TSTP Solution File: KRS149+1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : KRS149+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 : Tue May  7 07:52:00 EDT 2024

% Result   : Theorem 6.43s 2.57s
% Output   : Refutation 6.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  242
% Syntax   : Number of formulae    :  370 (  25 unt; 116 typ;   0 def)
%            Number of atoms       : 1047 (   0 equ;   0 cnn)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives : 2276 ( 265   ~;   0   |; 458   &;1218   @)
%                                         ( 109 <=>; 226  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  116 ( 116   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  117 ( 116 usr;   2 con; 0-2 aty)
%            Number of variables   :  394 (   0   ^ 232   !; 162   ?; 394   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cowlThing_type,type,
    cowlThing: $i > $o ).

thf(cowlNothing_type,type,
    cowlNothing: $i > $o ).

thf(xsd_string_type,type,
    xsd_string: $i > $o ).

thf(xsd_integer_type,type,
    xsd_integer: $i > $o ).

thf(cC216_type,type,
    cC216: $i > $o ).

thf(iV3102_type,type,
    iV3102: $i ).

thf(cC46_type,type,
    cC46: $i > $o ).

thf(cC30_type,type,
    cC30: $i > $o ).

thf(cC44_type,type,
    cC44: $i > $o ).

thf(cC28_type,type,
    cC28: $i > $o ).

thf(cC64_type,type,
    cC64: $i > $o ).

thf(cC14_type,type,
    cC14: $i > $o ).

thf(cC134_type,type,
    cC134: $i > $o ).

thf(cC132_type,type,
    cC132: $i > $o ).

thf(cC108_type,type,
    cC108: $i > $o ).

thf(cC204_type,type,
    cC204: $i > $o ).

thf(cC178_type,type,
    cC178: $i > $o ).

thf(cC202_type,type,
    cC202: $i > $o ).

thf(cC206_type,type,
    cC206: $i > $o ).

thf(cC170_type,type,
    cC170: $i > $o ).

thf(cC96_type,type,
    cC96: $i > $o ).

thf(cC84_type,type,
    cC84: $i > $o ).

thf(cC94_type,type,
    cC94: $i > $o ).

thf(cC190_type,type,
    cC190: $i > $o ).

thf(cC200_type,type,
    cC200: $i > $o ).

thf(cC210_type,type,
    cC210: $i > $o ).

thf(cC208_type,type,
    cC208: $i > $o ).

thf(cC168_type,type,
    cC168: $i > $o ).

thf(cC166_type,type,
    cC166: $i > $o ).

thf(cC142_type,type,
    cC142: $i > $o ).

thf(cC130_type,type,
    cC130: $i > $o ).

thf(cC120_type,type,
    cC120: $i > $o ).

thf(cC154_type,type,
    cC154: $i > $o ).

thf(cC164_type,type,
    cC164: $i > $o ).

thf(cC80_type,type,
    cC80: $i > $o ).

thf(cC16_type,type,
    cC16: $i > $o ).

thf(cC78_type,type,
    cC78: $i > $o ).

thf(cC58_type,type,
    cC58: $i > $o ).

thf(rR1_type,type,
    rR1: $i > $i > $o ).

thf(cC56_type,type,
    cC56: $i > $o ).

thf(cC8_type,type,
    cC8: $i > $o ).

thf(cC6_type,type,
    cC6: $i > $o ).

thf(cC82_type,type,
    cC82: $i > $o ).

thf(cC74_type,type,
    cC74: $i > $o ).

thf(cC138_type,type,
    cC138: $i > $o ).

thf(cC136_type,type,
    cC136: $i > $o ).

thf(cC66_type,type,
    cC66: $i > $o ).

thf(cC38_type,type,
    cC38: $i > $o ).

thf(cC36_type,type,
    cC36: $i > $o ).

thf(cC112_type,type,
    cC112: $i > $o ).

thf(cC110_type,type,
    cC110: $i > $o ).

thf(cC150_type,type,
    cC150: $i > $o ).

thf(cC148_type,type,
    cC148: $i > $o ).

thf(cC162_type,type,
    cC162: $i > $o ).

thf(cC2_type,type,
    cC2: $i > $o ).

thf(cC4_type,type,
    cC4: $i > $o ).

thf(cC104_type,type,
    cC104: $i > $o ).

thf(cC102_type,type,
    cC102: $i > $o ).

thf(cC184_type,type,
    cC184: $i > $o ).

thf(cC182_type,type,
    cC182: $i > $o ).

thf(cC106_type,type,
    cC106: $i > $o ).

thf(cC68_type,type,
    cC68: $i > $o ).

thf(cC76_type,type,
    cC76: $i > $o ).

thf(cC156_type,type,
    cC156: $i > $o ).

thf(cC32_type,type,
    cC32: $i > $o ).

thf(cC34_type,type,
    cC34: $i > $o ).

thf(cC198_type,type,
    cC198: $i > $o ).

thf(cC196_type,type,
    cC196: $i > $o ).

thf(cC18_type,type,
    cC18: $i > $o ).

thf(cC146_type,type,
    cC146: $i > $o ).

thf(cC144_type,type,
    cC144: $i > $o ).

thf(cC118_type,type,
    cC118: $i > $o ).

thf(cC50_type,type,
    cC50: $i > $o ).

thf(cC90_type,type,
    cC90: $i > $o ).

thf(cC88_type,type,
    cC88: $i > $o ).

thf(cC214_type,type,
    cC214: $i > $o ).

thf(cC100_type,type,
    cC100: $i > $o ).

thf(cC212_type,type,
    cC212: $i > $o ).

