TSTP Solution File: NUM629+3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM629+3 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n008.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 10:52:24 EDT 2023

% Result   : Theorem 140.70s 116.41s
% Output   : CNFRefutation 140.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :  124
% Syntax   : Number of formulae    :  265 (  71 unt;  97 typ;   4 def)
%            Number of atoms       :  399 (  63 equ)
%            Maximal formula atoms :   22 (   2 avg)
%            Number of connectives :  388 ( 157   ~; 131   |;  56   &)
%                                         (  10 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  154 (  76   >;  78   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   88 (  88 usr;  21 con; 0-4 aty)
%            Number of variables   :   94 (;  92   !;   2   ?;   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 > xp > xn > xk > xe > xd > xc > xT > xS > xQ > xP > xO > xN > xK > xD > xC > szNzAzT0 > sz00 > slcrc0 > #skF_53 > #skF_47 > #skF_7 > #skF_11 > #skF_41 > #skF_17 > #skF_31 > #skF_33 > #skF_44 > #skF_6 > #skF_1 > #skF_18 > #skF_55 > #skF_37 > #skF_56 > #skF_54 > #skF_38 > #skF_4 > #skF_29 > #skF_52 > #skF_12 > #skF_30 > #skF_32 > #skF_23 > #skF_35 > #skF_5 > #skF_49 > #skF_19 > #skF_10 > #skF_42 > #skF_8 > #skF_20 > #skF_28 > #skF_26 > #skF_24 > #skF_34 > #skF_15 > #skF_13 > #skF_14 > #skF_50 > #skF_25 > #skF_3 > #skF_2 > #skF_48 > #skF_40 > #skF_27 > #skF_36 > #skF_43 > #skF_46 > #skF_21 > #skF_45 > #skF_9 > #skF_22 > #skF_16 > #skF_51 > #skF_39

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_53',type,
    '#skF_53': $i > $i ).

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

tff('#skF_47',type,
    '#skF_47': ( $i * $i ) > $i ).

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

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

tff('#skF_41',type,
    '#skF_41': ( $i * $i ) > $i ).

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

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

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

tff('#skF_33',type,
    '#skF_33': ( $i * $i * $i ) > $i ).

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

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

tff('#skF_44',type,
    '#skF_44': ( $i * $i * $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(sdtmndt0,type,
    sdtmndt0: ( $i * $i ) > $i ).

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

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

tff('#skF_55',type,
    '#skF_55': $i ).

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

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

tff('#skF_37',type,
    '#skF_37': $i > $i ).

tff('#skF_56',type,
    '#skF_56': $i ).

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

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

tff('#skF_54',type,
    '#skF_54': $i ).

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

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

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

tff('#skF_38',type,
    '#skF_38': ( $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 * $i ) > $i ).

tff('#skF_52',type,
    '#skF_52': $i > $i ).

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

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

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

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

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

tff('#skF_32',type,
    '#skF_32': ( $i * $i * $i * $i ) > $i ).

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

tff('#skF_35',type,
    '#skF_35': ( $i * $i * $i ) > $i ).

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

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

tff('#skF_49',type,
    '#skF_49': ( $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_42',type,
    '#skF_42': ( $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_28',type,
    '#skF_28': ( $i * $i ) > $i ).

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

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

tff('#skF_34',type,
    '#skF_34': ( $i * $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('#skF_50',type,
    '#skF_50': ( $i * $i ) > $i ).

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

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

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

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(xp,type,
    xp: $i ).

tff('#skF_48',type,
    '#skF_48': $i > $i ).

tff('#skF_40',type,
    '#skF_40': ( $i * $i ) > $i ).

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

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

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

tff('#skF_36',type,
    '#skF_36': ( $i * $i * $i * $i ) > $i ).

tff('#skF_43',type,
    '#skF_43': ( $i * $i ) > $i ).

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

tff('#skF_46',type,
    '#skF_46': $i > $i ).

