TSTP Solution File: NUM604+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM604+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n023.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 Aug 22 10:52:17 EDT 2023

% Result   : Theorem 115.70s 94.23s
% Output   : CNFRefutation 115.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   95
% Syntax   : Number of formulae    :  184 (  39 unt;  69 typ;   5 def)
%            Number of atoms       :  297 (  54 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  301 ( 119   ~; 112   |;  35   &)
%                                         (   8 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  106 (  54   >;  52   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   60 (  60 usr;  15 con; 0-4 aty)
%            Number of variables   :   90 (;  87   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aFunction0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > sdtlpdtrp0 > sdtlcdtrc0 > sdtlbdtrb0 > sdtexdt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > szDzozmdt0 > szDzizrdt0 > slbdtrb0 > sbrdtbr0 > xx > xk > xi > xe > xd > xc > xT > xS > xO > xN > xK > xC > szNzAzT0 > sz00 > slcrc0 > #skF_26 > #skF_7 > #skF_11 > #skF_17 > #skF_6 > #skF_27 > #skF_1 > #skF_31 > #skF_18 > #skF_4 > #skF_29 > #skF_12 > #skF_23 > #skF_28 > #skF_5 > #skF_19 > #skF_10 > #skF_8 > #skF_20 > #skF_24 > #skF_15 > #skF_13 > #skF_14 > #skF_25 > #skF_3 > #skF_2 > #skF_21 > #skF_9 > #skF_22 > #skF_30 > #skF_16

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(xk,type,
    xk: $i ).

tff('#skF_26',type,
    '#skF_26': ( $i * $i * $i ) > $i ).

tff('#skF_7',type,
    '#skF_7': $i > $i ).

tff('#skF_11',type,
    '#skF_11': ( $i * $i ) > $i ).

tff(sbrdtbr0,type,
    sbrdtbr0: $i > $i ).

tff('#skF_17',type,
    '#skF_17': ( $i * $i * $i ) > $i ).

tff(aSet0,type,
    aSet0: $i > $o ).

tff(szszuzczcdt0,type,
    szszuzczcdt0: $i > $i ).

tff(sdtlbdtrb0,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff(szDzozmdt0,type,
    szDzozmdt0: $i > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i * $i ) > $i ).

tff(xd,type,
    xd: $i ).

tff('#skF_27',type,
    '#skF_27': ( $i * $i * $i ) > $i ).

tff(sdtmndt0,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff('#skF_1',type,
    '#skF_1': $i > $i ).

tff('#skF_31',type,
    '#skF_31': $i > $i ).

tff('#skF_18',type,
    '#skF_18': ( $i * $i * $i ) > $i ).

tff(aElement0,type,
    aElement0: $i > $o ).

tff(sdtexdt0,type,
    sdtexdt0: ( $i * $i ) > $i ).

tff(xi,type,
    xi: $i ).

tff(szNzAzT0,type,
    szNzAzT0: $i ).

tff(sdtlseqdt0,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(xS,type,
    xS: $i ).

tff(sz00,type,
    sz00: $i ).

tff(sdtlpdtrp0,type,
    sdtlpdtrp0: ( $i * $i ) > $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i * $i ) > $i ).

tff(xc,type,
    xc: $i ).

tff(xe,type,
    xe: $i ).

tff('#skF_29',type,
    '#skF_29': $i > $i ).

tff('#skF_12',type,
    '#skF_12': ( $i * $i ) > $i ).

tff(sdtpldt0,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(slbdtsldtrb0,type,
    slbdtsldtrb0: ( $i * $i ) > $i ).

tff(xx,type,
    xx: $i ).

tff('#skF_23',type,
    '#skF_23': ( $i * $i * $i ) > $i ).

tff('#skF_28',type,
    '#skF_28': $i > $i ).

tff(aSubsetOf0,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i * $i ) > $i ).

tff('#skF_19',type,
    '#skF_19': ( $i * $i * $i ) > $i ).