thf(cC24_type,type,
    cC24: $i > $o ).

thf(cC22_type,type,
    cC22: $i > $o ).

thf(cC180_type,type,
    cC180: $i > $o ).

thf(cC140_type,type,
    cC140: $i > $o ).

thf(cC86_type,type,
    cC86: $i > $o ).

thf(cC72_type,type,
    cC72: $i > $o ).

thf(cC70_type,type,
    cC70: $i > $o ).

thf(cC160_type,type,
    cC160: $i > $o ).

thf(cC158_type,type,
    cC158: $i > $o ).

thf(cC54_type,type,
    cC54: $i > $o ).

thf(cC194_type,type,
    cC194: $i > $o ).

thf(cC152_type,type,
    cC152: $i > $o ).

thf(cC126_type,type,
    cC126: $i > $o ).

thf(cC124_type,type,
    cC124: $i > $o ).

thf(cC92_type,type,
    cC92: $i > $o ).

thf(cC26_type,type,
    cC26: $i > $o ).

thf(cC12_type,type,
    cC12: $i > $o ).

thf(cC10_type,type,
    cC10: $i > $o ).

thf(cC20_type,type,
    cC20: $i > $o ).

thf(cC98_type,type,
    cC98: $i > $o ).

thf(cC52_type,type,
    cC52: $i > $o ).

thf(cC116_type,type,
    cC116: $i > $o ).

thf(cC114_type,type,
    cC114: $i > $o ).

thf(cC122_type,type,
    cC122: $i > $o ).

thf(cC60_type,type,
    cC60: $i > $o ).

thf(cC48_type,type,
    cC48: $i > $o ).

thf(cC188_type,type,
    cC188: $i > $o ).

thf(cC186_type,type,
    cC186: $i > $o ).

thf(cC62_type,type,
    cC62: $i > $o ).

thf(cC172_type,type,
    cC172: $i > $o ).

thf(cC192_type,type,
    cC192: $i > $o ).

thf(cC42_type,type,
    cC42: $i > $o ).

thf(cC40_type,type,
    cC40: $i > $o ).

thf(cC176_type,type,
    cC176: $i > $o ).

thf(cC174_type,type,
    cC174: $i > $o ).

thf(cC128_type,type,
    cC128: $i > $o ).

thf(cTEST_type,type,
    cTEST: $i > $o ).

thf(cTOP_type,type,
    cTOP: $i > $o ).

thf(117,axiom,
    ! [A: $i] :
      ( ( cC28 @ A )
    <=> ( ~ ( cC26 @ A )
        & ~ ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_69) ).

thf(779,plain,
    ! [A: $i] :
      ( ( ( cC28 @ A )
       => ( ~ ( cC26 @ A )
          & ~ ( cC16 @ A ) ) )
      & ( ( ~ ( cC26 @ A )
          & ~ ( cC16 @ A ) )
       => ( cC28 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( cC36 @ A )
    <=> ( ( cC32 @ A )
        & ( cC34 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_72) ).

thf(296,plain,
    ! [A: $i] :
      ( ( ( cC36 @ A )
       => ( ( cC32 @ A )
          & ( cC34 @ A ) ) )
      & ( ( ( cC32 @ A )
          & ( cC34 @ A ) )
       => ( cC36 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ~ ( cC60 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_110) ).

thf(739,plain,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ~ ( cC60 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(127,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC98 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_117) ).

thf(809,plain,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC98 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(111,axiom,
    ~ ( cC62 @ iV3102 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_119) ).

thf(760,plain,
    ~ ( cC62 @ iV3102 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ( cC188 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC186 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).

thf(518,plain,
    ! [A: $i] :
      ( ( ( cC188 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC186 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC186 @ B ) )
       => ( cC188 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( cC168 @ A )
    <=> ( ~ ( cC166 @ A )
        & ~ ( cC142 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).

thf(170,plain,
    ! [A: $i] :
      ( ( ( cC168 @ A )
       => ( ~ ( cC166 @ A )
          & ~ ( cC142 @ A ) ) )
      & ( ( ~ ( cC166 @ A )
          & ~ ( cC142 @ A ) )
       => ( cC168 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(112,axiom,
    ~ ( cC100 @ iV3102 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_124) ).

thf(762,plain,
    ~ ( cC100 @ iV3102 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( cC18 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).

thf(308,plain,
    ! [A: $i] :
      ( ( ( cC18 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC18 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(107,axiom,
    ! [A: $i] :
      ( ( cC30 @ A )
    <=> ( ( cC14 @ A )
        & ( cC28 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_70) ).

thf(741,plain,
    ! [A: $i] :
      ( ( ( cC30 @ A )
       => ( ( cC14 @ A )
          & ( cC28 @ A ) ) )
      & ( ( ( cC14 @ A )
          & ( cC28 @ A ) )
       => ( cC30 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( cC110 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).

thf(440,plain,
    ! [A: $i] :
      ( ( ( cC110 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC110 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( cC10 @ A )
    <=> ( ~ ( cC8 @ A )
        & ~ ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

thf(614,plain,
    ! [A: $i] :
      ( ( ( cC10 @ A )
       => ( ~ ( cC8 @ A )
          & ~ ( cC2 @ A ) ) )
      & ( ( ~ ( cC8 @ A )
          & ~ ( cC2 @ A ) )
       => ( cC10 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( cC136 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).

thf(500,plain,
    ! [A: $i] :
      ( ( ( cC136 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC136 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ( cC92 @ A )
    <=> ( ~ ( cC90 @ A )
        & ~ ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_103) ).