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

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

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

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

tff('#skF_45',type,
    '#skF_45': $i > $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_16',type,
    '#skF_16': ( $i * $i * $i ) > $i ).

tff('#skF_51',type,
    '#skF_51': $i > $i ).

tff('#skF_39',type,
    '#skF_39': ( $i * $i ) > $i ).

tff(f_1467,hypothesis,
    ( aElementOf0(xn,szDzozmdt0(xd))
    & ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
    & aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & aElementOf0(xn,szNzAzT0)
    & ( sdtlpdtrp0(xe,xn) = xp ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).

tff(f_886,hypothesis,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aSet0(sdtlpdtrp0(xN,W0))
        & ! [W1] :
            ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
           => aElementOf0(W1,szNzAzT0) )
        & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
        & isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).

tff(f_1501,negated_conjecture,
    ~ ( ! [W0] :
          ( aElementOf0(W0,xP)
         => aElementOf0(W0,xD) )
      | aSubsetOf0(xP,xD)
      | aElementOf0(xP,slbdtsldtrb0(xD,xk)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_1381,hypothesis,
    ( aSet0(xQ)
    & ! [W0] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xO) )
    & aSubsetOf0(xQ,xO)
    & ( sbrdtbr0(xQ) = xK )
    & aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).

tff(f_1440,hypothesis,
    aElementOf0(xp,xQ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).

tff(f_39,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

tff(f_1492,hypothesis,
    ( ! [W0] :
        ( aElementOf0(W0,sdtlpdtrp0(xN,xn))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0) )
    & aSet0(xD)
    & ! [W0] :
        ( aElementOf0(W0,xD)
      <=> ( aElement0(W0)
          & aElementOf0(W0,sdtlpdtrp0(xN,xn))
          & ( W0 != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
    & ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5585) ).

tff(f_1457,hypothesis,
    sbrdtbr0(xP) = xk,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5217) ).

tff(f_1439,hypothesis,
    ( aSet0(xP)
    & ! [W0] :
        ( aElementOf0(W0,xQ)
       => sdtlseqdt0(szmzizndt0(xQ),W0) )
    & ! [W0] :
        ( aElementOf0(W0,xP)
      <=> ( aElement0(W0)
          & aElementOf0(W0,xQ)
          & ( W0 != szmzizndt0(xQ) ) ) )
    & ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).

tff(f_330,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ( ( sbrdtbr0(W0) = sz00 )
      <=> ( W0 = slcrc0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).

tff(f_52,definition,
    ! [W0] :
      ( ( W0 = slcrc0 )
    <=> ( aSet0(W0)
        & ~ ? [W1] : aElementOf0(W1,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).

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/sandbox2/benchmark/theBenchmark.p',mDefMin) ).

tff(f_1474,hypothesis,
    ( ! [W0] :
        ( aElementOf0(W0,xP)
       => aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
    & aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5334) ).

tff(f_219,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
        & ( szszuzczcdt0(W0) != sz00 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).

tff(f_84,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
               => aElementOf0(W2,W0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).

tff(f_211,axiom,
    ( aSet0(szNzAzT0)
    & isCountable0(szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).

tff(f_467,axiom,
    ! [W0] :
      ( ( aSubsetOf0(W0,szNzAzT0)
        & isFinite0(W0) )
     => ? [W1] :
          ( aElementOf0(W1,szNzAzT0)
          & aSubsetOf0(W0,slbdtrb0(W1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinSubSeg) ).

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/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).

tff(f_824,hypothesis,
    ( aElementOf0(xk,szNzAzT0)
    & ( szszuzczcdt0(xk) = xK ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).

tff(f_324,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> isFinite0(W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).

tff(f_471,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( sbrdtbr0(slbdtrb0(W0)) = W0 ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).

tff(f_1276,hypothesis,
    ( aFunction0(xe)
    & ( szDzozmdt0(xe) = szNzAzT0 )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          & ! [W1] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
             => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
          & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).

tff(f_163,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).

tff(f_181,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ! [W1] :
          ( ( aSet0(W1)
            & isCountable0(W1) )
         => isCountable0(sdtpldt0(W1,W0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCConsSet) ).

tff(f_190,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ! [W1] :
          ( ( aSet0(W1)
            & isCountable0(W1) )
         => isCountable0(sdtmndt0(W1,W0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCDiffSet) ).

tff(f_873,hypothesis,
    ( aFunction0(xN)
    & ( szDzozmdt0(xN) = szNzAzT0 )
    & ( sdtlpdtrp0(xN,sz00) = xS )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                   => aElementOf0(W1,szNzAzT0) ) )
              | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
            & isCountable0(sdtlpdtrp0(xN,W0)) )
         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            & ! [W1] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
               => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).

tff(c_9858,plain,
    aElementOf0(xn,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_1467]) ).

tff(c_8396,plain,
    ! [W0_581] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_581),szNzAzT0)
      | ~ aElementOf0(W0_581,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_886]) ).

