TSTP Solution File: NUM453+6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM453+6 : 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 : n031.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 10:51:43 EDT 2023

% Result   : Theorem 32.54s 18.03s
% Output   : CNFRefutation 32.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   71
% Syntax   : Number of formulae    :  153 (  45 unt;  59 typ;   0 def)
%            Number of atoms       :  221 (  95 equ)
%            Maximal formula atoms :   26 (   2 avg)
%            Number of connectives :  193 (  66   ~;  68   |;  43   &)
%                                         (   5 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   87 (  50   >;  37   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   49 (  49 usr;   9 con; 0-3 aty)
%            Number of variables   :   62 (;  56   !;   6   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aSubsetOf0 > aElementOf0 > aDivisorOf0 > isPrime0 > isOpen0 > isFinite0 > isClosed0 > aSet0 > aInteger0 > szAzrzSzezqlpdtcmdtrp0 > sdtslmnbsdt0 > sdtpldt0 > sdtbsmnsldt0 > sdtasdt0 > #nlpp > stldt0 > smndt0 > sbsmnsldt0 > xp > xS > sz10 > sz00 > cS2076 > cS2043 > cS1395 > #skF_25 > #skF_33 > #skF_11 > #skF_2 > #skF_18 > #skF_24 > #skF_26 > #skF_6 > #skF_19 > #skF_17 > #skF_31 > #skF_22 > #skF_12 > #skF_8 > #skF_4 > #skF_3 > #skF_13 > #skF_14 > #skF_32 > #skF_28 > #skF_5 > #skF_10 > #skF_7 > #skF_15 > #skF_23 > #skF_27 > #skF_29 > #skF_21 > #skF_1 > #skF_9 > #skF_30 > #skF_20 > #skF_16 > #skF_34

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(aInteger0,type,
    aInteger0: $i > $o ).

tff(sbsmnsldt0,type,
    sbsmnsldt0: $i > $i ).

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

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

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

tff(cS2043,type,
    cS2043: $i ).

tff(stldt0,type,
    stldt0: $i > $i ).

tff(sdtasdt0,type,
    sdtasdt0: ( $i * $i ) > $i ).

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

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

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

tff(isClosed0,type,
    isClosed0: $i > $o ).

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

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

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

tff(szAzrzSzezqlpdtcmdtrp0,type,
    szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).

tff(sz10,type,
    sz10: $i ).

tff(cS1395,type,
    cS1395: $i ).

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

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

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

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

tff(cS2076,type,
    cS2076: $i ).

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

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

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

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

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

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

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

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

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

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

tff(sdtslmnbsdt0,type,
    sdtslmnbsdt0: ( $i * $i ) > $i ).

tff(isPrime0,type,
    isPrime0: $i > $o ).

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

tff(smndt0,type,
    smndt0: $i > $i ).

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

tff(isOpen0,type,
    isOpen0: $i > $o ).

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

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

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

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

tff(sdtbsmnsldt0,type,
    sdtbsmnsldt0: ( $i * $i ) > $i ).

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

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

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

tff(aDivisorOf0,type,
    aDivisorOf0: ( $i * $i ) > $o ).

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

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

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

tff(sdteqdtlpzmzozddtrp0,type,
    sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).

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

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

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

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

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

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

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

tff(f_737,hypothesis,
    ( aInteger0(xp)
    & ( xp != sz00 )
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & ! [W0] :
        ( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
         => ( aInteger0(W0)
            & ? [W1] :
                ( aInteger0(W1)
                & ( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10)) ) )
            & aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
            & sdteqdtlpzmzozddtrp0(W0,sz10,xp) ) )
        & ( ( aInteger0(W0)
            & ( ? [W1] :
                  ( aInteger0(W1)
                  & ( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10)) ) )
              | aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
              | sdteqdtlpzmzozddtrp0(W0,sz10,xp) ) )
         => aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [W0] :
        ( aElementOf0(W0,sbsmnsldt0(xS))
      <=> ( aInteger0(W0)
          & ? [W1] :
              ( aElementOf0(W1,xS)
              & aElementOf0(W0,W1) ) ) )
    & ! [W0] :
        ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
      <=> ( aInteger0(W0)
          & ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
    & ! [W0] :
        ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
       => aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
    & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).