thf(698,plain,
    ! [A: $i] :
      ( ( ( cC92 @ A )
       => ( ~ ( cC90 @ A )
          & ~ ( cC16 @ A ) ) )
      & ( ( ~ ( cC90 @ A )
          & ~ ( cC16 @ A ) )
       => ( cC92 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(108,axiom,
    ~ ( cC42 @ iV3102 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_114) ).

thf(747,plain,
    ~ ( cC42 @ iV3102 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ( cC102 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).

thf(404,plain,
    ! [A: $i] :
      ( ( ( cC102 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC102 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( cC120 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC118 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).

thf(320,plain,
    ! [A: $i] :
      ( ( ( cC120 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC118 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC118 @ B ) )
       => ( cC120 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(118,axiom,
    ~ ( cC16 @ iV3102 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_121) ).

thf(785,plain,
    ~ ( cC16 @ iV3102 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(38,axiom,
    ! [A: $i] :
      ( ( cC214 @ A )
    <=> ( ( cC100 @ A )
        & ~ ( cC212 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_64) ).

thf(344,plain,
    ! [A: $i] :
      ( ( ( cC214 @ A )
       => ( ( cC100 @ A )
          & ~ ( cC212 @ A ) ) )
      & ( ( ( cC100 @ A )
          & ~ ( cC212 @ A ) )
       => ( cC214 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( cC200 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC198 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_57) ).

thf(542,plain,
    ! [A: $i] :
      ( ( ( cC200 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC198 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC198 @ B ) )
       => ( cC200 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( cC76 @ A )
    <=> ( ( cC74 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_94) ).

thf(638,plain,
    ! [A: $i] :
      ( ( ( cC76 @ A )
       => ( ( cC74 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC74 @ A )
          & ( cC16 @ A ) )
       => ( cC76 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( cC152 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC150 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).

thf(416,plain,
    ! [A: $i] :
      ( ( ( cC152 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC150 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC150 @ B ) )
       => ( cC152 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( cC96 @ A )
    <=> ( ( cC84 @ A )
        & ~ ( cC94 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_105) ).

thf(152,plain,
    ! [A: $i] :
      ( ( ( cC96 @ A )
       => ( ( cC84 @ A )
          & ~ ( cC94 @ A ) ) )
      & ( ( ( cC84 @ A )
          & ~ ( cC94 @ A ) )
       => ( cC96 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( cC78 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC76 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_95) ).

thf(284,plain,
    ! [A: $i] :
      ( ( ( cC78 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC76 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC76 @ B ) )
       => ( cC78 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(114,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ~ ( cC24 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_113) ).

thf(770,plain,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ~ ( cC24 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( cC210 @ A )
    <=> ( ~ ( cC208 @ A )
        & ~ ( cC134 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).

thf(164,plain,
    ! [A: $i] :
      ( ( ( cC210 @ A )
       => ( ~ ( cC208 @ A )
          & ~ ( cC134 @ A ) ) )
      & ( ( ~ ( cC208 @ A )
          & ~ ( cC134 @ A ) )
       => ( cC210 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(120,axiom,
    ~ ( cC12 @ iV3102 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_115) ).

thf(789,plain,
    ~ ( cC12 @ iV3102 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( cC178 @ A )
    <=> ( ~ ( cC16 @ A )
        & ~ ( cC176 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).

thf(602,plain,
    ! [A: $i] :
      ( ( ( cC178 @ A )
       => ( ~ ( cC16 @ A )
          & ~ ( cC176 @ A ) ) )
      & ( ( ~ ( cC16 @ A )
          & ~ ( cC176 @ A ) )
       => ( cC178 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( cC40 @ A )
    <=> ( ~ ( cC38 @ A )
        & ~ ( cC32 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_75) ).

thf(692,plain,
    ! [A: $i] :
      ( ( ( cC40 @ A )
       => ( ~ ( cC38 @ A )
          & ~ ( cC32 @ A ) ) )
      & ( ( ~ ( cC38 @ A )
          & ~ ( cC32 @ A ) )
       => ( cC40 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( cC84 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC82 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_99) ).

thf(428,plain,
    ! [A: $i] :
      ( ( ( cC84 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC82 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC82 @ B ) )
       => ( cC84 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( cC82 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC80 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_98) ).

thf(206,plain,
    ! [A: $i] :
      ( ( ( cC82 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC80 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC80 @ B ) )
       => ( cC82 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ( cC148 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC146 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).

thf(452,plain,
    ! [A: $i] :
      ( ( ( cC148 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC146 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC146 @ B ) )
       => ( cC148 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( cC164 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC162 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).

thf(248,plain,
    ! [A: $i] :
      ( ( ( cC164 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC162 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC162 @ B ) )
       => ( cC164 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( cC88 @ A )
    <=> ( ( cC86 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_101) ).

thf(380,plain,
    ! [A: $i] :
      ( ( ( cC88 @ A )
       => ( ( cC86 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC86 @ A )
          & ( cC16 @ A ) )
       => ( cC88 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( cC154 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC152 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).

thf(512,plain,
    ! [A: $i] :
      ( ( ( cC154 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC152 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC152 @ B ) )
       => ( cC154 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(116,axiom,
    cowlThing @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_109) ).

thf(778,plain,
    cowlThing @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( cC198 @ A )
    <=> ( ~ ( cC196 @ A )
        & ~ ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_55) ).

thf(302,plain,
    ! [A: $i] :
      ( ( ( cC198 @ A )
       => ( ~ ( cC196 @ A )
          & ~ ( cC16 @ A ) ) )
      & ( ( ~ ( cC196 @ A )
          & ~ ( cC16 @ A ) )
       => ( cC198 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( cC104 @ A )
    <=> ( ( cC102 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

thf(260,plain,
    ! [A: $i] :
      ( ( ( cC104 @ A )
       => ( ( cC102 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC102 @ A )
          & ( cC16 @ A ) )
       => ( cC104 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( cC160 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC158 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).