tff(c_9890,plain,
    ~ aElementOf0('#skF_56',xD),
    inference(cnfTransformation,[status(thm)],[f_1501]) ).

tff(c_8394,plain,
    ! [W0_581] :
      ( isCountable0(sdtlpdtrp0(xN,W0_581))
      | ~ aElementOf0(W0_581,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_886]) ).

tff(c_9796,plain,
    aSet0(xQ),
    inference(cnfTransformation,[status(thm)],[f_1381]) ).

tff(c_9838,plain,
    aElementOf0(xp,xQ),
    inference(cnfTransformation,[status(thm)],[f_1440]) ).

tff(c_10318,plain,
    ! [W1_852,W0_853] :
      ( aElement0(W1_852)
      | ~ aElementOf0(W1_852,W0_853)
      | ~ aSet0(W0_853) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_10375,plain,
    ( aElement0(xp)
    | ~ aSet0(xQ) ),
    inference(resolution,[status(thm)],[c_9838,c_10318]) ).

tff(c_10444,plain,
    aElement0(xp),
    inference(demodulation,[status(thm),theory(equality)],[c_9796,c_10375]) ).

tff(c_9876,plain,
    aSet0(xD),
    inference(cnfTransformation,[status(thm)],[f_1492]) ).

tff(c_8400,plain,
    ! [W0_581] :
      ( aSet0(sdtlpdtrp0(xN,W0_581))
      | ~ aElementOf0(W0_581,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_886]) ).

tff(c_9852,plain,
    sbrdtbr0(xP) = xk,
    inference(cnfTransformation,[status(thm)],[f_1457]) ).

tff(c_9830,plain,
    aSet0(xP),
    inference(cnfTransformation,[status(thm)],[f_1439]) ).

tff(c_10250,plain,
    ! [W0_850] :
      ( ( slcrc0 = W0_850 )
      | ( sbrdtbr0(W0_850) != sz00 )
      | ~ aSet0(W0_850) ),
    inference(cnfTransformation,[status(thm)],[f_330]) ).

tff(c_10274,plain,
    ( ( xP = slcrc0 )
    | ( sbrdtbr0(xP) != sz00 ) ),
    inference(resolution,[status(thm)],[c_9830,c_10250]) ).

tff(c_10301,plain,
    ( ( xP = slcrc0 )
    | ( xk != sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9852,c_10274]) ).

tff(c_10313,plain,
    xk != sz00,
    inference(splitLeft,[status(thm)],[c_10301]) ).

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

tff(c_154,plain,
    ( ( sbrdtbr0(slcrc0) = sz00 )
    | ~ aSet0(slcrc0) ),
    inference(cnfTransformation,[status(thm)],[f_330]) ).

tff(c_9919,plain,
    sbrdtbr0(slcrc0) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_154]) ).

tff(c_11777,plain,
    ! [W0_914] :
      ( ( slcrc0 = W0_914 )
      | aElementOf0('#skF_1'(W0_914),W0_914)
      | ~ aSet0(W0_914) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_9836,plain,
    ! [W0_811] :
      ( aElement0(W0_811)
      | ~ aElementOf0(W0_811,xP) ),
    inference(cnfTransformation,[status(thm)],[f_1439]) ).

tff(c_11836,plain,
    ( aElement0('#skF_1'(xP))
    | ( xP = slcrc0 )
    | ~ aSet0(xP) ),
    inference(resolution,[status(thm)],[c_11777,c_9836]) ).

tff(c_11890,plain,
    ( aElement0('#skF_1'(xP))
    | ( xP = slcrc0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9830,c_11836]) ).

tff(c_11986,plain,
    xP = slcrc0,
    inference(splitLeft,[status(thm)],[c_11890]) ).

tff(c_12033,plain,
    sbrdtbr0(slcrc0) = xk,
    inference(demodulation,[status(thm),theory(equality)],[c_11986,c_9852]) ).

tff(c_12040,plain,
    xk = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_9919,c_12033]) ).

tff(c_12042,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10313,c_12040]) ).

tff(c_12044,plain,
    xP != slcrc0,
    inference(splitRight,[status(thm)],[c_11890]) ).

tff(c_12692,plain,
    ! [W0_949] :
      ( aElementOf0(szmzizndt0(W0_949),W0_949)
      | ( slcrc0 = W0_949 )
      | ~ aSubsetOf0(W0_949,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_388]) ).

tff(c_12763,plain,
    ( aElement0(szmzizndt0(xP))
    | ( xP = slcrc0 )
    | ~ aSubsetOf0(xP,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_12692,c_9836]) ).

