y))))) | ((~(~r1(X!0, Y!19))) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (~p13(Y!19)) & (p13(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p13(X)))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | ((r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))) | (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y))))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[472, 470, 468])).
% 0.46/0.59 tff(474,plain,
% 0.46/0.59 ((![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | p13(Y)) | (((~(~r1(X!0, Y!15))) & (~p14(Y!15)) & (p13(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p13(X))) & ((~(~r1(Y!15, X!16))) & (p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) & (~p13(X!16)))) | ((~(~r1(X!0, Y!17))) & (p14(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p14(X))) & (~p13(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y))))) | ((~(~r1(X!0, Y!19))) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (~p13(Y!19)) & (p13(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p13(X)))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))) | (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y)))))),
% 0.46/0.59 inference(transitivity,[status(thm)],[473, 439])).
% 0.46/0.59 tff(475,plain,
% 0.46/0.59 (((((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))) <=> (((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(476,plain,
% 0.46/0.59 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))) <=> (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))), (((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) <=> ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))))), ((p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))))), rewrite((p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))), ((p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))))),
% 0.46/0.59 inference(bind,[status(th)],[])).
% 0.46/0.59 tff(477,plain,
% 0.46/0.59 (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))) <=> ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))),
% 0.46/0.59 inference(quant_intro,[status(thm)],[476])).
% 0.46/0.59 tff(478,plain,
% 0.46/0.59 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.46/0.59 inference(bind,[status(th)],[])).
% 0.46/0.59 tff(479,plain,
% 0.46/0.59 (![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))),
% 0.46/0.59 inference(quant_intro,[status(thm)],[478])).
% 0.46/0.59 tff(480,plain,
% 0.46/0.59 ((((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))) | $false) <=> (((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(481,plain,
% 0.46/0.60 (((~p15(Y!12)) & r1(X!0, Y!12) & (~p14(Y!12)) & (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) & (p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))))) <=> $false),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(482,plain,
% 0.46/0.60 ((p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))) <=> (p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(483,plain,
% 0.46/0.60 ((p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) <=> (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(484,plain,
% 0.46/0.60 ((~(~r1(X!0, Y!12))) <=> r1(X!0, Y!12)),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(485,plain,
% 0.46/0.60 (((~p15(Y!12)) & (~(~r1(X!0, Y!12))) & (~p14(Y!12)) & (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X)))) <=> ((~p15(Y!12)) & r1(X!0, Y!12) & (~p14(Y!12)) & (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) & (p14(Y!12) & ![X: $i] : (p14(X) | (~r1(Y!12, X)))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[484, 483, 482])).
% 0.46/0.60 tff(486,plain,
% 0.46/0.60 (((~p15(Y!12)) & (~(~r1(X!0, Y!12))) & (~p14(Y!12)) & (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X)))) <=> $false),
% 0.46/0.60 inference(transitivity,[status(thm)],[485, 481])).
% 0.46/0.60 tff(487,plain,
% 0.46/0.60 ((r1(X!0, Y!10) & (~p14(Y!10)) & (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) & ((~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))))) <=> (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(488,plain,
% 0.46/0.60 (((~p15(X!11)) & r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))))) <=> ((~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(489,plain,
% 0.46/0.60 ((p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))) <=> (p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(490,plain,
% 0.46/0.60 ((~(~r1(Y!10, X!11))) <=> r1(Y!10, X!11)),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(491,plain,
% 0.46/0.60 (((~p15(X!11)) & (~(~r1(Y!10, X!11))) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y)))) <=> ((~p15(X!11)) & r1(Y!10, X!11) & (p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[490, 489])).
% 0.46/0.60 tff(492,plain,
% 0.46/0.60 (((~p15(X!11)) & (~(~r1(Y!10, X!11))) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y)))) <=> ((~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))))),
% 0.46/0.60 inference(transitivity,[status(thm)],[491, 488])).
% 0.46/0.60 tff(493,plain,
% 0.46/0.60 ((p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) <=> (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(494,plain,
% 0.46/0.60 ((~(~r1(X!0, Y!10))) <=> r1(X!0, Y!10)),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(495,plain,
% 0.46/0.60 (((~(~r1(X!0, Y!10))) & (~p14(Y!10)) & (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) & ((~p15(X!11)) & (~(~r1(Y!10, X!11))) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))))) <=> (r1(X!0, Y!10) & (~p14(Y!10)) & (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) & ((~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[494, 493, 492])).
% 0.46/0.60 tff(496,plain,
% 0.46/0.60 (((~(~r1(X!0, Y!10))) & (~p14(Y!10)) & (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) & ((~p15(X!11)) & (~(~r1(Y!10, X!11))) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))))) <=> (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))))),
% 0.46/0.60 inference(transitivity,[status(thm)],[495, 487])).