tff(isCountable0,type,
    isCountable0: $i > $o ).

tff('#skF_10',type,
    '#skF_10': ( $i * $i ) > $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

tff(xT,type,
    xT: $i ).

tff(xN,type,
    xN: $i ).

tff(aElementOf0,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(xC,type,
    xC: $i ).

tff('#skF_20',type,
    '#skF_20': ( $i * $i * $i ) > $i ).

tff(szDzizrdt0,type,
    szDzizrdt0: $i > $i ).

tff('#skF_24',type,
    '#skF_24': ( $i * $i ) > $i ).

tff('#skF_15',type,
    '#skF_15': ( $i * $i * $i ) > $i ).

tff('#skF_13',type,
    '#skF_13': $i > $i ).

tff(xO,type,
    xO: $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i * $i ) > $i ).

tff(slcrc0,type,
    slcrc0: $i ).

tff(aFunction0,type,
    aFunction0: $i > $o ).

tff(isFinite0,type,
    isFinite0: $i > $o ).

tff('#skF_25',type,
    '#skF_25': ( $i * $i ) > $i ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i * $i ) > $i ).

tff(sdtlcdtrc0,type,
    sdtlcdtrc0: ( $i * $i ) > $i ).

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

tff(iLess0,type,
    iLess0: ( $i * $i ) > $o ).

tff(szmzizndt0,type,
    szmzizndt0: $i > $i ).

tff(szmzazxdt0,type,
    szmzazxdt0: $i > $i ).

tff('#skF_21',type,
    '#skF_21': ( $i * $i * $i ) > $i ).

tff(xK,type,
    xK: $i ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

tff(slbdtrb0,type,
    slbdtrb0: $i > $i ).

tff('#skF_22',type,
    '#skF_22': ( $i * $i * $i * $i ) > $i ).

tff('#skF_30',type,
    '#skF_30': $i > $i ).

tff('#skF_16',type,
    '#skF_16': ( $i * $i * $i ) > $i ).

tff(f_868,negated_conjecture,
    ~ aElementOf0(xx,xS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_211,axiom,
    ( aSet0(szNzAzT0)
    & isCountable0(szNzAzT0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).

tff(f_667,hypothesis,
    ( aSubsetOf0(xS,szNzAzT0)
    & isCountable0(xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).

tff(f_84,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
               => aElementOf0(W2,W0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).

tff(f_866,hypothesis,
    aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5045) ).

tff(f_52,definition,
    ! [W0] :
      ( ( W0 = slcrc0 )
    <=> ( aSet0(W0)
        & ~ ? [W1] : aElementOf0(W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).

tff(f_72,axiom,
    ! [W0] :
      ( ( aSet0(W0)
        & isCountable0(W0) )
     => ( W0 != slcrc0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).

tff(f_852,hypothesis,
    ( aSet0(xO)
    & isCountable0(xO) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4908) ).

tff(f_862,hypothesis,
    aElementOf0(xx,xO),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5009) ).

tff(f_39,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).

tff(f_156,definition,
    ! [W0,W1] :
      ( ( aSet0(W0)
        & aElement0(W1) )
     => ! [W2] :
          ( ( W2 = sdtmndt0(W0,W1) )
        <=> ( aSet0(W2)
            & ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( aElement0(W3)
                  & aElementOf0(W3,W0)
                  & ( W3 != W1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).

tff(f_865,hypothesis,
    ( aElementOf0(xi,szNzAzT0)
    & ( sdtlpdtrp0(xe,xi) = xx ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5034) ).

tff(f_829,hypothesis,
    ( aFunction0(xe)
    & ( szDzozmdt0(xe) = szNzAzT0 )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).

tff(f_809,hypothesis,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ? [W1] :
          ( aElementOf0(W1,xT)
          & ? [W2] :
              ( aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(W2)
              & ! [W3] :
                  ( ( aSet0(W3)
                    & aElementOf0(W3,slbdtsldtrb0(W2,xk)) )
                 => ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W3) = W1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4411) ).