thf(392,plain,
    ! [A: $i] :
      ( ( ( cC160 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC158 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC158 @ B ) )
       => ( cC160 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(103,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ~ ( cC40 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_120) ).

thf(729,plain,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ~ ( cC40 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( cC186 @ A )
    <=> ( ~ ( cC16 @ A )
        & ~ ( cC184 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).

thf(566,plain,
    ! [A: $i] :
      ( ( ( cC186 @ A )
       => ( ~ ( cC16 @ A )
          & ~ ( cC184 @ A ) ) )
      & ( ( ~ ( cC16 @ A )
          & ~ ( cC184 @ A ) )
       => ( cC186 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ( cC158 @ A )
    <=> ( ( cC156 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).

thf(710,plain,
    ! [A: $i] :
      ( ( ( cC158 @ A )
       => ( ( cC156 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC156 @ A )
          & ( cC16 @ A ) )
       => ( cC158 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( cC66 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_89) ).

thf(224,plain,
    ! [A: $i] :
      ( ( ( cC66 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC66 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( cC176 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC174 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).

thf(578,plain,
    ! [A: $i] :
      ( ( ( cC176 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC174 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC174 @ B ) )
       => ( cC176 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( cC144 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).

thf(650,plain,
    ! [A: $i] :
      ( ( ( cC144 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC144 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( cC80 @ A )
    <=> ( ~ ( cC16 @ A )
        & ~ ( cC78 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_97) ).

thf(188,plain,
    ! [A: $i] :
      ( ( ( cC80 @ A )
       => ( ~ ( cC16 @ A )
          & ~ ( cC78 @ A ) ) )
      & ( ( ~ ( cC16 @ A )
          & ~ ( cC78 @ A ) )
       => ( cC80 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(40,axiom,
    ! [A: $i] :
      ( ( cC180 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_46) ).

thf(356,plain,
    ! [A: $i] :
      ( ( ( cC180 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC180 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( cC98 @ A )
    <=> ( ~ ( cC72 @ A )
        & ~ ( cC96 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_106) ).

thf(488,plain,
    ! [A: $i] :
      ( ( ( cC98 @ A )
       => ( ~ ( cC72 @ A )
          & ~ ( cC96 @ A ) ) )
      & ( ( ~ ( cC72 @ A )
          & ~ ( cC96 @ A ) )
       => ( cC98 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(73,axiom,
    ! [A: $i] :
      ( ( cC192 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_52) ).

thf(554,plain,
    ! [A: $i] :
      ( ( ( cC192 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC192 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(79,axiom,
    ! [A: $i] :
      ( ( cC182 @ A )
    <=> ( ( cC16 @ A )
        & ( cC180 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_47) ).

thf(590,plain,
    ! [A: $i] :
      ( ( ( cC182 @ A )
       => ( ( cC16 @ A )
          & ( cC180 @ A ) ) )
      & ( ( ( cC16 @ A )
          & ( cC180 @ A ) )
       => ( cC182 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( cC74 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_93) ).

thf(212,plain,
    ! [A: $i] :
      ( ( ( cC74 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC74 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ( cC20 @ A )
    <=> ( ( cC18 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).

thf(686,plain,
    ! [A: $i] :
      ( ( ( cC20 @ A )
       => ( ( cC18 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC18 @ A )
          & ( cC16 @ A ) )
       => ( cC20 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(60,axiom,
    ! [A: $i] :
      ( ( cC52 @ A )
    <=> ( ( cC50 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_81) ).

thf(476,plain,
    ! [A: $i] :
      ( ( ( cC52 @ A )
       => ( ( cC50 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC50 @ A )
          & ( cC16 @ A ) )
       => ( cC52 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( cC134 @ A )
    <=> ( ~ ( cC132 @ A )
        & ~ ( cC108 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).

thf(134,plain,
    ! [A: $i] :
      ( ( ( cC134 @ A )
       => ( ~ ( cC132 @ A )
          & ~ ( cC108 @ A ) ) )
      & ( ( ~ ( cC132 @ A )
          & ~ ( cC108 @ A ) )
       => ( cC134 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,conjecture,
    ( ! [A: $i] :
        ( ( cowlThing @ A )
        & ~ ( cowlNothing @ A ) )
    & ! [A: $i] :
        ( ( xsd_string @ A )
      <=> ~ ( xsd_integer @ A ) )
    & ( cC216 @ iV3102 )
    & ( cC46 @ iV3102 )
    & ( cC30 @ iV3102 )
    & ( cC44 @ iV3102 )
    & ( cC28 @ iV3102 )
    & ( cC64 @ iV3102 )
    & ( cC14 @ iV3102 )
    & ( cowlThing @ iV3102 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i] :
          ( ( cowlThing @ A )
          & ~ ( cowlNothing @ A ) )
      & ! [A: $i] :
          ( ( xsd_string @ A )
        <=> ~ ( xsd_integer @ A ) )
      & ( cC216 @ iV3102 )
      & ( cC46 @ iV3102 )
      & ( cC30 @ iV3102 )
      & ( cC44 @ iV3102 )
      & ( cC28 @ iV3102 )
      & ( cC64 @ iV3102 )
      & ( cC14 @ iV3102 )
      & ( cowlThing @ iV3102 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(128,plain,
    ~ ( ! [A: $i] :
          ( ( cowlThing @ A )
          & ~ ( cowlNothing @ A ) )
      & ! [A: $i] :
          ( ( ( xsd_string @ A )
           => ~ ( xsd_integer @ A ) )
          & ( ~ ( xsd_integer @ A )
           => ( xsd_string @ A ) ) )
      & ( cC216 @ iV3102 )
      & ( cC46 @ iV3102 )
      & ( cC30 @ iV3102 )
      & ( cC44 @ iV3102 )
      & ( cC28 @ iV3102 )
      & ( cC64 @ iV3102 )
      & ( cC14 @ iV3102 )
      & ( cowlThing @ iV3102 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(122,axiom,
    ~ ( cC2 @ iV3102 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_122) ).