tff(f_758,hypothesis,
    ( ? [W0] :
        ( aInteger0(W0)
        & ( sdtasdt0(xp,W0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) ) )
    & aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
    & sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
    & aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & ? [W0] :
        ( aInteger0(W0)
        & ( sdtasdt0(xp,W0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) ) )
    & aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
    & sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
    & aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2232) ).

tff(f_31,axiom,
    aInteger0(sz10),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).

tff(f_764,negated_conjecture,
    ~ ( ( sdtpldt0(sz10,xp) != sz10 )
      & ( sdtpldt0(sz10,smndt0(xp)) != sz10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_73,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
        & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).

tff(f_125,axiom,
    ! [W0,W1] :
      ( ( aInteger0(W0)
        & aInteger0(W1) )
     => ( ( sdtasdt0(W0,W1) = sz00 )
       => ( ( W0 = sz00 )
          | ( W1 = sz00 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).

tff(f_543,hypothesis,
    ( aSet0(sbsmnsldt0(xS))
    & ! [W0] :
        ( aElementOf0(W0,sbsmnsldt0(xS))
      <=> ( aInteger0(W0)
          & ? [W1] :
              ( aElementOf0(W1,xS)
              & aElementOf0(W0,W1) ) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [W0] :
        ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
      <=> ( aInteger0(W0)
          & ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
    & ! [W0] :
        ( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
      <=> ( ( W0 = sz10 )
          | ( W0 = smndt0(sz10) ) ) )
    & ( stldt0(sbsmnsldt0(xS)) = cS2076 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2079) ).

tff(f_67,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( ( sdtpldt0(W0,sz00) = W0 )
        & ( W0 = sdtpldt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).

tff(f_61,axiom,
    ! [W0,W1] :
      ( ( aInteger0(W0)
        & aInteger0(W1) )
     => ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).

tff(f_55,axiom,
    ! [W0,W1,W2] :
      ( ( aInteger0(W0)
        & aInteger0(W1)
        & aInteger0(W2) )
     => ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).

tff(f_87,axiom,
    ! [W0,W1] :
      ( ( aInteger0(W0)
        & aInteger0(W1) )
     => ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).

tff(f_35,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => aInteger0(smndt0(W0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).

tff(c_450,plain,
    xp != sz00,
    inference(cnfTransformation,[status(thm)],[f_737]) ).

tff(c_452,plain,
    aInteger0(xp),
    inference(cnfTransformation,[status(thm)],[f_737]) ).

tff(c_498,plain,
    aInteger0('#skF_34'),
    inference(cnfTransformation,[status(thm)],[f_758]) ).

tff(c_6,plain,
    aInteger0(sz10),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_500,plain,
    ( ( sdtpldt0(sz10,smndt0(xp)) = sz10 )
    | ( sdtpldt0(sz10,xp) = sz10 ) ),
    inference(cnfTransformation,[status(thm)],[f_764]) ).

tff(c_584,plain,
    sdtpldt0(sz10,xp) = sz10,
    inference(splitLeft,[status(thm)],[c_500]) ).

tff(c_496,plain,
    sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) = sdtasdt0(xp,'#skF_34'),
    inference(cnfTransformation,[status(thm)],[f_758]) ).

tff(c_2504,plain,
    sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,'#skF_34'),
    inference(demodulation,[status(thm),theory(equality)],[c_584,c_496]) ).

tff(c_24,plain,
    ! [W0_13] :
      ( ( sdtpldt0(W0_13,smndt0(W0_13)) = sz00 )
      | ~ aInteger0(W0_13) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_2511,plain,
    ( ( sdtasdt0(xp,'#skF_34') = sz00 )
    | ~ aInteger0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_2504,c_24]) ).

tff(c_2520,plain,
    sdtasdt0(xp,'#skF_34') = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_2511]) ).

tff(c_6434,plain,
    ! [W1_439,W0_440] :
      ( ( sz00 = W1_439 )
      | ( sz00 = W0_440 )
      | ( sdtasdt0(W0_440,W1_439) != sz00 )
      | ~ aInteger0(W1_439)
      | ~ aInteger0(W0_440) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_6524,plain,
    ( ( sz00 = '#skF_34' )
    | ( xp = sz00 )
    | ~ aInteger0('#skF_34')
    | ~ aInteger0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_2520,c_6434]) ).