tff(f_730,hypothesis,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
        & isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).

tff(f_190,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ! [W1] :
          ( ( aSet0(W1)
            & isCountable0(W1) )
         => isCountable0(sdtmndt0(W1,W0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCDiffSet) ).

tff(f_708,hypothesis,
    ( aElementOf0(xk,szNzAzT0)
    & ( szszuzczcdt0(xk) = xK ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).

tff(f_471,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardSeg) ).

tff(f_435,definition,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ! [W1] :
          ( ( W1 = slbdtrb0(W0) )
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
              <=> ( aElementOf0(W2,szNzAzT0)
                  & sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSeg) ).

tff(f_330,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ( ( sbrdtbr0(W0) = sz00 )
      <=> ( W0 = slcrc0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).

tff(f_774,hypothesis,
    ( aFunction0(xC)
    & ( szDzozmdt0(xC) = szNzAzT0 )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aFunction0(sdtlpdtrp0(xC,W0))
          & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          & ! [W1] :
              ( ( aSet0(W1)
                & aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
             => ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4151) ).

tff(f_519,axiom,
    ! [W0] :
      ( ( aSet0(W0)
        & isCountable0(W0) )
     => ! [W1] :
          ( ( aElementOf0(W1,szNzAzT0)
            & ( W1 != sz00 ) )
         => isCountable0(slbdtsldtrb0(W0,W1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSelCSet) ).

tff(f_163,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).

tff(f_181,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ! [W1] :
          ( ( aSet0(W1)
            & isCountable0(W1) )
         => isCountable0(sdtpldt0(W1,W0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCConsSet) ).

tff(f_119,axiom,
    ! [W0,W1,W2] :
      ( ( aSet0(W0)
        & aSet0(W1)
        & aSet0(W2) )
     => ( ( aSubsetOf0(W0,W1)
          & aSubsetOf0(W1,W2) )
       => aSubsetOf0(W0,W2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).

tff(f_388,definition,
    ! [W0] :
      ( ( aSubsetOf0(W0,szNzAzT0)
        & ( W0 != slcrc0 ) )
     => ! [W1] :
          ( ( W1 = szmzizndt0(W0) )
        <=> ( aElementOf0(W1,W0)
            & ! [W2] :
                ( aElementOf0(W2,W0)
               => sdtlseqdt0(W1,W2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).

tff(c_450,plain,
    ~ aElementOf0(xx,xS),
    inference(cnfTransformation,[status(thm)],[f_868]) ).

tff(c_108,plain,
    aSet0(szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_211]) ).

tff(c_340,plain,
    aSubsetOf0(xS,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_667]) ).

tff(c_660,plain,
    ! [W1_441,W0_442] :
      ( aSet0(W1_441)
      | ~ aSubsetOf0(W1_441,W0_442)
      | ~ aSet0(W0_442) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_675,plain,
    ( aSet0(xS)
    | ~ aSet0(szNzAzT0) ),
    inference(resolution,[status(thm)],[c_340,c_660]) ).

tff(c_686,plain,
    aSet0(xS),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_675]) ).

tff(c_448,plain,
    aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
    inference(cnfTransformation,[status(thm)],[f_866]) ).

tff(c_14,plain,
    aSet0(slcrc0),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_22,plain,
    ( ~ isCountable0(slcrc0)
    | ~ aSet0(slcrc0) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_457,plain,
    ~ isCountable0(slcrc0),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_22]) ).

tff(c_434,plain,
    aSet0(xO),
    inference(cnfTransformation,[status(thm)],[f_852]) ).

tff(c_442,plain,
    aElementOf0(xx,xO),
    inference(cnfTransformation,[status(thm)],[f_862]) ).

tff(c_595,plain,
    ! [W1_438,W0_439] :
      ( aElement0(W1_438)
      | ~ aElementOf0(W1_438,W0_439)
      | ~ aSet0(W0_439) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_613,plain,
    ( aElement0(xx)
    | ~ aSet0(xO) ),
    inference(resolution,[status(thm)],[c_442,c_595]) ).