thf(792,plain,
    ~ ( cC2 @ iV3102 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( cC184 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC182 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).

thf(266,plain,
    ! [A: $i] :
      ( ( ( cC184 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC182 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC182 @ B ) )
       => ( cC184 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( cC56 @ A )
    <=> ( ~ ( cC16 @ A )
        & ~ ( cC54 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_83) ).

thf(398,plain,
    ! [A: $i] :
      ( ( ( cC56 @ A )
       => ( ~ ( cC16 @ A )
          & ~ ( cC54 @ A ) ) )
      & ( ( ~ ( cC16 @ A )
          & ~ ( cC54 @ A ) )
       => ( cC56 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ( cC114 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC112 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).

thf(674,plain,
    ! [A: $i] :
      ( ( ( cC114 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC112 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC112 @ B ) )
       => ( cC114 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( cC124 @ A )
    <=> ( ( cC122 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).

thf(530,plain,
    ! [A: $i] :
      ( ( ( cC124 @ A )
       => ( ( cC122 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC122 @ A )
          & ( cC16 @ A ) )
       => ( cC124 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(123,axiom,
    ~ ( cC32 @ iV3102 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_123) ).

thf(794,plain,
    ~ ( cC32 @ iV3102 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ( cC162 @ A )
    <=> ( ~ ( cC16 @ A )
        & ~ ( cC160 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).

thf(662,plain,
    ! [A: $i] :
      ( ( ( cC162 @ A )
       => ( ~ ( cC16 @ A )
          & ~ ( cC160 @ A ) ) )
      & ( ( ~ ( cC16 @ A )
          & ~ ( cC160 @ A ) )
       => ( cC162 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( cC48 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_79) ).

thf(584,plain,
    ! [A: $i] :
      ( ( ( cC48 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC48 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( cC132 @ A )
    <=> ( ~ ( cC130 @ A )
        & ( cC120 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).

thf(176,plain,
    ! [A: $i] :
      ( ( ( cC132 @ A )
       => ( ~ ( cC130 @ A )
          & ( cC120 @ A ) ) )
      & ( ( ~ ( cC130 @ A )
          & ( cC120 @ A ) )
       => ( cC132 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(115,axiom,
    ! [A: $i] :
      ( ( cTEST @ A )
    <=> ( ( cC216 @ A )
        & ( cC46 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_107) ).

thf(772,plain,
    ! [A: $i] :
      ( ( ( cTEST @ A )
       => ( ( cC216 @ A )
          & ( cC46 @ A ) ) )
      & ( ( ( cC216 @ A )
          & ( cC46 @ A ) )
       => ( cTEST @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( cC42 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC40 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_76) ).

thf(572,plain,
    ! [A: $i] :
      ( ( ( cC42 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC40 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC40 @ B ) )
       => ( cC42 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(119,axiom,
    ~ ( cC26 @ iV3102 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_116) ).

thf(787,plain,
    ~ ( cC26 @ iV3102 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( cC112 @ A )
    <=> ( ( cC110 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).

thf(236,plain,
    ! [A: $i] :
      ( ( ( cC112 @ A )
       => ( ( cC110 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC110 @ A )
          & ( cC16 @ A ) )
       => ( cC112 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(98,axiom,
    ! [A: $i] :
      ( ( cC70 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC68 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_91) ).

thf(704,plain,
    ! [A: $i] :
      ( ( ( cC70 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC68 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC68 @ B ) )
       => ( cC70 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( cC24 @ A )
    <=> ( ~ ( cC22 @ A )
        & ~ ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_67) ).

thf(350,plain,
    ! [A: $i] :
      ( ( ( cC24 @ A )
       => ( ~ ( cC22 @ A )
          & ~ ( cC16 @ A ) ) )
      & ( ( ~ ( cC22 @ A )
          & ~ ( cC16 @ A ) )
       => ( cC24 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(113,axiom,
    ! [A: $i] :
      ( ( cC64 @ A )
    <=> ( ~ ( cC62 @ A )
        & ( cTOP @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_88) ).

thf(764,plain,
    ! [A: $i] :
      ( ( ( cC64 @ A )
       => ( ~ ( cC62 @ A )
          & ( cTOP @ A ) ) )
      & ( ( ~ ( cC62 @ A )
          & ( cTOP @ A ) )
       => ( cC64 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( cC38 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC36 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_73) ).

thf(230,plain,
    ! [A: $i] :
      ( ( ( cC38 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC36 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC36 @ B ) )
       => ( cC38 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( cC140 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC138 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).

thf(362,plain,
    ! [A: $i] :
      ( ( ( cC140 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC138 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC138 @ B ) )
       => ( cC140 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(105,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ~ ( cC10 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_111) ).

thf(737,plain,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ~ ( cC10 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( cC94 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC92 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_104) ).

thf(434,plain,
    ! [A: $i] :
      ( ( ( cC94 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC92 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC92 @ B ) )
       => ( cC94 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(63,axiom,
    ! [A: $i] :
      ( ( cC122 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).