tff(c_12826,plain,
    ( aElement0(szmzizndt0(xP))
    | ~ aSubsetOf0(xP,szNzAzT0) ),
    inference(negUnitSimplification,[status(thm)],[c_12044,c_12763]) ).

tff(c_12872,plain,
    ~ aSubsetOf0(xP,szNzAzT0),
    inference(splitLeft,[status(thm)],[c_12826]) ).

tff(c_9868,plain,
    aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(cnfTransformation,[status(thm)],[f_1474]) ).

tff(c_114,plain,
    ! [W0_72] :
      ( aElementOf0(szszuzczcdt0(W0_72),szNzAzT0)
      | ~ aElementOf0(W0_72,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_219]) ).

tff(c_9892,plain,
    aElementOf0('#skF_56',xP),
    inference(cnfTransformation,[status(thm)],[f_1501]) ).

tff(c_14123,plain,
    ! [W2_1020,W0_1021,W1_1022] :
      ( aElementOf0(W2_1020,W0_1021)
      | ~ aElementOf0(W2_1020,W1_1022)
      | ~ aSubsetOf0(W1_1022,W0_1021)
      | ~ aSet0(W0_1021) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_14305,plain,
    ! [W0_1023] :
      ( aElementOf0('#skF_56',W0_1023)
      | ~ aSubsetOf0(xP,W0_1023)
      | ~ aSet0(W0_1023) ),
    inference(resolution,[status(thm)],[c_9892,c_14123]) ).

tff(c_14326,plain,
    ( aElementOf0('#skF_56',sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(resolution,[status(thm)],[c_9868,c_14305]) ).

tff(c_14945,plain,
    ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(splitLeft,[status(thm)],[c_14326]) ).

tff(c_14949,plain,
    ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0),
    inference(resolution,[status(thm)],[c_8400,c_14945]) ).

tff(c_14952,plain,
    ~ aElementOf0(xn,szNzAzT0),
    inference(resolution,[status(thm)],[c_114,c_14949]) ).

tff(c_14956,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_14952]) ).

tff(c_14958,plain,
    aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(splitRight,[status(thm)],[c_14326]) ).

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

tff(c_220,plain,
    ! [W0_148] :
      ( aSubsetOf0(W0_148,slbdtrb0('#skF_13'(W0_148)))
      | ~ isFinite0(W0_148)
      | ~ aSubsetOf0(W0_148,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_467]) ).

tff(c_14957,plain,
    aElementOf0('#skF_56',sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(splitRight,[status(thm)],[c_14326]) ).

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_15514,plain,
    ! [W0_1056] :
      ( aElementOf0('#skF_56',W0_1056)
      | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),W0_1056)
      | ~ aSet0(W0_1056) ),
    inference(resolution,[status(thm)],[c_14957,c_24]) ).

tff(c_15527,plain,
    ( aElementOf0('#skF_56',slbdtrb0('#skF_13'(sdtlpdtrp0(xN,szszuzczcdt0(xn)))))
    | ~ aSet0(slbdtrb0('#skF_13'(sdtlpdtrp0(xN,szszuzczcdt0(xn)))))
    | ~ isFinite0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0) ),
    inference(resolution,[status(thm)],[c_220,c_15514]) ).

tff(c_15568,plain,
    ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0),
    inference(splitLeft,[status(thm)],[c_15527]) ).

tff(c_15572,plain,
    ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0),
    inference(resolution,[status(thm)],[c_8396,c_15568]) ).

tff(c_15575,plain,
    ~ aElementOf0(xn,szNzAzT0),
    inference(resolution,[status(thm)],[c_114,c_15572]) ).

tff(c_15579,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_15575]) ).

tff(c_15581,plain,
    aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0),
    inference(splitRight,[status(thm)],[c_15527]) ).

tff(c_26807,plain,
    ! [W0_1282,W2_1283,W1_1284] :
      ( aSubsetOf0(W0_1282,W2_1283)
      | ~ aSubsetOf0(W1_1284,W2_1283)
      | ~ aSubsetOf0(W0_1282,W1_1284)
      | ~ aSet0(W2_1283)
      | ~ aSet0(W1_1284)
      | ~ aSet0(W0_1282) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_26835,plain,
    ! [W0_1282] :
      ( aSubsetOf0(W0_1282,szNzAzT0)
      | ~ aSubsetOf0(W0_1282,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ aSet0(szNzAzT0)
      | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ aSet0(W0_1282) ),
    inference(resolution,[status(thm)],[c_15581,c_26807]) ).