tff(c_631,plain,
    aElement0(xx),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_613]) ).

tff(c_114368,plain,
    ! [W0_2127,W1_2128,W2_2129] :
      ( aElementOf0('#skF_5'(W0_2127,W1_2128,W2_2129),W0_2127)
      | aElementOf0('#skF_6'(W0_2127,W1_2128,W2_2129),W2_2129)
      | ( sdtmndt0(W0_2127,W1_2128) = W2_2129 )
      | ~ aSet0(W2_2129)
      | ~ aElement0(W1_2128)
      | ~ aSet0(W0_2127) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_12,plain,
    ! [W1_10] : ~ aElementOf0(W1_10,slcrc0),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_114572,plain,
    ! [W0_2127,W1_2128] :
      ( aElementOf0('#skF_5'(W0_2127,W1_2128,slcrc0),W0_2127)
      | ( sdtmndt0(W0_2127,W1_2128) = slcrc0 )
      | ~ aSet0(slcrc0)
      | ~ aElement0(W1_2128)
      | ~ aSet0(W0_2127) ),
    inference(resolution,[status(thm)],[c_114368,c_12]) ).

tff(c_189711,plain,
    ! [W0_3124,W1_3125] :
      ( aElementOf0('#skF_5'(W0_3124,W1_3125,slcrc0),W0_3124)
      | ( sdtmndt0(W0_3124,W1_3125) = slcrc0 )
      | ~ aElement0(W1_3125)
      | ~ aSet0(W0_3124) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_114572]) ).

tff(c_189849,plain,
    ! [W1_3125] :
      ( ( sdtmndt0(slcrc0,W1_3125) = slcrc0 )
      | ~ aElement0(W1_3125)
      | ~ aSet0(slcrc0) ),
    inference(resolution,[status(thm)],[c_189711,c_12]) ).

tff(c_189919,plain,
    ! [W1_3126] :
      ( ( sdtmndt0(slcrc0,W1_3126) = slcrc0 )
      | ~ aElement0(W1_3126) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_189849]) ).

tff(c_190084,plain,
    sdtmndt0(slcrc0,xx) = slcrc0,
    inference(resolution,[status(thm)],[c_631,c_189919]) ).

tff(c_680,plain,
    ( aSet0(sdtlpdtrp0(xN,xi))
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_448,c_660]) ).

tff(c_726,plain,
    aSet0(sdtlpdtrp0(xN,xi)),
    inference(demodulation,[status(thm),theory(equality)],[c_686,c_680]) ).

tff(c_70,plain,
    ! [W0_44,W1_45] :
      ( aSet0(sdtmndt0(W0_44,W1_45))
      | ~ aElement0(W1_45)
      | ~ aSet0(W0_44) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_446,plain,
    aElementOf0(xi,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_865]) ).

tff(c_444,plain,
    sdtlpdtrp0(xe,xi) = xx,
    inference(cnfTransformation,[status(thm)],[f_865]) ).

tff(c_410,plain,
    ! [W0_420] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,W0_420)) = sdtlpdtrp0(xe,W0_420) )
      | ~ aElementOf0(W0_420,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_829]) ).

tff(c_4009,plain,
    ! [W0_675] :
      ( aSubsetOf0('#skF_29'(W0_675),sdtmndt0(sdtlpdtrp0(xN,W0_675),szmzizndt0(sdtlpdtrp0(xN,W0_675))))
      | ~ aElementOf0(W0_675,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_809]) ).

tff(c_239201,plain,
    ! [W0_3537] :
      ( aSubsetOf0('#skF_29'(W0_3537),sdtmndt0(sdtlpdtrp0(xN,W0_3537),sdtlpdtrp0(xe,W0_3537)))
      | ~ aElementOf0(W0_3537,szNzAzT0)
      | ~ aElementOf0(W0_3537,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_410,c_4009]) ).