% 0.46/0.60 tff(497,plain,
% 0.46/0.60 (((~p15(Y!8)) & r1(X!0, Y!8) & (p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X)))) & (r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y))))) <=> ((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(498,plain,
% 0.46/0.60 ((r1(Y!8, X!9) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y))))) <=> (r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(499,plain,
% 0.46/0.60 ((p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) <=> (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(500,plain,
% 0.46/0.60 ((~(~r1(Y!8, X!9))) <=> r1(Y!8, X!9)),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(501,plain,
% 0.46/0.60 (((~(~r1(Y!8, X!9))) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y))))) <=> (r1(Y!8, X!9) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[500, 499])).
% 0.46/0.60 tff(502,plain,
% 0.46/0.60 (((~(~r1(Y!8, X!9))) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y))))) <=> (r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y))))),
% 0.46/0.60 inference(transitivity,[status(thm)],[501, 498])).
% 0.46/0.60 tff(503,plain,
% 0.46/0.60 ((p14(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p14(X))) <=> (p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(504,plain,
% 0.46/0.60 ((~(~r1(X!0, Y!8))) <=> r1(X!0, Y!8)),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(505,plain,
% 0.46/0.60 (((~p15(Y!8)) & (~(~r1(X!0, Y!8))) & (p14(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p14(X))) & ((~(~r1(Y!8, X!9))) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))))) <=> ((~p15(Y!8)) & r1(X!0, Y!8) & (p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X)))) & (r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[504, 503, 502])).
% 0.46/0.60 tff(506,plain,
% 0.46/0.60 (((~p15(Y!8)) & (~(~r1(X!0, Y!8))) & (p14(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p14(X))) & ((~(~r1(Y!8, X!9))) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))))) <=> ((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y))))),
% 0.46/0.60 inference(transitivity,[status(thm)],[505, 497])).
% 0.46/0.60 tff(507,plain,
% 0.46/0.60 ((((~p15(Y!8)) & (~(~r1(X!0, Y!8))) & (p14(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p14(X))) & ((~(~r1(Y!8, X!9))) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p14(Y!10)) & (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) & ((~p15(X!11)) & (~(~r1(Y!10, X!11))) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))))) | ((~p15(Y!12)) & (~(~r1(X!0, Y!12))) & (~p14(Y!12)) & (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))))) <=> (((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))) | $false)),
% 0.46/0.60 inference(monotonicity,[status(thm)],[506, 496, 486])).
% 0.46/0.60 tff(508,plain,
% 0.46/0.60 ((((~p15(Y!8)) & (~(~r1(X!0, Y!8))) & (p14(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p14(X))) & ((~(~r1(Y!8, X!9))) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p14(Y!10)) & (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) & ((~p15(X!11)) & (~(~r1(Y!10, X!11))) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))))) | ((~p15(Y!12)) & (~(~r1(X!0, Y!12))) & (~p14(Y!12)) & (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))))) <=> (((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))))),
% 0.46/0.61 inference(transitivity,[status(thm)],[507, 480])).
% 0.46/0.61 tff(509,plain,
% 0.46/0.61 (((((~p15(Y!8)) & (~(~r1(X!0, Y!8))) & (p14(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p14(X))) & ((~(~r1(Y!8, X!9))) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p14(Y!10)) & (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) & ((~p15(X!11)) & (~(~r1(Y!10, X!11))) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))))) | ((~p15(Y!12)) & (~(~r1(X!0, Y!12))) & (~p14(Y!12)) & (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))))) <=> ((((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y))))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[508, 479, 477])).
% 0.46/0.61 tff(510,plain,
% 0.46/0.61 (((((~p15(Y!8)) & (~(~r1(X!0, Y!8))) & (p14(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p14(X))) & ((~(~r1(Y!8, X!9))) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p14(Y!10)) & (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) & ((~p15(X!11)) & (~(~r1(Y!10, X!11))) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))))) | ((~p15(Y!12)) & (~(~r1(X!0, Y!12))) & (~p14(Y!12)) & (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))))) <=> (((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))))),
% 0.46/0.61 inference(transitivity,[status(thm)],[509, 475])).
% 0.46/0.61 tff(511,plain,
% 0.46/0.61 (((((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) | ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) | ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(512,plain,
% 0.46/0.61 (^[Y: $i] : rewrite((p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.46/0.61 inference(bind,[status(th)],[])).
% 0.46/0.61 tff(513,plain,
% 0.46/0.61 (![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))),
% 0.46/0.61 inference(quant_intro,[status(thm)],[512])).
% 0.46/0.61 tff(514,plain,
% 0.46/0.61 (^[Y: $i] : rewrite((p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.46/0.61 inference(bind,[status(th)],[])).
% 0.46/0.61 tff(515,plain,
% 0.46/0.61 (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) <=> ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.46/0.61 inference(quant_intro,[status(thm)],[514])).