thf(494,plain,
    ! [A: $i] :
      ( ( ( cC122 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC122 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( cC204 @ A )
    <=> ( ~ ( cC178 @ A )
        & ~ ( cC202 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).

thf(140,plain,
    ! [A: $i] :
      ( ( ( cC204 @ A )
       => ( ~ ( cC178 @ A )
          & ~ ( cC202 @ A ) ) )
      & ( ( ~ ( cC178 @ A )
          & ~ ( cC202 @ A ) )
       => ( cC204 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(85,axiom,
    ! [A: $i] :
      ( ( cC34 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC32 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_71) ).

thf(626,plain,
    ! [A: $i] :
      ( ( ( cC34 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC32 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC32 @ B ) )
       => ( cC34 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( cC190 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC188 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).

thf(668,plain,
    ! [A: $i] :
      ( ( ( cC190 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC188 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC188 @ B ) )
       => ( cC190 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( cC68 @ A )
    <=> ( ( cC66 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_90) ).

thf(278,plain,
    ! [A: $i] :
      ( ( ( cC68 @ A )
       => ( ( cC66 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC66 @ A )
          & ( cC16 @ A ) )
       => ( cC68 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ( cC212 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC210 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_63) ).

thf(608,plain,
    ! [A: $i] :
      ( ( ( cC212 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC210 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC210 @ B ) )
       => ( cC212 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(101,axiom,
    ! [A: $i] :
      ( ( cC14 @ A )
    <=> ( ~ ( cC12 @ A )
        & ~ ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).

thf(722,plain,
    ! [A: $i] :
      ( ( ( cC14 @ A )
       => ( ~ ( cC12 @ A )
          & ~ ( cC2 @ A ) ) )
      & ( ( ~ ( cC12 @ A )
          & ~ ( cC2 @ A ) )
       => ( cC14 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ( cC128 @ A )
    <=> ( ~ ( cC16 @ A )
        & ~ ( cC126 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).

thf(680,plain,
    ! [A: $i] :
      ( ( ( cC128 @ A )
       => ( ~ ( cC16 @ A )
          & ~ ( cC126 @ A ) ) )
      & ( ( ~ ( cC16 @ A )
          & ~ ( cC126 @ A ) )
       => ( cC128 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(72,axiom,
    ! [A: $i] :
      ( ( cC118 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC116 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).

thf(548,plain,
    ! [A: $i] :
      ( ( ( cC118 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC116 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC116 @ B ) )
       => ( cC118 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( cC170 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC168 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).

thf(374,plain,
    ! [A: $i] :
      ( ( ( cC170 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC168 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC168 @ B ) )
       => ( cC170 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(109,axiom,
    ! [A: $i] :
      ( ( xsd_string @ A )
    <=> ~ ( xsd_integer @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).

thf(749,plain,
    ! [A: $i] :
      ( ( ( xsd_string @ A )
       => ~ ( xsd_integer @ A ) )
      & ( ~ ( xsd_integer @ A )
       => ( xsd_string @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( cC216 @ A )
    <=> ( ~ ( cC214 @ A )
        & ( cC64 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).

thf(754,plain,
    ! [A: $i] :
      ( ( ( cC216 @ A )
       => ( ~ ( cC214 @ A )
          & ( cC64 @ A ) ) )
      & ( ( ~ ( cC214 @ A )
          & ( cC64 @ A ) )
       => ( cC216 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ( cC12 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC10 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).

thf(458,plain,
    ! [A: $i] :
      ( ( ( cC12 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC10 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC10 @ B ) )
       => ( cC12 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( cC58 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC56 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_84) ).

thf(194,plain,
    ! [A: $i] :
      ( ( ( cC58 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC56 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC56 @ B ) )
       => ( cC58 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( cC106 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC104 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

thf(338,plain,
    ! [A: $i] :
      ( ( ( cC106 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC104 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC104 @ B ) )
       => ( cC106 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( cC100 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC98 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

thf(470,plain,
    ! [A: $i] :
      ( ( ( cC100 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC98 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC98 @ B ) )
       => ( cC100 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(121,axiom,
    cTOP @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_112) ).

thf(791,plain,
    cTOP @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( cC166 @ A )
    <=> ( ( cC154 @ A )
        & ~ ( cC164 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).

thf(182,plain,
    ! [A: $i] :
      ( ( ( cC166 @ A )
       => ( ( cC154 @ A )
          & ~ ( cC164 @ A ) ) )
      & ( ( ( cC154 @ A )
          & ~ ( cC164 @ A ) )
       => ( cC166 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ( cC54 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC52 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_82) ).

thf(656,plain,
    ! [A: $i] :
      ( ( ( cC54 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC52 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC52 @ B ) )
       => ( cC54 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( cC72 @ A )
    <=> ( ~ ( cC70 @ A )
        & ~ ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_92) ).

thf(386,plain,
    ! [A: $i] :
      ( ( ( cC72 @ A )
       => ( ~ ( cC70 @ A )
          & ~ ( cC16 @ A ) ) )
      & ( ( ~ ( cC70 @ A )
          & ~ ( cC16 @ A ) )
       => ( cC72 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( cC146 @ A )
    <=> ( ( cC144 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).

thf(314,plain,
    ! [A: $i] :
      ( ( ( cC146 @ A )
       => ( ( cC144 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC144 @ A )
          & ( cC16 @ A ) )
       => ( cC146 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( cC26 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC24 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_68) ).

thf(446,plain,
    ! [A: $i] :
      ( ( ( cC26 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC24 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC24 @ B ) )
       => ( cC26 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( cC116 @ A )
    <=> ( ~ ( cC16 @ A )
        & ~ ( cC114 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).