tff(c_6750,plain,
    ( ( sz00 = '#skF_34' )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_452,c_498,c_6524]) ).

tff(c_6751,plain,
    sz00 = '#skF_34',
    inference(negUnitSimplification,[status(thm)],[c_450,c_6750]) ).

tff(c_7000,plain,
    xp != '#skF_34',
    inference(demodulation,[status(thm),theory(equality)],[c_6751,c_450]) ).

tff(c_322,plain,
    stldt0(sbsmnsldt0(xS)) = cS2076,
    inference(cnfTransformation,[status(thm)],[f_543]) ).

tff(c_334,plain,
    aElementOf0(smndt0(sz10),stldt0(sbsmnsldt0(xS))),
    inference(cnfTransformation,[status(thm)],[f_543]) ).

tff(c_513,plain,
    aElementOf0(smndt0(sz10),cS2076),
    inference(demodulation,[status(thm),theory(equality)],[c_322,c_334]) ).

tff(c_456,plain,
    ! [W0_288] :
      ( aInteger0(W0_288)
      | ~ aElementOf0(W0_288,stldt0(sbsmnsldt0(xS))) ),
    inference(cnfTransformation,[status(thm)],[f_737]) ).

tff(c_599,plain,
    ! [W0_299] :
      ( aInteger0(W0_299)
      | ~ aElementOf0(W0_299,cS2076) ),
    inference(demodulation,[status(thm),theory(equality)],[c_322,c_456]) ).

tff(c_606,plain,
    aInteger0(smndt0(sz10)),
    inference(resolution,[status(thm)],[c_513,c_599]) ).

tff(c_610,plain,
    ! [W0_301] :
      ( ( sdtpldt0(W0_301,sz00) = W0_301 )
      | ~ aInteger0(W0_301) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_636,plain,
    sdtpldt0(xp,sz00) = xp,
    inference(resolution,[status(thm)],[c_452,c_610]) ).

tff(c_6991,plain,
    sdtpldt0(xp,'#skF_34') = xp,
    inference(demodulation,[status(thm),theory(equality)],[c_6751,c_636]) ).

tff(c_2549,plain,
    sdtpldt0(sz10,smndt0(sz10)) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_2520,c_2504]) ).

tff(c_6932,plain,
    sdtpldt0(sz10,smndt0(sz10)) = '#skF_34',
    inference(demodulation,[status(thm),theory(equality)],[c_6751,c_2549]) ).

tff(c_6966,plain,
    ! [W0_13] :
      ( ( sdtpldt0(W0_13,smndt0(W0_13)) = '#skF_34' )
      | ~ aInteger0(W0_13) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6751,c_24]) ).

tff(c_2592,plain,
    ! [W1_377,W0_378] :
      ( ( sdtpldt0(W1_377,W0_378) = sdtpldt0(W0_378,W1_377) )
      | ~ aInteger0(W1_377)
      | ~ aInteger0(W0_378) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_2643,plain,
    ! [W0_379] :
      ( ( sdtpldt0(sz10,W0_379) = sdtpldt0(W0_379,sz10) )
      | ~ aInteger0(W0_379) ),
    inference(resolution,[status(thm)],[c_6,c_2592]) ).

tff(c_2685,plain,
    sdtpldt0(xp,sz10) = sdtpldt0(sz10,xp),
    inference(resolution,[status(thm)],[c_452,c_2643]) ).

tff(c_2709,plain,
    sdtpldt0(xp,sz10) = sz10,
    inference(demodulation,[status(thm),theory(equality)],[c_584,c_2685]) ).