% 0.46/0.61 tff(516,plain,
% 0.46/0.61 ((((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) | ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))) | $false) <=> (((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) | ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(517,plain,
% 0.46/0.61 (((~p16(Y!5)) & (~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X))))) <=> $false),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(518,plain,
% 0.46/0.61 ((p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X)))) <=> (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X))))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(519,plain,
% 0.46/0.61 ((p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) <=> (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X))))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(520,plain,
% 0.46/0.61 ((~(~r1(X!0, Y!5))) <=> r1(X!0, Y!5)),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(521,plain,
% 0.46/0.61 (((~p16(Y!5)) & (~p15(Y!5)) & (~(~r1(X!0, Y!5))) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X))))) <=> ((~p16(Y!5)) & (~p15(Y!5)) & r1(X!0, Y!5) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X)))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[520, 519, 518])).
% 0.46/0.61 tff(522,plain,
% 0.46/0.61 (((~p16(Y!5)) & (~p15(Y!5)) & (~(~r1(X!0, Y!5))) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X))))) <=> $false),
% 0.46/0.61 inference(transitivity,[status(thm)],[521, 517])).
% 0.46/0.61 tff(523,plain,
% 0.46/0.61 (((~p15(Y!3)) & r1(X!0, Y!3) & (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) & ((~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))) <=> ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(524,plain,
% 0.46/0.61 (((~p16(X!4)) & r1(Y!3, X!4) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))) <=> ((~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(525,plain,
% 0.46/0.61 ((p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))) <=> (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(526,plain,
% 0.46/0.61 ((~(~r1(Y!3, X!4))) <=> r1(Y!3, X!4)),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(527,plain,
% 0.46/0.62 (((~p16(X!4)) & (~(~r1(Y!3, X!4))) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))) <=> ((~p16(X!4)) & r1(Y!3, X!4) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[526, 525])).
% 0.46/0.62 tff(528,plain,
% 0.46/0.62 (((~p16(X!4)) & (~(~r1(Y!3, X!4))) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))) <=> ((~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))),
% 0.46/0.62 inference(transitivity,[status(thm)],[527, 524])).
% 0.46/0.62 tff(529,plain,
% 0.46/0.62 ((p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) <=> (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(530,plain,
% 0.46/0.62 ((~(~r1(X!0, Y!3))) <=> r1(X!0, Y!3)),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(531,plain,
% 0.46/0.62 (((~p15(Y!3)) & (~(~r1(X!0, Y!3))) & (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) & ((~p16(X!4)) & (~(~r1(Y!3, X!4))) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))) <=> ((~p15(Y!3)) & r1(X!0, Y!3) & (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) & ((~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[530, 529, 528])).
% 0.46/0.62 tff(532,plain,
% 0.46/0.62 (((~p15(Y!3)) & (~(~r1(X!0, Y!3))) & (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) & ((~p16(X!4)) & (~(~r1(Y!3, X!4))) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))) <=> ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))),
% 0.46/0.62 inference(transitivity,[status(thm)],[531, 523])).
% 0.46/0.62 tff(533,plain,
% 0.46/0.62 (((~p16(Y!1)) & r1(X!0, Y!1) & (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) & ((~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y))))) <=> ((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y))))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(534,plain,
% 0.46/0.62 (((~p15(X!2)) & r1(Y!1, X!2) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y))))) <=> ((~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y))))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(535,plain,
% 0.46/0.62 ((p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) <=> (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y))))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(536,plain,
% 0.46/0.62 ((~(~r1(Y!1, X!2))) <=> r1(Y!1, X!2)),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(537,plain,
% 0.46/0.62 (((~p15(X!2)) & (~(~r1(Y!1, X!2))) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y))))) <=> ((~p15(X!2)) & r1(Y!1, X!2) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[536, 535])).
% 0.46/0.62 tff(538,plain,
% 0.46/0.62 (((~p15(X!2)) & (~(~r1(Y!1, X!2))) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y))))) <=> ((~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y))))),
% 0.46/0.62 inference(transitivity,[status(thm)],[537, 534])).
% 0.46/0.62 tff(539,plain,
% 0.46/0.62 ((p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) <=> (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(540,plain,
% 0.46/0.62 ((~(~r1(X!0, Y!1))) <=> r1(X!0, Y!1)),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(541,plain,
% 0.46/0.62 (((~p16(Y!1)) & (~(~r1(X!0, Y!1))) & (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) & ((~p15(X!2)) & (~(~r1(Y!1, X!2))) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))))) <=> ((~p16(Y!1)) & r1(X!0, Y!1) & (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) & ((~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[540, 539, 538])).
% 0.46/0.62 tff(542,plain,
% 0.46/0.62 (((~p16(Y!1)) & (~(~r1(X!0, Y!1))) & (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) & ((~p15(X!2)) & (~(~r1(Y!1, X!2))) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))))) <=> ((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y))))),
% 0.46/0.62 inference(transitivity,[status(thm)],[541, 533])).
