TSTP Solution File: NUM564+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM564+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 : n021.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 10:52:08 EDT 2023

% Result   : Theorem 7.37s 2.65s
% Output   : CNFRefutation 7.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   71
% Syntax   : Number of formulae    :  127 (  27 unt;  57 typ;   3 def)
%            Number of atoms       :  158 (  33 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  153 (  65   ~;  60   |;  12   &)
%                                         (   6 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  102 (  50   >;  52   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   48 (  48 usr;   7 con; 0-4 aty)
%            Number of variables   :   40 (;  39   !;   1   ?;   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 > xc > xT > xS > xK > szNzAzT0 > sz00 > slcrc0 > #skF_26 > #skF_7 > #skF_11 > #skF_17 > #skF_6 > #skF_27 > #skF_1 > #skF_18 > #skF_4 > #skF_12 > #skF_23 > #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_16

%Foreground sorts:

%Background operators:

%Foreground operators:
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('#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_18',type,
    '#skF_18': ( $i * $i * $i ) > $i ).

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

tff(sdtexdt0,type,
    sdtexdt0: ( $i * $i ) > $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('#skF_12',type,
    '#skF_12': ( $i * $i ) > $i ).

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

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

tff('#skF_23',type,
    '#skF_23': ( $i * $i * $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(aElementOf0,type,
    aElementOf0: ( $i * $i ) > $o ).

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

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_702,hypothesis,
    xK = sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).

tff(f_672,hypothesis,
    ( aFunction0(xc)
    & ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
    & aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).

tff(f_704,negated_conjecture,
    ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_664,hypothesis,
    aElementOf0(xK,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).

tff(f_496,axiom,
    ! [W0] :
      ( ( aSet0(W0)
        & isFinite0(W0) )
     => ! [W1] :
          ( aElementOf0(W1,szNzAzT0)
         => isFinite0(slbdtsldtrb0(W0,W1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSelFSet) ).

tff(f_507,axiom,
    ! [W0] :
      ( ( aSet0(W0)
        & ~ isFinite0(W0) )
     => ! [W1] :
          ( aElementOf0(W1,szNzAzT0)
         => ( slbdtsldtrb0(W0,W1) != slcrc0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSelNSet) ).

tff(f_487,definition,
    ! [W0,W1] :
      ( ( aSet0(W0)
        & aElementOf0(W1,szNzAzT0) )
     => ! [W2] :
          ( ( W2 = slbdtsldtrb0(W0,W1) )
        <=> ( aSet0(W2)
            & ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( aSubsetOf0(W3,W0)
                  & ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).

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

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

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

tff(f_65,axiom,
    ! [W0] :
      ( ( aSet0(W0)
        & isCountable0(W0) )
     => ~ isFinite0(W0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).

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_489,plain,
    ! [W1_399,W0_400] :
      ( aSet0(W1_399)
      | ~ aSubsetOf0(W1_399,W0_400)
      | ~ aSet0(W0_400) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_498,plain,
    ( aSet0(xS)
    | ~ aSet0(szNzAzT0) ),
    inference(resolution,[status(thm)],[c_340,c_489]) ).

tff(c_505,plain,
    aSet0(xS),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_498]) ).

tff(c_338,plain,
    isCountable0(xS),
    inference(cnfTransformation,[status(thm)],[f_667]) ).

tff(c_356,plain,
    xK = sz00,
    inference(cnfTransformation,[status(thm)],[f_702]) ).

tff(c_344,plain,
    slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
    inference(cnfTransformation,[status(thm)],[f_672]) ).

tff(c_363,plain,
    slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
    inference(demodulation,[status(thm),theory(equality)],[c_356,c_344]) ).

tff(c_358,plain,
    ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    inference(cnfTransformation,[status(thm)],[f_704]) ).

tff(c_364,plain,
    ~ aElementOf0(slcrc0,szDzozmdt0(xc)),
    inference(demodulation,[status(thm),theory(equality)],[c_363,c_358]) ).