tff(c_239243,plain,
    ( aSubsetOf0('#skF_29'(xi),sdtmndt0(sdtlpdtrp0(xN,xi),xx))
    | ~ aElementOf0(xi,szNzAzT0)
    | ~ aElementOf0(xi,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_444,c_239201]) ).

tff(c_239261,plain,
    aSubsetOf0('#skF_29'(xi),sdtmndt0(sdtlpdtrp0(xN,xi),xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_446,c_446,c_239243]) ).

tff(c_26,plain,
    ! [W1_20,W0_14] :
      ( aSet0(W1_20)
      | ~ aSubsetOf0(W1_20,W0_14)
      | ~ aSet0(W0_14) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_239340,plain,
    ( aSet0('#skF_29'(xi))
    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),xx)) ),
    inference(resolution,[status(thm)],[c_239261,c_26]) ).

tff(c_239897,plain,
    ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),xx)),
    inference(splitLeft,[status(thm)],[c_239340]) ).

tff(c_239900,plain,
    ( ~ aElement0(xx)
    | ~ aSet0(sdtlpdtrp0(xN,xi)) ),
    inference(resolution,[status(thm)],[c_70,c_239897]) ).

tff(c_239904,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_726,c_631,c_239900]) ).

tff(c_239906,plain,
    aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),xx)),
    inference(splitRight,[status(thm)],[c_239340]) ).

tff(c_374,plain,
    ! [W0_382] :
      ( isCountable0(sdtlpdtrp0(xN,W0_382))
      | ~ aElementOf0(W0_382,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_730]) ).

tff(c_100,plain,
    ! [W1_65,W0_63] :
      ( isCountable0(sdtmndt0(W1_65,W0_63))
      | ~ isCountable0(W1_65)
      | ~ aSet0(W1_65)
      | ~ aElement0(W0_63) ),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_362,plain,
    aElementOf0(xk,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_708]) ).

tff(c_224,plain,
    ! [W0_150] :
      ( ( sbrdtbr0(slbdtrb0(W0_150)) = W0_150 )
      | ~ aElementOf0(W0_150,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_471]) ).

tff(c_188,plain,
    ! [W0_133] :
      ( aSet0(slbdtrb0(W0_133))
      | ~ aElementOf0(W0_133,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_435]) ).

tff(c_632,plain,
    ! [W0_440] :
      ( ( slcrc0 = W0_440 )
      | ( sbrdtbr0(W0_440) != sz00 )
      | ~ aSet0(W0_440) ),
    inference(cnfTransformation,[status(thm)],[f_330]) ).

tff(c_2368,plain,
    ! [W0_589] :
      ( ( slbdtrb0(W0_589) = slcrc0 )
      | ( sbrdtbr0(slbdtrb0(W0_589)) != sz00 )
      | ~ aElementOf0(W0_589,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_188,c_632]) ).

tff(c_114651,plain,
    ! [W0_2130] :
      ( ( slbdtrb0(W0_2130) = slcrc0 )
      | ( sz00 != W0_2130 )
      | ~ aElementOf0(W0_2130,szNzAzT0)
      | ~ aElementOf0(W0_2130,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_224,c_2368]) ).

tff(c_114708,plain,
    ( ( slbdtrb0(xk) = slcrc0 )
    | ( xk != sz00 )
    | ~ aElementOf0(xk,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_362,c_114651]) ).

tff(c_114764,plain,
    ( ( slbdtrb0(xk) = slcrc0 )
    | ( xk != sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_362,c_114708]) ).

tff(c_114771,plain,
    xk != sz00,
    inference(splitLeft,[status(thm)],[c_114764]) ).

tff(c_7091,plain,
    ! [W0_775] :
      ( ( slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0_775),szmzizndt0(sdtlpdtrp0(xN,W0_775))),xk) = szDzozmdt0(sdtlpdtrp0(xC,W0_775)) )
      | ~ aElementOf0(W0_775,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_774]) ).