% 0.46/0.62 tff(543,plain,
% 0.46/0.62 ((((~p16(Y!1)) & (~(~r1(X!0, Y!1))) & (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) & ((~p15(X!2)) & (~(~r1(Y!1, X!2))) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))))) | ((~p15(Y!3)) & (~(~r1(X!0, Y!3))) & (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) & ((~p16(X!4)) & (~(~r1(Y!3, X!4))) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))) | ((~p16(Y!5)) & (~p15(Y!5)) & (~(~r1(X!0, Y!5))) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X)))))) <=> (((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) | ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))) | $false)),
% 0.49/0.62 inference(monotonicity,[status(thm)],[542, 532, 522])).
% 0.49/0.62 tff(544,plain,
% 0.49/0.62 ((((~p16(Y!1)) & (~(~r1(X!0, Y!1))) & (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) & ((~p15(X!2)) & (~(~r1(Y!1, X!2))) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))))) | ((~p15(Y!3)) & (~(~r1(X!0, Y!3))) & (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) & ((~p16(X!4)) & (~(~r1(Y!3, X!4))) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))) | ((~p16(Y!5)) & (~p15(Y!5)) & (~(~r1(X!0, Y!5))) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X)))))) <=> (((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) | ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))),
% 0.49/0.62 inference(transitivity,[status(thm)],[543, 516])).
% 0.49/0.62 tff(545,plain,
% 0.49/0.62 (((((~p16(Y!1)) & (~(~r1(X!0, Y!1))) & (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) & ((~p15(X!2)) & (~(~r1(Y!1, X!2))) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))))) | ((~p15(Y!3)) & (~(~r1(X!0, Y!3))) & (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) & ((~p16(X!4)) & (~(~r1(Y!3, X!4))) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))) | ((~p16(Y!5)) & (~p15(Y!5)) & (~(~r1(X!0, Y!5))) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) <=> ((((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) | ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.49/0.62 inference(monotonicity,[status(thm)],[544, 515, 513])).
% 0.49/0.62 tff(546,plain,
% 0.49/0.62 (((((~p16(Y!1)) & (~(~r1(X!0, Y!1))) & (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) & ((~p15(X!2)) & (~(~r1(Y!1, X!2))) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))))) | ((~p15(Y!3)) & (~(~r1(X!0, Y!3))) & (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) & ((~p16(X!4)) & (~(~r1(Y!3, X!4))) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))) | ((~p16(Y!5)) & (~p15(Y!5)) & (~(~r1(X!0, Y!5))) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) <=> (((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) | ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.50/0.63 inference(transitivity,[status(thm)],[545, 511])).
% 0.50/0.63 tff(547,plain,
% 0.50/0.63 ((((((~p16(Y!1)) & (~(~r1(X!0, Y!1))) & (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) & ((~p15(X!2)) & (~(~r1(Y!1, X!2))) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))))) | ((~p15(Y!3)) & (~(~r1(X!0, Y!3))) & (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) & ((~p16(X!4)) & (~(~r1(Y!3, X!4))) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))) | ((~p16(Y!5)) & (~p15(Y!5)) & (~(~r1(X!0, Y!5))) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ((((~p15(Y!8)) & (~(~r1(X!0, Y!8))) & (p14(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p14(X))) & ((~(~r1(Y!8, X!9))) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p14(Y!10)) & (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) & ((~p15(X!11)) & (~(~r1(Y!10, X!11))) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))))) | ((~p15(Y!12)) & (~(~r1(X!0, Y!12))) & (~p14(Y!12)) & (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | p13(Y)) | (((~(~r1(X!0, Y!15))) & (~p14(Y!15)) & (p13(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p13(X))) & ((~(~r1(Y!15, X!16))) & (p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) & (~p13(X!16)))) | ((~(~r1(X!0, Y!17))) & (p14(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p14(X))) & (~p13(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y))))) | ((~(~r1(X!0, Y!19))) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (~p13(Y!19)) & (p13(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p13(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | p12(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))) | (((~(~r1(X!0, Y!21))) & (~p13(Y!21)) & (p12(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p12(X))) & ((~(~r1(Y!21, X!22))) & (p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) & (~p12(X!22)))) | ((~(~r1(X!0, Y!23))) & (p13(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p13(X))) & (~p12(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!25))) & (~p13(Y!25)) & (p13(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p13(X))) & (~p12(Y!25)) & (p12(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p12(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!27))) & ((~(~r1(Y!27, X!28))) & (p