tff(c_27177,plain,
    ! [W0_1286] :
      ( aSubsetOf0(W0_1286,szNzAzT0)
      | ~ aSubsetOf0(W0_1286,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ aSet0(W0_1286) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14958,c_108,c_26835]) ).

tff(c_27184,plain,
    ( aSubsetOf0(xP,szNzAzT0)
    | ~ aSet0(xP) ),
    inference(resolution,[status(thm)],[c_9868,c_27177]) ).

tff(c_27194,plain,
    aSubsetOf0(xP,szNzAzT0),
    inference(demodulation,[status(thm),theory(equality)],[c_9830,c_27184]) ).

tff(c_27196,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_12872,c_27194]) ).

tff(c_27198,plain,
    aSubsetOf0(xP,szNzAzT0),
    inference(splitRight,[status(thm)],[c_12826]) ).

tff(c_8320,plain,
    aElementOf0(xk,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_824]) ).

tff(c_12045,plain,
    ! [W0_918] :
      ( isFinite0(W0_918)
      | ~ aElementOf0(sbrdtbr0(W0_918),szNzAzT0)
      | ~ aSet0(W0_918) ),
    inference(cnfTransformation,[status(thm)],[f_324]) ).

tff(c_12054,plain,
    ( isFinite0(xP)
    | ~ aElementOf0(xk,szNzAzT0)
    | ~ aSet0(xP) ),
    inference(superposition,[status(thm),theory(equality)],[c_9852,c_12045]) ).

tff(c_12063,plain,
    isFinite0(xP),
    inference(demodulation,[status(thm),theory(equality)],[c_9830,c_8320,c_12054]) ).

tff(c_222,plain,
    ! [W0_148] :
      ( aElementOf0('#skF_13'(W0_148),szNzAzT0)
      | ~ isFinite0(W0_148)
      | ~ aSubsetOf0(W0_148,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_467]) ).

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_152780,plain,
    ! [W2_3448,W0_3449,W1_3450] :
      ( aElementOf0(W2_3448,W0_3449)
      | ~ aElementOf0(W2_3448,W1_3450)
      | ~ aSubsetOf0(W1_3450,W0_3449)
      | ~ aSet0(W0_3449) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_153197,plain,
    ! [W0_3458] :
      ( aElementOf0('#skF_56',W0_3458)
      | ~ aSubsetOf0(xP,W0_3458)
      | ~ aSet0(W0_3458) ),
    inference(resolution,[status(thm)],[c_9892,c_152780]) ).

tff(c_153201,plain,
    ( aElementOf0('#skF_56',slbdtrb0('#skF_13'(xP)))
    | ~ aSet0(slbdtrb0('#skF_13'(xP)))
    | ~ isFinite0(xP)
    | ~ aSubsetOf0(xP,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_220,c_153197]) ).

tff(c_153220,plain,
    ( aElementOf0('#skF_56',slbdtrb0('#skF_13'(xP)))
    | ~ aSet0(slbdtrb0('#skF_13'(xP))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_27198,c_12063,c_153201]) ).

tff(c_154027,plain,
    ~ aSet0(slbdtrb0('#skF_13'(xP))),
    inference(splitLeft,[status(thm)],[c_153220]) ).

tff(c_154031,plain,
    ~ aElementOf0('#skF_13'(xP),szNzAzT0),
    inference(resolution,[status(thm)],[c_188,c_154027]) ).

tff(c_154034,plain,
    ( ~ isFinite0(xP)
    | ~ aSubsetOf0(xP,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_222,c_154031]) ).

tff(c_154038,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_27198,c_12063,c_154034]) ).

tff(c_154040,plain,
    aSet0(slbdtrb0('#skF_13'(xP))),
    inference(splitRight,[status(thm)],[c_153220]) ).

tff(c_156,plain,
    ! [W0_98] :
      ( ( slcrc0 = W0_98 )
      | ( sbrdtbr0(W0_98) != sz00 )
      | ~ aSet0(W0_98) ),
    inference(cnfTransformation,[status(thm)],[f_330]) ).

tff(c_154044,plain,
    ( ( slbdtrb0('#skF_13'(xP)) = slcrc0 )
    | ( sbrdtbr0(slbdtrb0('#skF_13'(xP))) != sz00 ) ),
    inference(resolution,[status(thm)],[c_154040,c_156]) ).