tff(c_33876,plain,
    ! [W0_803,W1_804,W2_805] :
      ( ( sdtpldt0(sdtpldt0(W0_803,W1_804),W2_805) = sdtpldt0(W0_803,sdtpldt0(W1_804,W2_805)) )
      | ~ aInteger0(W2_805)
      | ~ aInteger0(W1_804)
      | ~ aInteger0(W0_803) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_33951,plain,
    ! [W2_805] :
      ( ( sdtpldt0(xp,sdtpldt0(sz10,W2_805)) = sdtpldt0(sz10,W2_805) )
      | ~ aInteger0(W2_805)
      | ~ aInteger0(sz10)
      | ~ aInteger0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_2709,c_33876]) ).

tff(c_107026,plain,
    ! [W2_1516] :
      ( ( sdtpldt0(xp,sdtpldt0(sz10,W2_1516)) = sdtpldt0(sz10,W2_1516) )
      | ~ aInteger0(W2_1516) ),
    inference(demodulation,[status(thm),theory(equality)],[c_452,c_6,c_33951]) ).

tff(c_107109,plain,
    ( ( sdtpldt0(sz10,smndt0(sz10)) = sdtpldt0(xp,'#skF_34') )
    | ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_6966,c_107026]) ).

tff(c_107147,plain,
    xp = '#skF_34',
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_606,c_6991,c_6932,c_107109]) ).

tff(c_107149,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7000,c_107147]) ).

tff(c_107151,plain,
    sdtpldt0(sz10,xp) != sz10,
    inference(splitRight,[status(thm)],[c_500]) ).

tff(c_490,plain,
    aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
    inference(cnfTransformation,[status(thm)],[f_758]) ).

tff(c_440,plain,
    ! [W0_287] :
      ( aElementOf0(W0_287,stldt0(sbsmnsldt0(xS)))
      | ~ aElementOf0(W0_287,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
    inference(cnfTransformation,[status(thm)],[f_737]) ).

tff(c_108254,plain,
    ! [W0_1564] :
      ( aElementOf0(W0_1564,cS2076)
      | ~ aElementOf0(W0_1564,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_322,c_440]) ).

tff(c_108263,plain,
    aElementOf0(sdtpldt0(sz10,xp),cS2076),
    inference(resolution,[status(thm)],[c_490,c_108254]) ).

tff(c_324,plain,
    ! [W0_221] :
      ( ( smndt0(sz10) = W0_221 )
      | ( sz10 = W0_221 )
      | ~ aElementOf0(W0_221,stldt0(sbsmnsldt0(xS))) ),
    inference(cnfTransformation,[status(thm)],[f_543]) ).

tff(c_108291,plain,
    ! [W0_1568] :
      ( ( smndt0(sz10) = W0_1568 )
      | ( sz10 = W0_1568 )
      | ~ aElementOf0(W0_1568,cS2076) ),
    inference(demodulation,[status(thm),theory(equality)],[c_322,c_324]) ).

tff(c_108294,plain,
    ( ( sdtpldt0(sz10,xp) = smndt0(sz10) )
    | ( sdtpldt0(sz10,xp) = sz10 ) ),
    inference(resolution,[status(thm)],[c_108263,c_108291]) ).

tff(c_108303,plain,
    sdtpldt0(sz10,xp) = smndt0(sz10),
    inference(negUnitSimplification,[status(thm)],[c_107151,c_108294]) ).

tff(c_108319,plain,
    smndt0(sz10) != sz10,
    inference(demodulation,[status(thm),theory(equality)],[c_108303,c_107151]) ).

tff(c_488,plain,
    aInteger0('#skF_33'),
    inference(cnfTransformation,[status(thm)],[f_758]) ).

tff(c_109236,plain,
    ! [W1_1597,W0_1598] :
      ( ( sdtasdt0(W1_1597,W0_1598) = sdtasdt0(W0_1598,W1_1597) )
      | ~ aInteger0(W1_1597)
      | ~ aInteger0(W0_1598) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_109433,plain,
    ! [W0_1601] :
      ( ( sdtasdt0(xp,W0_1601) = sdtasdt0(W0_1601,xp) )
      | ~ aInteger0(W0_1601) ),
    inference(resolution,[status(thm)],[c_452,c_109236]) ).

tff(c_109499,plain,
    sdtasdt0(xp,'#skF_33') = sdtasdt0('#skF_33',xp),
    inference(resolution,[status(thm)],[c_488,c_109433]) ).