tff(c_310714,plain,
    ! [W0_4133] :
      ( ( slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0_4133),sdtlpdtrp0(xe,W0_4133)),xk) = szDzozmdt0(sdtlpdtrp0(xC,W0_4133)) )
      | ~ aElementOf0(W0_4133,szNzAzT0)
      | ~ aElementOf0(W0_4133,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_410,c_7091]) ).

tff(c_310800,plain,
    ( ( slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),xx),xk) = szDzozmdt0(sdtlpdtrp0(xC,xi)) )
    | ~ aElementOf0(xi,szNzAzT0)
    | ~ aElementOf0(xi,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_444,c_310714]) ).

tff(c_310849,plain,
    slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),xx),xk) = szDzozmdt0(sdtlpdtrp0(xC,xi)),
    inference(demodulation,[status(thm),theory(equality)],[c_446,c_446,c_310800]) ).

tff(c_250,plain,
    ! [W0_168,W1_170] :
      ( isCountable0(slbdtsldtrb0(W0_168,W1_170))
      | ( sz00 = W1_170 )
      | ~ aElementOf0(W1_170,szNzAzT0)
      | ~ isCountable0(W0_168)
      | ~ aSet0(W0_168) ),
    inference(cnfTransformation,[status(thm)],[f_519]) ).

tff(c_310976,plain,
    ( isCountable0(szDzozmdt0(sdtlpdtrp0(xC,xi)))
    | ( xk = sz00 )
    | ~ aElementOf0(xk,szNzAzT0)
    | ~ isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),xx))
    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),xx)) ),
    inference(superposition,[status(thm),theory(equality)],[c_310849,c_250]) ).

tff(c_311009,plain,
    ( isCountable0(szDzozmdt0(sdtlpdtrp0(xC,xi)))
    | ( xk = sz00 )
    | ~ isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_239906,c_362,c_310976]) ).

tff(c_311010,plain,
    ( isCountable0(szDzozmdt0(sdtlpdtrp0(xC,xi)))
    | ~ isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),xx)) ),
    inference(negUnitSimplification,[status(thm)],[c_114771,c_311009]) ).

tff(c_313194,plain,
    ~ isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),xx)),
    inference(splitLeft,[status(thm)],[c_311010]) ).

tff(c_313491,plain,
    ( ~ isCountable0(sdtlpdtrp0(xN,xi))
    | ~ aSet0(sdtlpdtrp0(xN,xi))
    | ~ aElement0(xx) ),
    inference(resolution,[status(thm)],[c_100,c_313194]) ).

tff(c_313494,plain,
    ~ isCountable0(sdtlpdtrp0(xN,xi)),
    inference(demodulation,[status(thm),theory(equality)],[c_631,c_726,c_313491]) ).

tff(c_313497,plain,
    ~ aElementOf0(xi,szNzAzT0),
    inference(resolution,[status(thm)],[c_374,c_313494]) ).

tff(c_313501,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_446,c_313497]) ).

tff(c_313503,plain,
    isCountable0(sdtmndt0(sdtlpdtrp0(xN,xi),xx)),
    inference(splitRight,[status(thm)],[c_311010]) ).

tff(c_2037,plain,
    ! [W0_567,W1_568] :
      ( ( sdtpldt0(sdtmndt0(W0_567,W1_568),W1_568) = W0_567 )
      | ~ aElementOf0(W1_568,W0_567)
      | ~ aSet0(W0_567) ),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_98,plain,
    ! [W1_62,W0_60] :
      ( isCountable0(sdtpldt0(W1_62,W0_60))
      | ~ isCountable0(W1_62)
      | ~ aSet0(W1_62)
      | ~ aElement0(W0_60) ),
    inference(cnfTransformation,[status(thm)],[f_181]) ).