tff(c_154570,plain,
    sbrdtbr0(slbdtrb0('#skF_13'(xP))) != sz00,
    inference(splitLeft,[status(thm)],[c_154044]) ).

tff(c_154573,plain,
    ( ( '#skF_13'(xP) != sz00 )
    | ~ aElementOf0('#skF_13'(xP),szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_224,c_154570]) ).

tff(c_155351,plain,
    ~ aElementOf0('#skF_13'(xP),szNzAzT0),
    inference(splitLeft,[status(thm)],[c_154573]) ).

tff(c_155354,plain,
    ( ~ isFinite0(xP)
    | ~ aSubsetOf0(xP,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_222,c_155351]) ).

tff(c_155358,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_27198,c_12063,c_155354]) ).

tff(c_155360,plain,
    aElementOf0('#skF_13'(xP),szNzAzT0),
    inference(splitRight,[status(thm)],[c_154573]) ).

tff(c_157242,plain,
    ! [W0_3555] :
      ( aElementOf0('#skF_13'(xP),W0_3555)
      | ~ aSubsetOf0(szNzAzT0,W0_3555)
      | ~ aSet0(W0_3555) ),
    inference(resolution,[status(thm)],[c_155360,c_24]) ).

tff(c_9856,plain,
    sdtlpdtrp0(xe,xn) = xp,
    inference(cnfTransformation,[status(thm)],[f_1467]) ).

tff(c_9706,plain,
    ! [W0_780] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,W0_780)) = sdtlpdtrp0(xe,W0_780) )
      | ~ aElementOf0(W0_780,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_1276]) ).

tff(c_151737,plain,
    ! [W0_3412] :
      ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0_3412)
      | ~ aElementOf0(W0_3412,sdtlpdtrp0(xN,xn)) ),
    inference(cnfTransformation,[status(thm)],[f_1492]) ).

tff(c_151740,plain,
    ! [W0_3412] :
      ( sdtlseqdt0(sdtlpdtrp0(xe,xn),W0_3412)
      | ~ aElementOf0(W0_3412,sdtlpdtrp0(xN,xn))
      | ~ aElementOf0(xn,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_9706,c_151737]) ).

tff(c_151742,plain,
    ! [W0_3412] :
      ( sdtlseqdt0(xp,W0_3412)
      | ~ aElementOf0(W0_3412,sdtlpdtrp0(xN,xn)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_9856,c_151740]) ).

tff(c_157455,plain,
    ( sdtlseqdt0(xp,'#skF_13'(xP))
    | ~ aSubsetOf0(szNzAzT0,sdtlpdtrp0(xN,xn))
    | ~ aSet0(sdtlpdtrp0(xN,xn)) ),
    inference(resolution,[status(thm)],[c_157242,c_151742]) ).

tff(c_157610,plain,
    ~ aSet0(sdtlpdtrp0(xN,xn)),
    inference(splitLeft,[status(thm)],[c_157455]) ).

tff(c_157613,plain,
    ~ aElementOf0(xn,szNzAzT0),
    inference(resolution,[status(thm)],[c_8400,c_157610]) ).

tff(c_157617,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_157613]) ).

tff(c_157619,plain,
    aSet0(sdtlpdtrp0(xN,xn)),
    inference(splitRight,[status(thm)],[c_157455]) ).

tff(c_151201,plain,
    ! [W0_3381] :
      ( aElementOf0(sdtlpdtrp0(xe,W0_3381),sdtlpdtrp0(xN,W0_3381))
      | ~ aElementOf0(W0_3381,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_1276]) ).

tff(c_151221,plain,
    ( aElementOf0(xp,sdtlpdtrp0(xN,xn))
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_9856,c_151201]) ).

tff(c_151229,plain,
    aElementOf0(xp,sdtlpdtrp0(xN,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_151221]) ).

tff(c_151335,plain,
    ! [W0_3385] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,W0_3385)) = sdtlpdtrp0(xe,W0_3385) )
      | ~ aElementOf0(W0_3385,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_1276]) ).

tff(c_9872,plain,
    sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) = xD,
    inference(cnfTransformation,[status(thm)],[f_1492]) ).

tff(c_151341,plain,
    ( ( sdtmndt0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xe,xn)) = xD )
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_151335,c_9872]) ).

tff(c_151356,plain,
    sdtmndt0(sdtlpdtrp0(xN,xn),xp) = xD,
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_9856,c_151341]) ).