thf(482,plain,
    ! [A: $i] :
      ( ( ( cC116 @ A )
       => ( ~ ( cC16 @ A )
          & ~ ( cC114 @ A ) ) )
      & ( ( ~ ( cC16 @ A )
          & ~ ( cC114 @ A ) )
       => ( cC116 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( cC62 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC60 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_87) ).

thf(524,plain,
    ! [A: $i] :
      ( ( ( cC62 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC60 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC60 @ B ) )
       => ( cC62 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( cC138 @ A )
    <=> ( ( cC136 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).

thf(218,plain,
    ! [A: $i] :
      ( ( ( cC138 @ A )
       => ( ( cC136 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC136 @ A )
          & ( cC16 @ A ) )
       => ( cC138 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( cC86 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_100) ).

thf(368,plain,
    ! [A: $i] :
      ( ( ( cC86 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC86 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( cC202 @ A )
    <=> ( ( cC190 @ A )
        & ~ ( cC200 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).

thf(158,plain,
    ! [A: $i] :
      ( ( ( cC202 @ A )
       => ( ( cC190 @ A )
          & ~ ( cC200 @ A ) ) )
      & ( ( ( cC190 @ A )
          & ~ ( cC200 @ A ) )
       => ( cC202 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( cC130 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC128 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).

thf(632,plain,
    ! [A: $i] :
      ( ( ( cC130 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC128 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC128 @ B ) )
       => ( cC130 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(104,axiom,
    ! [A: $i] :
      ( ( cC44 @ A )
    <=> ( ~ ( cC32 @ A )
        & ~ ( cC42 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_77) ).

thf(731,plain,
    ! [A: $i] :
      ( ( ( cC44 @ A )
       => ( ~ ( cC32 @ A )
          & ~ ( cC42 @ A ) ) )
      & ( ( ~ ( cC32 @ A )
          & ~ ( cC42 @ A ) )
       => ( cC44 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( cC156 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).

thf(290,plain,
    ! [A: $i] :
      ( ( ( cC156 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC156 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( cC108 @ A )
    <=> ( ~ ( cC106 @ A )
        & ~ ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).

thf(272,plain,
    ! [A: $i] :
      ( ( ( cC108 @ A )
       => ( ~ ( cC106 @ A )
          & ~ ( cC16 @ A ) ) )
      & ( ( ~ ( cC106 @ A )
          & ~ ( cC16 @ A ) )
       => ( cC108 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ( cC172 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).

thf(536,plain,
    ! [A: $i] :
      ( ( ( cC172 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC172 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(100,axiom,
    ! [A: $i] :
      ( ( cC174 @ A )
    <=> ( ( cC172 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).

thf(716,plain,
    ! [A: $i] :
      ( ( ( cC174 @ A )
       => ( ( cC172 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC172 @ A )
          & ( cC16 @ A ) )
       => ( cC174 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(84,axiom,
    ! [A: $i] :
      ( ( cC4 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_74) ).

thf(620,plain,
    ! [A: $i] :
      ( ( ( cC4 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC4 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(49,axiom,
    ! [A: $i] :
      ( ( cC196 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC194 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_54) ).

thf(410,plain,
    ! [A: $i] :
      ( ( ( cC196 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC194 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC194 @ B ) )
       => ( cC196 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( cC206 @ A )
    <=> ( ( cC170 @ A )
        & ( cC204 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).

thf(146,plain,
    ! [A: $i] :
      ( ( ( cC206 @ A )
       => ( ( cC170 @ A )
          & ( cC204 @ A ) ) )
      & ( ( ( cC170 @ A )
          & ( cC204 @ A ) )
       => ( cC206 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ( cC126 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC124 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).

thf(422,plain,
    ! [A: $i] :
      ( ( ( cC126 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC124 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC124 @ B ) )
       => ( cC126 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( cC50 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC16 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_80) ).

thf(326,plain,
    ! [A: $i] :
      ( ( ( cC50 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC16 @ B ) )
       => ( cC50 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( cC150 @ A )
    <=> ( ~ ( cC16 @ A )
        & ~ ( cC148 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).

thf(242,plain,
    ! [A: $i] :
      ( ( ( cC150 @ A )
       => ( ~ ( cC16 @ A )
          & ~ ( cC148 @ A ) ) )
      & ( ( ~ ( cC16 @ A )
          & ~ ( cC148 @ A ) )
       => ( cC150 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(125,axiom,
    ~ ( cC214 @ iV3102 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_118) ).

thf(801,plain,
    ~ ( cC214 @ iV3102 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( cC60 @ A )
    <=> ( ( cC48 @ A )
        & ~ ( cC58 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_86) ).

thf(506,plain,
    ! [A: $i] :
      ( ( ( cC60 @ A )
       => ( ( cC48 @ A )
          & ~ ( cC58 @ A ) ) )
      & ( ( ( cC48 @ A )
          & ~ ( cC58 @ A ) )
       => ( cC60 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).

thf(796,plain,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(102,axiom,
    cTEST @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_108) ).

thf(728,plain,
    cTEST @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( cC22 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC20 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_66) ).

thf(464,plain,
    ! [A: $i] :
      ( ( ( cC22 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC20 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC20 @ B ) )
       => ( cC22 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(36,axiom,
    ! [A: $i] :
      ( ( cC90 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC88 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_102) ).

thf(332,plain,
    ! [A: $i] :
      ( ( ( cC90 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC88 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC88 @ B ) )
       => ( cC90 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ( cC142 @ A )
    <=> ( ~ ( cC140 @ A )
        & ~ ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).