tff(c_2046,plain,
    ! [W0_567,W1_568] :
      ( isCountable0(W0_567)
      | ~ isCountable0(sdtmndt0(W0_567,W1_568))
      | ~ aSet0(sdtmndt0(W0_567,W1_568))
      | ~ aElement0(W1_568)
      | ~ aElementOf0(W1_568,W0_567)
      | ~ aSet0(W0_567) ),
    inference(superposition,[status(thm),theory(equality)],[c_2037,c_98]) ).

tff(c_313513,plain,
    ( isCountable0(sdtlpdtrp0(xN,xi))
    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),xx))
    | ~ aElement0(xx)
    | ~ aElementOf0(xx,sdtlpdtrp0(xN,xi))
    | ~ aSet0(sdtlpdtrp0(xN,xi)) ),
    inference(resolution,[status(thm)],[c_313503,c_2046]) ).

tff(c_313519,plain,
    ( isCountable0(sdtlpdtrp0(xN,xi))
    | ~ aElementOf0(xx,sdtlpdtrp0(xN,xi)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_726,c_631,c_239906,c_313513]) ).

tff(c_313523,plain,
    ~ aElementOf0(xx,sdtlpdtrp0(xN,xi)),
    inference(splitLeft,[status(thm)],[c_313519]) ).

tff(c_5201,plain,
    ! [W0_695,W2_696,W1_697] :
      ( aSubsetOf0(W0_695,W2_696)
      | ~ aSubsetOf0(W1_697,W2_696)
      | ~ aSubsetOf0(W0_695,W1_697)
      | ~ aSet0(W2_696)
      | ~ aSet0(W1_697)
      | ~ aSet0(W0_695) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_5241,plain,
    ! [W0_695] :
      ( aSubsetOf0(W0_695,szNzAzT0)
      | ~ aSubsetOf0(W0_695,xS)
      | ~ aSet0(szNzAzT0)
      | ~ aSet0(xS)
      | ~ aSet0(W0_695) ),
    inference(resolution,[status(thm)],[c_340,c_5201]) ).

tff(c_5292,plain,
    ! [W0_698] :
      ( aSubsetOf0(W0_698,szNzAzT0)
      | ~ aSubsetOf0(W0_698,xS)
      | ~ aSet0(W0_698) ),
    inference(demodulation,[status(thm),theory(equality)],[c_686,c_108,c_5241]) ).

tff(c_5306,plain,
    ( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
    | ~ aSet0(sdtlpdtrp0(xN,xi)) ),
    inference(resolution,[status(thm)],[c_448,c_5292]) ).

tff(c_5318,plain,
    aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0),
    inference(demodulation,[status(thm),theory(equality)],[c_726,c_5306]) ).

tff(c_1381,plain,
    ! [W0_507] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,W0_507)) = sdtlpdtrp0(xe,W0_507) )
      | ~ aElementOf0(W0_507,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_829]) ).

tff(c_170,plain,
    ! [W0_111] :
      ( aElementOf0(szmzizndt0(W0_111),W0_111)
      | ( slcrc0 = W0_111 )
      | ~ aSubsetOf0(W0_111,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_388]) ).

tff(c_316198,plain,
    ! [W0_4179] :
      ( aElementOf0(sdtlpdtrp0(xe,W0_4179),sdtlpdtrp0(xN,W0_4179))
      | ( sdtlpdtrp0(xN,W0_4179) = slcrc0 )
      | ~ aSubsetOf0(sdtlpdtrp0(xN,W0_4179),szNzAzT0)
      | ~ aElementOf0(W0_4179,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_1381,c_170]) ).

tff(c_316245,plain,
    ( aElementOf0(xx,sdtlpdtrp0(xN,xi))
    | ( sdtlpdtrp0(xN,xi) = slcrc0 )
    | ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
    | ~ aElementOf0(xi,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_444,c_316198]) ).

tff(c_316266,plain,
    ( aElementOf0(xx,sdtlpdtrp0(xN,xi))
    | ( sdtlpdtrp0(xN,xi) = slcrc0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_446,c_5318,c_316245]) ).