tff(c_336,plain,
    aElementOf0(xK,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_664]) ).

tff(c_365,plain,
    aElementOf0(sz00,szNzAzT0),
    inference(demodulation,[status(thm),theory(equality)],[c_356,c_336]) ).

tff(c_1020,plain,
    ! [W0_469,W1_470] :
      ( isFinite0(slbdtsldtrb0(W0_469,W1_470))
      | ~ aElementOf0(W1_470,szNzAzT0)
      | ~ isFinite0(W0_469)
      | ~ aSet0(W0_469) ),
    inference(cnfTransformation,[status(thm)],[f_496]) ).

tff(c_1026,plain,
    ( isFinite0(szDzozmdt0(xc))
    | ~ aElementOf0(sz00,szNzAzT0)
    | ~ isFinite0(xS)
    | ~ aSet0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_363,c_1020]) ).

tff(c_1029,plain,
    ( isFinite0(szDzozmdt0(xc))
    | ~ isFinite0(xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_505,c_365,c_1026]) ).

tff(c_1030,plain,
    ~ isFinite0(xS),
    inference(splitLeft,[status(thm)],[c_1029]) ).

tff(c_1108,plain,
    ! [W0_477,W1_478] :
      ( ( slbdtsldtrb0(W0_477,W1_478) != slcrc0 )
      | ~ aElementOf0(W1_478,szNzAzT0)
      | isFinite0(W0_477)
      | ~ aSet0(W0_477) ),
    inference(cnfTransformation,[status(thm)],[f_507]) ).

tff(c_1110,plain,
    ( ( szDzozmdt0(xc) != slcrc0 )
    | ~ aElementOf0(sz00,szNzAzT0)
    | isFinite0(xS)
    | ~ aSet0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_363,c_1108]) ).

tff(c_1112,plain,
    ( ( szDzozmdt0(xc) != slcrc0 )
    | isFinite0(xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_505,c_365,c_1110]) ).

tff(c_1113,plain,
    szDzozmdt0(xc) != slcrc0,
    inference(negUnitSimplification,[status(thm)],[c_1030,c_1112]) ).

tff(c_742,plain,
    ! [W0_427,W1_428] :
      ( aSet0(slbdtsldtrb0(W0_427,W1_428))
      | ~ aElementOf0(W1_428,szNzAzT0)
      | ~ aSet0(W0_427) ),
    inference(cnfTransformation,[status(thm)],[f_487]) ).

tff(c_748,plain,
    ( aSet0(szDzozmdt0(xc))
    | ~ aElementOf0(sz00,szNzAzT0)
    | ~ aSet0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_363,c_742]) ).

tff(c_751,plain,
    aSet0(szDzozmdt0(xc)),
    inference(demodulation,[status(thm),theory(equality)],[c_505,c_365,c_748]) ).

tff(c_10,plain,
    ! [W0_7] :
      ( ( slcrc0 = W0_7 )
      | aElementOf0('#skF_1'(W0_7),W0_7)
      | ~ aSet0(W0_7) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_1660,plain,
    ! [W3_518,W1_519,W0_520] :
      ( ( sbrdtbr0(W3_518) = W1_519 )
      | ~ aElementOf0(W3_518,slbdtsldtrb0(W0_520,W1_519))
      | ~ aElementOf0(W1_519,szNzAzT0)
      | ~ aSet0(W0_520) ),
    inference(cnfTransformation,[status(thm)],[f_487]) ).

tff(c_1683,plain,
    ! [W3_518] :
      ( ( sbrdtbr0(W3_518) = sz00 )
      | ~ aElementOf0(W3_518,szDzozmdt0(xc))
      | ~ aElementOf0(sz00,szNzAzT0)
      | ~ aSet0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_363,c_1660]) ).