tff(c_107150,plain,
    sdtpldt0(sz10,smndt0(xp)) = sz10,
    inference(splitRight,[status(thm)],[c_500]) ).

tff(c_486,plain,
    sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) = sdtasdt0(xp,'#skF_33'),
    inference(cnfTransformation,[status(thm)],[f_758]) ).

tff(c_110033,plain,
    sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0('#skF_33',xp),
    inference(demodulation,[status(thm),theory(equality)],[c_109499,c_107150,c_486]) ).

tff(c_110040,plain,
    ( ( sdtasdt0('#skF_33',xp) = sz00 )
    | ~ aInteger0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_110033,c_24]) ).

tff(c_110049,plain,
    sdtasdt0('#skF_33',xp) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_110040]) ).

tff(c_110058,plain,
    sdtasdt0(xp,'#skF_33') = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_110049,c_109499]) ).

tff(c_112629,plain,
    ! [W1_1649,W0_1650] :
      ( ( sz00 = W1_1649 )
      | ( sz00 = W0_1650 )
      | ( sdtasdt0(W0_1650,W1_1649) != sz00 )
      | ~ aInteger0(W1_1649)
      | ~ aInteger0(W0_1650) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_112697,plain,
    ( ( sz00 = '#skF_33' )
    | ( xp = sz00 )
    | ~ aInteger0('#skF_33')
    | ~ aInteger0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_110058,c_112629]) ).

tff(c_112911,plain,
    ( ( sz00 = '#skF_33' )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_452,c_488,c_112697]) ).

tff(c_112912,plain,
    sz00 = '#skF_33',
    inference(negUnitSimplification,[status(thm)],[c_450,c_112911]) ).

tff(c_107238,plain,
    ! [W0_1526] :
      ( ( sdtpldt0(sz00,W0_1526) = W0_1526 )
      | ~ aInteger0(W0_1526) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_107266,plain,
    sdtpldt0(sz00,sz10) = sz10,
    inference(resolution,[status(thm)],[c_6,c_107238]) ).

tff(c_113170,plain,
    sdtpldt0('#skF_33',sz10) = sz10,
    inference(demodulation,[status(thm),theory(equality)],[c_112912,c_107266]) ).

tff(c_109647,plain,
    ! [W1_1603,W0_1604] :
      ( ( sdtpldt0(W1_1603,W0_1604) = sdtpldt0(W0_1604,W1_1603) )
      | ~ aInteger0(W1_1603)
      | ~ aInteger0(W0_1604) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_109899,plain,
    ! [W0_1611] :
      ( ( sdtpldt0(W0_1611,'#skF_33') = sdtpldt0('#skF_33',W0_1611) )
      | ~ aInteger0(W0_1611) ),
    inference(resolution,[status(thm)],[c_488,c_109647]) ).

tff(c_109967,plain,
    sdtpldt0(sz10,'#skF_33') = sdtpldt0('#skF_33',sz10),
    inference(resolution,[status(thm)],[c_6,c_109899]) ).

tff(c_113314,plain,
    sdtpldt0(sz10,'#skF_33') = sz10,
    inference(demodulation,[status(thm),theory(equality)],[c_113170,c_109967]) ).

tff(c_22,plain,
    ! [W0_13] :
      ( ( sdtpldt0(smndt0(W0_13),W0_13) = sz00 )
      | ~ aInteger0(W0_13) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_113142,plain,
    ! [W0_13] :
      ( ( sdtpldt0(smndt0(W0_13),W0_13) = '#skF_33' )
      | ~ aInteger0(W0_13) ),
    inference(demodulation,[status(thm),theory(equality)],[c_112912,c_22]) ).

tff(c_8,plain,
    ! [W0_2] :
      ( aInteger0(smndt0(W0_2))
      | ~ aInteger0(W0_2) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_117014,plain,
    ! [W0_1753,W1_1754,W2_1755] :
      ( ( sdtpldt0(sdtpldt0(W0_1753,W1_1754),W2_1755) = sdtpldt0(W0_1753,sdtpldt0(W1_1754,W2_1755)) )
      | ~ aInteger0(W2_1755)
      | ~ aInteger0(W1_1754)
      | ~ aInteger0(W0_1753) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_117115,plain,
    ! [W2_1755] :
      ( ( sdtpldt0(sz10,sdtpldt0(smndt0(xp),W2_1755)) = sdtpldt0(sz10,W2_1755) )
      | ~ aInteger0(W2_1755)
      | ~ aInteger0(smndt0(xp))
      | ~ aInteger0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_107150,c_117014]) ).