tff(c_316267,plain,
    sdtlpdtrp0(xN,xi) = slcrc0,
    inference(negUnitSimplification,[status(thm)],[c_313523,c_316266]) ).

tff(c_316269,plain,
    isCountable0(sdtmndt0(slcrc0,xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_316267,c_313503]) ).

tff(c_316288,plain,
    isCountable0(slcrc0),
    inference(demodulation,[status(thm),theory(equality)],[c_190084,c_316269]) ).

tff(c_316290,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_457,c_316288]) ).

tff(c_316292,plain,
    aElementOf0(xx,sdtlpdtrp0(xN,xi)),
    inference(splitRight,[status(thm)],[c_313519]) ).

tff(c_24,plain,
    ! [W2_23,W0_14,W1_20] :
      ( aElementOf0(W2_23,W0_14)
      | ~ aElementOf0(W2_23,W1_20)
      | ~ aSubsetOf0(W1_20,W0_14)
      | ~ aSet0(W0_14) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_316305,plain,
    ! [W0_4180] :
      ( aElementOf0(xx,W0_4180)
      | ~ aSubsetOf0(sdtlpdtrp0(xN,xi),W0_4180)
      | ~ aSet0(W0_4180) ),
    inference(resolution,[status(thm)],[c_316292,c_24]) ).

tff(c_316367,plain,
    ( aElementOf0(xx,xS)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_448,c_316305]) ).

tff(c_316415,plain,
    aElementOf0(xx,xS),
    inference(demodulation,[status(thm),theory(equality)],[c_686,c_316367]) ).

tff(c_316417,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_450,c_316415]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUM604+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36  % Computer : n023.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 15:28:07 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 115.70/94.23  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 115.70/94.24  
% 115.70/94.24  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 115.70/94.28  
% 115.70/94.28  Inference rules
% 115.70/94.28  ----------------------
% 115.70/94.29  #Ref     : 11
% 115.70/94.29  #Sup     : 62499
% 115.70/94.29  #Fact    : 18
% 115.70/94.29  #Define  : 0
% 115.70/94.29  #Split   : 1110
% 115.70/94.29  #Chain   : 0
% 115.70/94.29  #Close   : 0
% 115.70/94.29  
% 115.70/94.29  Ordering : KBO
% 115.70/94.29  
% 115.70/94.29  Simplification rules
% 115.70/94.29  ----------------------
% 115.70/94.29  #Subsume      : 14585
% 115.70/94.29  #Demod        : 78894
% 115.70/94.29  #Tautology    : 11918
% 115.70/94.29  #SimpNegUnit  : 5576
% 115.70/94.29  #BackRed      : 3972
% 115.70/94.29  
% 115.70/94.29  #Partial instantiations: 0
% 115.70/94.29  #Strategies tried      : 1
% 115.70/94.29  
% 115.70/94.29  Timing (in seconds)
% 115.70/94.29  ----------------------
% 115.70/94.29  Preprocessing        : 0.91
% 115.70/94.29  Parsing              : 0.44
% 115.70/94.29  CNF conversion       : 0.09
% 115.70/94.29  Main loop            : 92.28
% 115.70/94.29  Inferencing          : 15.72
% 115.70/94.29  Reduction            : 47.33
% 115.70/94.29  Demodulation         : 37.08
% 115.70/94.29  BG Simplification    : 0.48
% 115.70/94.29  Subsumption          : 21.53
% 115.70/94.29  Abstraction          : 0.87
% 115.70/94.29  MUC search           : 0.00
% 115.70/94.29  Cooper               : 0.00
% 115.70/94.29  Total                : 93.26
% 115.70/94.29  Index Insertion      : 0.00
% 115.70/94.29  Index Deletion       : 0.00
% 115.70/94.29  Index Matching       : 0.00
% 115.70/94.29  BG Taut test         : 0.00
%------------------------------------------------------------------------------