tff(c_1749,plain,
    ! [W3_521] :
      ( ( sbrdtbr0(W3_521) = sz00 )
      | ~ aElementOf0(W3_521,szDzozmdt0(xc)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_505,c_365,c_1683]) ).

tff(c_1769,plain,
    ( ( sbrdtbr0('#skF_1'(szDzozmdt0(xc))) = sz00 )
    | ( szDzozmdt0(xc) = slcrc0 )
    | ~ aSet0(szDzozmdt0(xc)) ),
    inference(resolution,[status(thm)],[c_10,c_1749]) ).

tff(c_1784,plain,
    ( ( sbrdtbr0('#skF_1'(szDzozmdt0(xc))) = sz00 )
    | ( szDzozmdt0(xc) = slcrc0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_751,c_1769]) ).

tff(c_1785,plain,
    sbrdtbr0('#skF_1'(szDzozmdt0(xc))) = sz00,
    inference(negUnitSimplification,[status(thm)],[c_1113,c_1784]) ).

tff(c_152,plain,
    ! [W0_97] :
      ( isFinite0(W0_97)
      | ~ aElementOf0(sbrdtbr0(W0_97),szNzAzT0)
      | ~ aSet0(W0_97) ),
    inference(cnfTransformation,[status(thm)],[f_324]) ).

tff(c_1807,plain,
    ( isFinite0('#skF_1'(szDzozmdt0(xc)))
    | ~ aElementOf0(sz00,szNzAzT0)
    | ~ aSet0('#skF_1'(szDzozmdt0(xc))) ),
    inference(superposition,[status(thm),theory(equality)],[c_1785,c_152]) ).

tff(c_1817,plain,
    ( isFinite0('#skF_1'(szDzozmdt0(xc)))
    | ~ aSet0('#skF_1'(szDzozmdt0(xc))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_365,c_1807]) ).

tff(c_1967,plain,
    ~ aSet0('#skF_1'(szDzozmdt0(xc))),
    inference(splitLeft,[status(thm)],[c_1817]) ).

tff(c_1999,plain,
    ! [W3_528,W0_529,W1_530] :
      ( aSubsetOf0(W3_528,W0_529)
      | ~ aElementOf0(W3_528,slbdtsldtrb0(W0_529,W1_530))
      | ~ aElementOf0(W1_530,szNzAzT0)
      | ~ aSet0(W0_529) ),
    inference(cnfTransformation,[status(thm)],[f_487]) ).

tff(c_2022,plain,
    ! [W3_528] :
      ( aSubsetOf0(W3_528,xS)
      | ~ aElementOf0(W3_528,szDzozmdt0(xc))
      | ~ aElementOf0(sz00,szNzAzT0)
      | ~ aSet0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_363,c_1999]) ).

tff(c_2030,plain,
    ! [W3_531] :
      ( aSubsetOf0(W3_531,xS)
      | ~ aElementOf0(W3_531,szDzozmdt0(xc)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_505,c_365,c_2022]) ).

tff(c_2050,plain,
    ( aSubsetOf0('#skF_1'(szDzozmdt0(xc)),xS)
    | ( szDzozmdt0(xc) = slcrc0 )
    | ~ aSet0(szDzozmdt0(xc)) ),
    inference(resolution,[status(thm)],[c_10,c_2030]) ).

tff(c_2065,plain,
    ( aSubsetOf0('#skF_1'(szDzozmdt0(xc)),xS)
    | ( szDzozmdt0(xc) = slcrc0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_751,c_2050]) ).

tff(c_2066,plain,
    aSubsetOf0('#skF_1'(szDzozmdt0(xc)),xS),
    inference(negUnitSimplification,[status(thm)],[c_1113,c_2065]) ).

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_2074,plain,
    ( aSet0('#skF_1'(szDzozmdt0(xc)))
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_2066,c_26]) ).

tff(c_2083,plain,
    aSet0('#skF_1'(szDzozmdt0(xc))),
    inference(demodulation,[status(thm),theory(equality)],[c_505,c_2074]) ).

tff(c_2085,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1967,c_2083]) ).

tff(c_2087,plain,
    aSet0('#skF_1'(szDzozmdt0(xc))),
    inference(splitRight,[status(thm)],[c_1817]) ).