tff(c_153097,plain,
    ! [W0_3455,W1_3456] :
      ( ( sdtpldt0(sdtmndt0(W0_3455,W1_3456),W1_3456) = W0_3455 )
      | ~ aElementOf0(W1_3456,W0_3455)
      | ~ aSet0(W0_3455) ),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_153121,plain,
    ( ( sdtpldt0(xD,xp) = sdtlpdtrp0(xN,xn) )
    | ~ aElementOf0(xp,sdtlpdtrp0(xN,xn))
    | ~ aSet0(sdtlpdtrp0(xN,xn)) ),
    inference(superposition,[status(thm),theory(equality)],[c_151356,c_153097]) ).

tff(c_153131,plain,
    ( ( sdtpldt0(xD,xp) = sdtlpdtrp0(xN,xn) )
    | ~ aSet0(sdtlpdtrp0(xN,xn)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151229,c_153121]) ).

tff(c_199015,plain,
    sdtpldt0(xD,xp) = sdtlpdtrp0(xN,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_157619,c_153131]) ).

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_199040,plain,
    ( isCountable0(sdtlpdtrp0(xN,xn))
    | ~ isCountable0(xD)
    | ~ aSet0(xD)
    | ~ aElement0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_199015,c_98]) ).

tff(c_199066,plain,
    ( isCountable0(sdtlpdtrp0(xN,xn))
    | ~ isCountable0(xD) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10444,c_9876,c_199040]) ).

tff(c_199530,plain,
    ~ isCountable0(xD),
    inference(splitLeft,[status(thm)],[c_199066]) ).

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_151404,plain,
    ( isCountable0(xD)
    | ~ isCountable0(sdtlpdtrp0(xN,xn))
    | ~ aSet0(sdtlpdtrp0(xN,xn))
    | ~ aElement0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_151356,c_100]) ).

tff(c_151416,plain,
    ( isCountable0(xD)
    | ~ isCountable0(sdtlpdtrp0(xN,xn))
    | ~ aSet0(sdtlpdtrp0(xN,xn)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10444,c_151404]) ).

tff(c_201750,plain,
    ( isCountable0(xD)
    | ~ isCountable0(sdtlpdtrp0(xN,xn)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_157619,c_151416]) ).

tff(c_201751,plain,
    ~ isCountable0(sdtlpdtrp0(xN,xn)),
    inference(negUnitSimplification,[status(thm)],[c_199530,c_201750]) ).

tff(c_201754,plain,
    ~ aElementOf0(xn,szNzAzT0),
    inference(resolution,[status(thm)],[c_8394,c_201751]) ).

tff(c_201758,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_201754]) ).

tff(c_201759,plain,
    isCountable0(sdtlpdtrp0(xN,xn)),
    inference(splitRight,[status(thm)],[c_199066]) ).

tff(c_9880,plain,
    ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),xD),
    inference(cnfTransformation,[status(thm)],[f_1492]) ).

tff(c_151347,plain,
    ( ~ aElementOf0(sdtlpdtrp0(xe,xn),xD)
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_151335,c_9880]) ).

tff(c_151358,plain,
    ~ aElementOf0(xp,xD),
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_9856,c_151347]) ).

tff(c_9710,plain,
    ! [W0_780] :
      ( aElementOf0(sdtlpdtrp0(xe,W0_780),sdtlpdtrp0(xN,W0_780))
      | ~ aElementOf0(W0_780,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_1276]) ).

tff(c_162770,plain,
    ! [W0_3645] :
      ( aElementOf0(W0_3645,xD)
      | ( szmzizndt0(sdtlpdtrp0(xN,xn)) = W0_3645 )
      | ~ aElementOf0(W0_3645,sdtlpdtrp0(xN,xn))
      | ~ aElement0(W0_3645) ),
    inference(cnfTransformation,[status(thm)],[f_1492]) ).

tff(c_162837,plain,
    ( aElementOf0(sdtlpdtrp0(xe,xn),xD)
    | ( szmzizndt0(sdtlpdtrp0(xN,xn)) = sdtlpdtrp0(xe,xn) )
    | ~ aElement0(sdtlpdtrp0(xe,xn))
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_9710,c_162770]) ).

tff(c_162900,plain,
    ( aElementOf0(xp,xD)
    | ( szmzizndt0(sdtlpdtrp0(xN,xn)) = xp ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_10444,c_9856,c_9856,c_9856,c_162837]) ).