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) & (~p10(X!28))) & (~p11(Y!27)) & (p10(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p10(X)))) | ((~(~r1(X!0, Y!29))) & (p11(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p11(X))) & (~p10(Y!29)) & ((~(~r1(Y!29, X!30))) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!31))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))) & (~p10(Y!31)) & (p10(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | p11(Y)) | (((~(~r1(X!0, Y!33))) & (~p12(Y!33)) & (p11(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p11(X))) & ((~(~r1(Y!33, X!34))) & (p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) & (~p11(X!34)))) | ((~(~r1(X!0, Y!35))) & (p12(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p12(X))) & (~p11(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!37))) & (~p12(Y!37)) & (p12(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p12(X))) & (~p11(Y!37)) & (p11(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p11(X))))) | ![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] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | p9(Y)) | (((~(~r1(X!0, Y!38))) & (~p10(Y!38)) & (p9(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p9(X))) & ((~(~r1(Y!38, X!39))) & (p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) & (~p9(X!39)))) | ((~(~r1(X!0, Y!40))) & (p10(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p10(X))) & (~p9(Y!40)) & ((~(~r1(Y!40, X!41))) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))))) | ((~(~r1(X!0, Y!42))) & (~p10(Y!42)) & (p10(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p10(X))) & (~p9(Y!42)) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))) | (((~(~r1(X!0, Y!45))) & (~p9(Y!45)) & (p8(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p8(X))) & ((~(~r1(Y!45, X!46))) & (p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) & (~p8(X!46)))) | ((~(~r1(X!0, Y!47))) & (p9(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p9(X))) & (~p8(Y!47)) & ((~(~r1(Y!47, X!48))) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!49))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))) & (~p8(Y!49)) & (p8(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p8(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | p7(Y)) | (((~(~r1(X!0, Y!50))) & (~p8(Y!50)) & (p7(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p7(X))) & ((~(~r1(Y!50, X!51))) & (p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) & (~p7(X!51)))) | ((~(~r1(X!0, Y!52))) & (p8(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p8(X))) & (~p7(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!54))) & (~p8(Y!54)) & (p8(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p8(X))) & (~p7(Y!54)) & (p7(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))))) & ((~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_55(Y))) | p7(tptp_fun_X_55(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)) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))) | (((~(~r1(X!0, Y!82))) & (~p3(Y!82)) & (p2(Y!82) & ![X: $i] : ((~r1(Y!82, X)) | p2(X))) & ((~(~r1(Y!82, X!83))) & (p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) & (~p2(X!83)))) | ((~(~r1(X!0, Y!84))) & (p3(Y!84) & ![X: $i] : ((~r1(Y!84, X)) | p3(X))) & (~p2(Y!84)) & ((~(~r1(Y!84, X!85))) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!86))) & (~p3(Y!86)) & (p3(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p3(X))) & (~p2(Y!86)) & (p2(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p2(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(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)))))))) <=> ((((~p16(Y!1)) & r1(X!0, Y!1) & p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X))) & (~p15(X!2)) & r1(Y!1, X!2) & p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))) | ((~p15(Y!3)) & r1(X!0, Y!3) & p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X))) & (~p16(X!4)) & r1(Y!3, X!4) & p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) & (((~p15(Y!8)) & r1(X!0, Y!8) & p14(Y!8) & ![X: $i] : (p14(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p14(X!9)) & p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p14(Y!10)) & p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X))) & (~p15(X!11)) & r1(Y!10, X!11) & p14(X!11) & ![Y: $i] : (p14(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y)))))) & (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p14(Y!15)) & p13(Y!15) & ![X: $i] : (p13(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p14(X!16) & ![Y: $i] : (p14(Y) | (~r1(X!16, Y))) & (~p13(X!16))) | (r1(X!0, Y!17) & p14(Y!17) & ![X: $i] : (p14(X) | (~r1(Y!17, X))) & (~p13(Y!17)) & r1(Y!17, X!18) & (~p14(X!18)) & p13(X!18) & ![Y: $i] : (p13(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | (r1(X!0, Y!21) & (~p13(Y!21)) & p12(Y!21) & ![X: $i] : (p12(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p13(X!22) & ![Y: $i] : (p13(Y) | (~r1(X!22, Y))) & (~p12(X!22))) | (r1(X!0, Y!23) & p13(Y!23) & ![X: $i] : (p13(X) | (~r1(Y!23, X))) & (~p12(Y!23)) & r1(Y!23, X!24) & (~p13(X!24)) & p12(X!24) & ![Y: $i] : (p12(Y) | (~r1(X!24, Y))))) & (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & r1(Y!27, X!28) & p11(X!28) & ![Y: $i] : (p11(Y) | (~r1(X!28, Y))) & (~p10(X!28)) & (~p11(Y!27)) & p10(Y!27) & ![X: $i] : (p10(X) | (~r1(Y!27, X)))) | (r1(X!0, Y!29) & p11(Y!29) & ![X: $i] : (p11(X) | (~r1(Y!29, X))) & (~p10(Y!29)) & r1(Y!29, X!30) & (~p11(X!30)) & p10(X!30) & ![Y: $i] : (p10(Y) | (~r1(X!30, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y)))))) & (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | (r1(X!0, Y!33) & (~p12(Y!33)) & p11(Y!33) & ![X: $i] : (p11(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p12(X!34) & ![Y: $i] : (p12(Y) | (~r1(X!34, Y))) & (~p11(X!34))) | (r1(X!0, Y!35) & p12(Y!35) & ![X: $i] : (p12(X) | (~r1(Y!35, X))) & (~p11(Y!35)) & r1(Y!35, X!36) & (~p12(X!36)) & p11(X!36) & ![Y: $i] : (p11(Y) | (~r1(X!36, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p11(tptp_fun_X_26(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | (r1(X!0, Y!38) & (~p10(Y!38)) & p9(Y!38) & ![X: $i] : (p9(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p10(X!39) & ![Y: $i] : (p10(Y) | (~r1(X!39, Y))) & (~p9(X!39))) | (r1(X!0, Y!40) & p10(Y!40) & ![X: $i] : (p10(X) | (~r1(Y!40, X))) & (~p9(Y!40)) & r1(Y!40, X!41) & (~p10(X!41)) & p9(X!41) & ![Y: $i] : (p9(Y) | (~r1(X!41, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | (r1(X!0, Y!45) & (~p9(Y!45)) & p8(Y!45) & ![X: $i] : (p8(X) | (~r1(Y!45, X))) & r1(Y!45, X!46) & p9(X!46) & ![Y: $i] : (p9(Y) | (~r1(X!46, Y))) & (~p8(X!46))) | (r1(X!0, Y!47) & p9(Y!47) & ![X: $i] : (p9(X) | (~r1(Y!47, X))) & (~p8(Y!47)) & r1(Y!47, X!48) & (~p9(X!48)) & p8(X!48) & ![Y: $i] : (p8(Y) | (~r1(X!48, Y))))) & (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | (r1(X!0, Y!50) & (~p8(Y!50)) & p7(Y!50) & ![X: $i] : (p7(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p8(X!51) & ![Y: $i] : (p8(Y) | (~r1(X!51, Y))) & (~p7(X!51))) | (r1(X!0, Y!52) & p8(Y!52) & ![X: $i] : (p8(X) | (~r1(Y!52, X))) & (~p7(Y!52)) & r1(Y!52, X!53) & (~p8(X!53)) & p7(X!53) & ![Y: $i] : (p7(Y) | (~r1(X!53, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y)))))) & $false & (![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(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] : ((~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] : (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))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y))))) | (r1(X!0, Y!82) & (~p3(Y!82)) & p2(Y!82) & ![X: $i] : (p2(X) | (~r1(Y!82, X))) & r1(Y!82, X!83) & p3(X!83) & ![Y: $i] : (p3(Y) | (~r1(X!83, Y))) & (~p2(X!83))) | (r1(X!0, Y!84) & p3(Y!84) & ![X: $i] : (p3(X) | (~r1(Y!84, X))) & (~p2(Y!84)) & r1(Y!84, X!85) & (~p3(X!85)) & p2(X!85) & ![Y: $i] : (p2(Y) | (~r1(X!85, Y))))) & (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(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)))))))),
% 0.50/0.65 inference(monotonicity,[status(thm)],[546, 510, 474, 438, 402, 366, 330, 294, 258, 222, 217, 181, 145, 109, 73, 37])).
% 0.50/0.65 tff(548,plain,
% 0.50/0.65 ((((((~p16(Y!1)) & (~(~r1(X!0, Y!1))) & (p15(Y!1) & ![X: $i] : (p15(X) | (~r1(Y!1, X)))) & ((~p15(X!2)) & (~(~r1(Y!1, X!2))) & (p16(X!2) & ![Y: $i] : (p16(Y) | (~r1(X!2, Y)))))) | ((~p15(Y!3)) & (~(~r1(X!0, Y!3))) & (p16(Y!3) & ![X: $i] : (p16(X) | (~r1(Y!3, X)))) & ((~p16(X!4)) & (~(~r1(Y!3, X!4))) & (p15(X!4) & ![Y: $i] : (p15(Y) | (~r1(X!4, Y)))))) | ((~p16(Y!5)) & (~p15(Y!5)) & (~(~r1(X!0, Y!5))) & (p16(Y!5) & ![X: $i] : (p16(X) | (~r1(Y!5, X)))) & (p15(Y!5) & ![X: $i] : (p15(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p16(Y)) | (~(p16(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ((((~p15(Y!8)) & (~(~r1(X!0, Y!8))) & (p14(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p14(X))) & ((~(~r1(Y!8, X!9))) & (~p14(X!9)) & (p15(X!9) & ![Y: $i] : (p15(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p14(Y!10)) & (p15(Y!10) & ![X: $i] : (p15(X) | (~r1(Y!10, X)))) & ((~p15(X!11)) & (~(~r1(Y!10, X!11))) & (p14(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p14(Y))))) | ((~p15(Y!12)) & (~(~r1(X!0, Y!12))) & (~p14(Y!12)) & (p15(Y!12) & ![X: $i] : (p15(X) | (~r1(Y!12, X)))) & (p14(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p14(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p15(Y)) | (~(p15(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p14(tptp_fun_X_13(Y))))) | p13(Y)) | (((~(~r1(X!0, Y!15))) & (~p14(Y!15)) & (p13(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p13(X))) & ((~(~r1(Y!15, X!16))) & (p14(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p14(Y))) & (~p13(X!16)))) | ((~(~r1(X!0, Y!17))) & (p14(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p14(X))) & (~p13(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p14(X!18)) & (p13(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p13(Y))))) | ((~(~r1(X!0, Y!19))) & (~p14(Y!19)) & (p14(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p14(X))) & (~p13(Y!19)) & (p13(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p13(