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

tff(c_2120,plain,
    ( ( '#skF_1'(szDzozmdt0(xc)) = slcrc0 )
    | ( sbrdtbr0('#skF_1'(szDzozmdt0(xc))) != sz00 ) ),
    inference(resolution,[status(thm)],[c_2087,c_156]) ).

tff(c_2123,plain,
    '#skF_1'(szDzozmdt0(xc)) = slcrc0,
    inference(demodulation,[status(thm),theory(equality)],[c_1785,c_2120]) ).

tff(c_2136,plain,
    ( ( szDzozmdt0(xc) = slcrc0 )
    | aElementOf0(slcrc0,szDzozmdt0(xc))
    | ~ aSet0(szDzozmdt0(xc)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2123,c_10]) ).

tff(c_2143,plain,
    ( ( szDzozmdt0(xc) = slcrc0 )
    | aElementOf0(slcrc0,szDzozmdt0(xc)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_751,c_2136]) ).

tff(c_2145,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_364,c_1113,c_2143]) ).

tff(c_2147,plain,
    isFinite0(xS),
    inference(splitRight,[status(thm)],[c_1029]) ).

tff(c_20,plain,
    ! [W0_12] :
      ( ~ isFinite0(W0_12)
      | ~ isCountable0(W0_12)
      | ~ aSet0(W0_12) ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_2150,plain,
    ( ~ isCountable0(xS)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_2147,c_20]) ).

tff(c_2154,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_505,c_338,c_2150]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM564+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % 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
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 14:33:51 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 7.37/2.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.37/2.66  
% 7.37/2.66  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.79/2.70  
% 7.79/2.70  Inference rules
% 7.79/2.70  ----------------------
% 7.79/2.70  #Ref     : 1
% 7.79/2.70  #Sup     : 344
% 7.79/2.70  #Fact    : 0
% 7.79/2.70  #Define  : 0
% 7.79/2.70  #Split   : 17
% 7.79/2.70  #Chain   : 0
% 7.79/2.70  #Close   : 0
% 7.79/2.70  
% 7.79/2.70  Ordering : KBO
% 7.79/2.70  
% 7.79/2.70  Simplification rules
% 7.79/2.70  ----------------------
% 7.79/2.70  #Subsume      : 55
% 7.79/2.70  #Demod        : 241
% 7.79/2.70  #Tautology    : 101
% 7.79/2.70  #SimpNegUnit  : 21
% 7.79/2.70  #BackRed      : 29
% 7.79/2.70  
% 7.79/2.70  #Partial instantiations: 0
% 7.79/2.70  #Strategies tried      : 1
% 7.79/2.70  
% 7.79/2.70  Timing (in seconds)
% 7.79/2.70  ----------------------
% 7.79/2.70  Preprocessing        : 0.82
% 7.79/2.70  Parsing              : 0.39
% 7.79/2.70  CNF conversion       : 0.08
% 7.79/2.70  Main loop            : 0.81
% 7.79/2.70  Inferencing          : 0.25
% 7.79/2.70  Reduction            : 0.27
% 7.79/2.70  Demodulation         : 0.18
% 7.79/2.70  BG Simplification    : 0.07
% 7.79/2.70  Subsumption          : 0.18
% 7.79/2.70  Abstraction          : 0.03
% 7.79/2.70  MUC search           : 0.00
% 7.79/2.70  Cooper               : 0.00
% 7.79/2.70  Total                : 1.70
% 7.79/2.70  Index Insertion      : 0.00
% 7.79/2.70  Index Deletion       : 0.00
% 7.79/2.70  Index Matching       : 0.00
% 7.79/2.70  BG Taut test         : 0.00
%------------------------------------------------------------------------------