tff(c_117161,plain,
    ! [W2_1755] :
      ( ( sdtpldt0(sz10,sdtpldt0(smndt0(xp),W2_1755)) = sdtpldt0(sz10,W2_1755) )
      | ~ aInteger0(W2_1755)
      | ~ aInteger0(smndt0(xp)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_117115]) ).

tff(c_117259,plain,
    ~ aInteger0(smndt0(xp)),
    inference(splitLeft,[status(thm)],[c_117161]) ).

tff(c_117262,plain,
    ~ aInteger0(xp),
    inference(resolution,[status(thm)],[c_8,c_117259]) ).

tff(c_117266,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_452,c_117262]) ).

tff(c_117481,plain,
    ! [W2_1758] :
      ( ( sdtpldt0(sz10,sdtpldt0(smndt0(xp),W2_1758)) = sdtpldt0(sz10,W2_1758) )
      | ~ aInteger0(W2_1758) ),
    inference(splitRight,[status(thm)],[c_117161]) ).

tff(c_117500,plain,
    ( ( sdtpldt0(sz10,xp) = sdtpldt0(sz10,'#skF_33') )
    | ~ aInteger0(xp)
    | ~ aInteger0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_113142,c_117481]) ).

tff(c_117515,plain,
    smndt0(sz10) = sz10,
    inference(demodulation,[status(thm),theory(equality)],[c_452,c_452,c_108303,c_113314,c_117500]) ).

tff(c_117517,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_108319,c_117515]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : NUM453+6 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15  % 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
% 0.16/0.36  % Computer : n031.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 15:04:14 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 32.54/18.03  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.54/18.04  
% 32.54/18.04  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.61/18.07  
% 32.61/18.07  Inference rules
% 32.61/18.07  ----------------------
% 32.61/18.07  #Ref     : 0
% 32.61/18.07  #Sup     : 24090
% 32.61/18.07  #Fact    : 0
% 32.61/18.07  #Define  : 0
% 32.61/18.07  #Split   : 100
% 32.61/18.07  #Chain   : 0
% 32.61/18.07  #Close   : 0
% 32.61/18.07  
% 32.61/18.07  Ordering : KBO
% 32.61/18.07  
% 32.61/18.07  Simplification rules
% 32.61/18.07  ----------------------
% 32.61/18.07  #Subsume      : 2068
% 32.61/18.07  #Demod        : 31819
% 32.61/18.07  #Tautology    : 10268
% 32.61/18.07  #SimpNegUnit  : 733
% 32.61/18.07  #BackRed      : 1083
% 32.61/18.07  
% 32.61/18.07  #Partial instantiations: 0
% 32.61/18.07  #Strategies tried      : 1
% 32.61/18.07  
% 32.61/18.07  Timing (in seconds)
% 32.61/18.07  ----------------------
% 32.61/18.08  Preprocessing        : 0.84
% 32.61/18.08  Parsing              : 0.40
% 32.61/18.08  CNF conversion       : 0.09
% 32.61/18.08  Main loop            : 16.07
% 32.61/18.08  Inferencing          : 3.13
% 32.61/18.08  Reduction            : 7.58
% 32.61/18.08  Demodulation         : 6.34
% 32.61/18.08  BG Simplification    : 0.25
% 32.61/18.08  Subsumption          : 3.95
% 32.61/18.08  Abstraction          : 0.32
% 32.61/18.08  MUC search           : 0.00
% 32.61/18.08  Cooper               : 0.00
% 32.61/18.08  Total                : 16.98
% 32.61/18.08  Index Insertion      : 0.00
% 32.61/18.08  Index Deletion       : 0.00
% 32.61/18.08  Index Matching       : 0.00
% 32.61/18.08  BG Taut test         : 0.00
%------------------------------------------------------------------------------