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p13(tptp_fun_X_14(Y))))) | p12(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y)))))) | (((~(~r1(X!0, Y!21))) & (~p13(Y!21)) & (p12(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p12(X))) & ((~(~r1(Y!21, X!22))) & (p13(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p13(Y))) & (~p12(X!22)))) | ((~(~r1(X!0, Y!23))) & (p13(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p13(X))) & (~p12(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p13(X!24)) & (p12(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!25))) & (~p13(Y!25)) & (p13(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p13(X))) & (~p12(Y!25)) & (p12(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p12(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!27))) & ((~(~r1(Y!27, X!28))) & (p11(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p11(Y))) & (~p10(X!28))) & (~p11(Y!27)) & (p10(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p10(X)))) | ((~(~r1(X!0, Y!29))) & (p11(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p11(X))) & (~p10(Y!29)) & ((~(~r1(Y!29, X!30))) & (~p11(X!30)) & (p10(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!31))) & (~p11(Y!31)) & (p11(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p11(X))) & (~p10(Y!31)) & (p10(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p12(tptp_fun_X_20(Y))))) | p11(Y)) | (((~(~r1(X!0, Y!33))) & (~p12(Y!33)) & (p11(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p11(X))) & ((~(~r1(Y!33, X!34))) & (p12(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p12(Y))) & (~p11(X!34)))) | ((~(~r1(X!0, Y!35))) & (p12(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p12(X))) & (~p11(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p12(X!36)) & (p11(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!37))) & (~p12(Y!37)) & (p12(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p12(X))) & (~p11(Y!37)) & (p11(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p11(X))))) | ![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] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_32(Y))) | p10(tptp_fun_X_32(Y))))) | p9(Y)) | (((~(~r1(X!0, Y!38))) & (~p10(Y!38)) & (p9(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p9(X))) & ((~(~r1(Y!38, X!39))) & (p10(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p10(Y))) & (~p9(X!39)))) | ((~(~r1(X!0, Y!40))) & (p10(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p10(X))) & (~p9(Y!40)) & ((~(~r1(Y!40, X!41))) & (~p10(X!41)) & (p9(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p9(Y))))) | ((~(~r1(X!0, Y!42))) & (~p10(Y!42)) & (p10(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p10(X))) & (~p9(Y!42)) & (p9(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p9(tptp_fun_X_43(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y)))))) | (((~(~r1(X!0, Y!45))) & (~p9(Y!45)) & (p8(Y!45) & ![X: $i] : ((~r1(Y!45, X)) | p8(X))) & ((~(~r1(Y!45, X!46))) & (p9(X!46) & ![Y: $i] : ((~r1(X!46, Y)) | p9(Y))) & (~p8(X!46)))) | ((~(~r1(X!0, Y!47))) & (p9(Y!47) & ![X: $i] : ((~r1(Y!47, X)) | p9(X))) & (~p8(Y!47)) & ((~(~r1(Y!47, X!48))) & (~p9(X!48)) & (p8(X!48) & ![Y: $i] : ((~r1(X!48, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!49))) & (~p9(Y!49)) & (p9(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p9(X))) & (~p8(Y!49)) & (p8(Y!49) & ![X: $i] : ((~r1(Y!49, X)) | p8(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p8(tptp_fun_X_44(Y))))) | p7(Y)) | (((~(~r1(X!0, Y!50))) & (~p8(Y!50)) & (p7(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p7(X))) & ((~(~r1(Y!50, X!51))) & (p8(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p8(Y))) & (~p7(X!51)))) | ((~(~r1(X!0, Y!52))) & (p8(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p8(X))) & (~p7(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p8(X!53)) & (p7(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!54))) & (~p8(Y!54)) & (p8(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p8(X))) & (~p7(Y!54)) & (p7(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p7(tptp_fun_X_55(Y))))))) & ((~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_55(Y))) | p7(tptp_fun_X_55(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)) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(Y)))))) | (((~(~r1(X!0, Y!82))) & (~p3(Y!82)) & (p2(Y!82) & ![X: $i] : ((~r1(Y!82, X)) | p2(X))) & ((~(~r1(Y!82, X!83))) & (p3(X!83) & ![Y: $i] : ((~r1(X!83, Y)) | p3(Y))) & (~p2(X!83)))) | ((~(~r1(X!0, Y!84))) & (p3(Y!84) & ![X: $i] : ((~r1(Y!84, X)) | p3(X))) & (~p2(Y!84)) & ((~(~r1(Y!84, X!85))) & (~p3(X!85)) & (p2(X!85) & ![Y: $i] : ((~r1(X!85, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!86))) & (~p3(Y!86)) & (p3(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p3(X))) & (~p2(Y!86)) & (p2(Y!86) & ![X: $i] : ((~r1(Y!86, X)) | p2(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_81(Y))) | p2(tptp_fun_X_81(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),
% 0.50/0.66 inference(transitivity,[status(thm)],[547, 1])).