thf(596,plain,
    ! [A: $i] :
      ( ( ( cC142 @ A )
       => ( ~ ( cC140 @ A )
          & ~ ( cC16 @ A ) ) )
      & ( ( ~ ( cC140 @ A )
          & ~ ( cC16 @ A ) )
       => ( cC142 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ( cC208 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC206 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_61) ).

thf(644,plain,
    ! [A: $i] :
      ( ( ( cC208 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC206 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC206 @ B ) )
       => ( cC208 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( cC8 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC6 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_96) ).

thf(200,plain,
    ! [A: $i] :
      ( ( ( cC8 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC6 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC6 @ B ) )
       => ( cC8 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( cC6 @ A )
    <=> ( ( cC2 @ A )
        & ( cC4 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_85) ).

thf(254,plain,
    ! [A: $i] :
      ( ( ( cC6 @ A )
       => ( ( cC2 @ A )
          & ( cC4 @ A ) ) )
      & ( ( ( cC2 @ A )
          & ( cC4 @ A ) )
       => ( cC6 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(126,axiom,
    ! [A: $i] :
      ( ( cC46 @ A )
    <=> ( ( cC30 @ A )
        & ( cC44 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_78) ).

thf(803,plain,
    ! [A: $i] :
      ( ( ( cC46 @ A )
       => ( ( cC30 @ A )
          & ( cC44 @ A ) ) )
      & ( ( ( cC30 @ A )
          & ( cC44 @ A ) )
       => ( cC46 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( cC194 @ A )
    <=> ( ( cC192 @ A )
        & ( cC16 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_53) ).

thf(560,plain,
    ! [A: $i] :
      ( ( ( cC194 @ A )
       => ( ( cC192 @ A )
          & ( cC16 @ A ) ) )
      & ( ( ( cC192 @ A )
          & ( cC16 @ A ) )
       => ( cC194 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(811,plain,
    $false,
    inference(e,[status(thm)],[779,296,739,809,760,518,170,762,308,741,440,614,500,698,747,404,320,785,344,542,638,416,152,284,770,164,789,602,692,428,206,452,248,380,512,778,302,260,392,729,566,710,224,578,650,188,356,488,554,590,212,686,476,134,128,792,266,398,674,530,794,662,584,176,772,572,787,236,704,350,764,230,362,737,434,494,140,626,668,278,608,722,680,548,374,749,754,458,194,338,470,791,182,656,386,314,446,482,524,218,368,158,632,731,290,272,536,716,620,410,146,422,326,242,801,506,796,728,464,332,596,644,200,254,803,560]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KRS149+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n003.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 15:17:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.00/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.41/1.04  % [INFO] 	 Parsing done (176ms). 
% 1.41/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.99/1.26  % [INFO] 	 eprover registered as external prover. 
% 1.99/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 1.99/1.27  % [INFO] 	 Scanning for conjecture ... 
% 2.22/1.35  % [INFO] 	 Found a conjecture and 125 axioms. Running axiom selection ... 
% 2.37/1.42  % [INFO] 	 Axiom selection finished. Selected 125 axioms (removed 0 axioms). 
% 2.80/1.51  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.80/1.52  % [INFO] 	 Type checking passed. 
% 2.80/1.52  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 6.17/2.57  % External prover 'e' found a proof!
% 6.17/2.57  % [INFO] 	 Killing All external provers ... 
% 6.17/2.57  % Time passed: 2041ms (effective reasoning time: 1518ms)
% 6.17/2.57  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.43/2.57  % Axioms used in derivation (125): axiom_53, axiom_75, axiom_7, axiom_26, axiom_55, axiom_108, axiom_88, axiom_114, axiom_119, axiom_33, axiom_10, axiom_40, axiom_22, axiom_59, axiom_77, axiom_44, axiom_49, axiom_15, axiom_95, axiom_121, axiom_73, axiom_67, axiom_69, axiom_51, axiom_21, axiom_19, axiom_99, axiom_84, axiom_63, axiom_110, axiom_103, axiom_38, axiom_2, axiom_79, axiom_89, axiom_43, axiom_107, axiom_27, axiom_32, axiom_6, axiom_91, axiom_60, axiom_118, axiom_78, axiom_54, axiom_92, axiom_100, axiom_64, axiom_16, axiom_50, axiom_122, axiom_81, axiom_74, axiom_111, axiom_3, axiom_96, axiom_68, axiom_46, axiom_104, axiom_20, axiom_85, axiom_70, axiom_115, axiom_42, axiom_31, axiom_24, axiom_90, axiom_1, axiom_57, axiom_116, axiom_61, axiom_105, axiom_35, axiom_28, axiom_101, axiom_112, axiom_65, axiom_36, axiom_39, axiom_80, axiom_71, axiom_8, axiom_97, axiom_17, axiom_86, axiom_5, axiom_47, axiom_13, axiom_93, axiom_123, axiom_82, axiom_41, axiom_109, axiom_25, axiom_76, axiom_52, axiom_34, axiom_0, axiom_58, axiom_62, axiom_45, axiom_29, axiom_11, axiom_117, axiom_56, axiom_30, axiom_23, axiom_106, axiom_18, axiom_87, axiom_113, axiom_12, axiom_9, axiom_98, axiom_102, axiom_48, axiom_83, axiom_14, axiom_124, axiom_72, axiom_120, axiom_94, axiom_4, axiom_66, axiom_37
% 6.43/2.57  % No. of inferences in proof: 254
% 6.43/2.57  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2041 ms resp. 1518 ms w/o parsing
% 6.43/2.65  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.43/2.65  % [INFO] 	 Killing All external provers ... 
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