tff(c_162901,plain,
    szmzizndt0(sdtlpdtrp0(xN,xn)) = xp,
    inference(negUnitSimplification,[status(thm)],[c_151358,c_162900]) ).

tff(c_207297,plain,
    ! [W0_4167] :
      ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0_4167),szNzAzT0)
      | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0_4167)),sdtmndt0(sdtlpdtrp0(xN,W0_4167),szmzizndt0(sdtlpdtrp0(xN,W0_4167))))
      | ~ isCountable0(sdtlpdtrp0(xN,W0_4167))
      | ~ aElementOf0(W0_4167,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_873]) ).

tff(c_153224,plain,
    ( aElementOf0('#skF_56',sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(resolution,[status(thm)],[c_9868,c_153197]) ).

tff(c_153941,plain,
    ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(splitLeft,[status(thm)],[c_153224]) ).

tff(c_153945,plain,
    ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0),
    inference(resolution,[status(thm)],[c_8400,c_153941]) ).

tff(c_153948,plain,
    ~ aElementOf0(xn,szNzAzT0),
    inference(resolution,[status(thm)],[c_114,c_153945]) ).

tff(c_153952,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_153948]) ).

tff(c_153953,plain,
    aElementOf0('#skF_56',sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(splitRight,[status(thm)],[c_153224]) ).

tff(c_153969,plain,
    ! [W0_14] :
      ( aElementOf0('#skF_56',W0_14)
      | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),W0_14)
      | ~ aSet0(W0_14) ),
    inference(resolution,[status(thm)],[c_153953,c_24]) ).

tff(c_207315,plain,
    ( aElementOf0('#skF_56',sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
    | ~ isCountable0(sdtlpdtrp0(xN,xn))
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_207297,c_153969]) ).

tff(c_207366,plain,
    ( aElementOf0('#skF_56',xD)
    | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_201759,c_9876,c_151356,c_162901,c_151356,c_162901,c_207315]) ).

tff(c_207367,plain,
    ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0),
    inference(negUnitSimplification,[status(thm)],[c_9890,c_207366]) ).

tff(c_207387,plain,
    ~ aElementOf0(xn,szNzAzT0),
    inference(resolution,[status(thm)],[c_8396,c_207367]) ).

tff(c_207394,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_207387]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM629+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 14:34:48 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 140.70/116.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 140.70/116.43  
% 140.70/116.43  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 140.95/116.48  
% 140.95/116.48  Inference rules
% 140.95/116.48  ----------------------
% 140.95/116.48  #Ref     : 10
% 140.95/116.48  #Sup     : 35231
% 140.95/116.48  #Fact    : 6
% 140.95/116.48  #Define  : 0
% 140.95/116.48  #Split   : 1106
% 140.95/116.48  #Chain   : 0
% 140.95/116.48  #Close   : 0
% 140.95/116.48  
% 140.95/116.48  Ordering : KBO
% 140.95/116.48  
% 140.95/116.48  Simplification rules
% 140.95/116.48  ----------------------
% 140.95/116.48  #Subsume      : 9442
% 140.95/116.48  #Demod        : 33696
% 140.95/116.48  #Tautology    : 6177
% 140.95/116.48  #SimpNegUnit  : 1648
% 140.95/116.48  #BackRed      : 867
% 140.95/116.48  
% 140.95/116.48  #Partial instantiations: 0
% 140.95/116.48  #Strategies tried      : 1
% 140.95/116.48  
% 140.95/116.48  Timing (in seconds)
% 140.95/116.48  ----------------------
% 140.95/116.49  Preprocessing        : 2.31
% 140.95/116.49  Parsing              : 0.55
% 140.95/116.49  CNF conversion       : 0.18
% 140.95/116.49  Main loop            : 113.08
% 140.95/116.49  Inferencing          : 8.81
% 140.95/116.49  Reduction            : 73.32
% 140.95/116.49  Demodulation         : 61.18
% 140.95/116.49  BG Simplification    : 0.94
% 140.95/116.49  Subsumption          : 23.27
% 140.95/116.49  Abstraction          : 0.90
% 140.95/116.49  MUC search           : 0.00
% 140.95/116.49  Cooper               : 0.00
% 140.95/116.49  Total                : 115.48
% 140.95/116.49  Index Insertion      : 0.00
% 140.95/116.49  Index Deletion       : 0.00
% 140.95/116.49  Index Matching       : 0.00
% 140.95/116.49  BG Taut test         : 0.00
%------------------------------------------------------------------------------