% 0.50/0.66 tff(549,plain,
% 0.50/0.66 (?[X: $i] : (~((~((~(![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] : (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] : (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) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(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] : ((~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)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | 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)) | (~(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))))) | (~(![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)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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))))) & ![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)) | (~(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)))) | ![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)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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)) | (~(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)) | (~(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)))) | ![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] : ((~r1(X, Y)) | p8(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))))) | (~(![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)) | (~(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] : (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] : (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] : (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) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(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] : ((~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)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | 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)) | (~(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))))) | (~(![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)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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))))) & ![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)) | (~(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)))) | ![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)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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)) | (~(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)) | (~(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)))) | ![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] : ((~r1(X, Y)) | p8(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))))) | (~(![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)) | (~(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)))))))))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(550,plain,
% 0.50/0.67 ((~(~?[X: $i] : (~((~((~(![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] : (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] : (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) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(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] : ((~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)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | 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)) | (~(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))))) | (~(![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)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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))))) & ![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)) | (~(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)))) | ![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)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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)) | (~(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)) | (~(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)))) | ![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] : ((~r1(X, Y)) | p8(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))))) | (~(![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)) | (~(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] : (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] : (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] : (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) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(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] : ((~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)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | 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)) | (~(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))))) | (~(![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)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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))))) & ![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)) | (~(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)))) | ![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)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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)) | (~(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)) | (~(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)))) | ![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] : ((~r1(X, Y)) | p8(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))))) | (~(![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)) | (~(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)))))))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(551,plain,
% 0.50/0.68 ((~?[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] : (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] : (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] : (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) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(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] : ((~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)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | 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)) | (~(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))))) | (~(![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)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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))))) & ![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)) | (~(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)))) | ![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)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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)) | (~(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)) | (~(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)))) | ![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] : ((~r1(X, Y)) | p8(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))))) | (~(![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)) | (~(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))))))))))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(552,plain,
% 0.50/0.69 ((~(~?[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] : (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] : (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] : (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) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(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] : ((~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)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | 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)) | (~(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))))) | (~(![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)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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))))) & ![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)) | (~(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)))) | ![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)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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)) | (~(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)) | (~(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)))) | ![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] : ((~r1(X, Y)) | p8(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))))) | (~(![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)) | (~(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)))))))))))),
% 0.50/0.70 inference(monotonicity,[status(thm)],[551])).
% 0.50/0.70 tff(553,plain,
% 0.50/0.70 ((~(~?[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] : (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] : (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] : (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) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(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] : ((~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)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | 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)) | (~(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))))) | (~(![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)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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))))) & ![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)) | (~(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)))) | ![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)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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)) | (~(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)) | (~(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)))) | ![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] : ((~r1(X, Y)) | p8(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))))) | (~(![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)) | (~(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)))))))))),
% 0.58/0.70 inference(transitivity,[status(thm)],[552, 550])).
% 0.58/0.70 tff(554,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/sandbox/benchmark/theBenchmark.p','main')).
% 0.58/0.71 tff(555,plain,
% 0.58/0.71 (?[X: $i] : (~((~((~(![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] : (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] : (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) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(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] : ((~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)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | 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)) | (~(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))))) | (~(![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)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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))))) & ![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)) | (~(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)))) | ![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)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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)) | (~(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)) | (~(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)))) | ![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] : ((~r1(X, Y)) | p8(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))))) | (~(![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)) | (~(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)))))))))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.58/0.71 tff(556,plain,
% 0.58/0.71 (?[X: $i] : (~((~((~(![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] : (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] : (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) | (~(p15(Y) & ![X: $i] : (p15(X) | (~r1(Y, X))))) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(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] : ((~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)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | 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)) | (~(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))))) | (~(![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)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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))))) & ![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)) | (~(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)))) | ![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)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(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)) | (~(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)) | (~(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)))) | ![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] : ((~r1(X, Y)) | p8(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))))) | (~(![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)) | (~(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: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[555, 549])).
% 0.58/0.72 tff(557,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[556, 548])).
% 0.58/0.72 % SZS output end Proof
%------------------------------------------------------------------------------