TSTP Solution File: NUM448+5 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM448+5 : 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 : n007.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 10:51:42 EDT 2023

% Result   : Theorem 30.90s 15.97s
% Output   : CNFRefutation 31.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   58
% Syntax   : Number of formulae    :  202 (  74 unt;  53 typ;   0 def)
%            Number of atoms       :  325 (  70 equ)
%            Maximal formula atoms :   38 (   2 avg)
%            Number of connectives :  295 ( 119   ~; 111   |;  46   &)
%                                         (   4 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   80 (  45   >;  35   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   43 (  43 usr;   8 con; 0-3 aty)
%            Number of variables   :   57 (;  43   !;  14   ?;   0   :)

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

%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_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_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_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(sdtpldt0,type,
    sdtpldt0: ( $i * $i ) > $i ).

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

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

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

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

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

tff('#skF_27',type,
    '#skF_27': $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_20',type,
    '#skF_20': $i > $i ).

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

tff(f_591,negated_conjecture,
    ~ ( ! [W0] :
          ( aInteger0(W0)
         => ( ( ( ? [W1] :
                    ( aElementOf0(W1,xS)
                    & aElementOf0(W0,W1) )
                | aElementOf0(W0,sbsmnsldt0(xS)) )
             => ? [W1] :
                  ( aInteger0(W1)
                  & ( W1 != sz00 )
                  & ? [W2] :
                      ( aInteger0(W2)
                      & ( sdtasdt0(W1,W2) = W0 ) )
                  & aDivisorOf0(W1,W0)
                  & isPrime0(W1) ) )
            & ( ? [W1] :
                  ( ( ( aInteger0(W1)
                      & ( W1 != sz00 )
                      & ? [W2] :
                          ( aInteger0(W2)
                          & ( sdtasdt0(W1,W2) = W0 ) ) )
                    | aDivisorOf0(W1,W0) )
                  & isPrime0(W1) )
             => ( ? [W1] :
                    ( aElementOf0(W1,xS)
                    & aElementOf0(W0,W1) )
                & aElementOf0(W0,sbsmnsldt0(xS)) ) ) ) )
     => ( ( 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/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_513,hypothesis,
    ( aSet0(xS)
    & ! [W0] :
        ( ( aElementOf0(W0,xS)
         => ? [W1] :
              ( aInteger0(W1)
              & ( W1 != sz00 )
              & isPrime0(W1)
              & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1))
              & ! [W2] :
                  ( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
                   => ( aInteger0(W2)
                      & ? [W3] :
                          ( aInteger0(W3)
                          & ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00)) ) )
                      & aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
                      & sdteqdtlpzmzozddtrp0(W2,sz00,W1) ) )
                  & ( ( aInteger0(W2)
                      & ( ? [W3] :
                            ( aInteger0(W3)
                            & ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00)) ) )
                        | aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
                        | sdteqdtlpzmzozddtrp0(W2,sz00,W1) ) )
                   => aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) ) )
              & ( szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0 ) ) )
        & ( ? [W1] :
              ( aInteger0(W1)
              & ( W1 != sz00 )
              & isPrime0(W1)
              & ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,W1))
                  & ! [W2] :
                      ( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1))
                       => ( aInteger0(W2)
                          & ? [W3] :
                              ( aInteger0(W3)
                              & ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00)) ) )
                          & aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
                          & sdteqdtlpzmzozddtrp0(W2,sz00,W1) ) )
                      & ( ( aInteger0(W2)
                          & ( ? [W3] :
                                ( aInteger0(W3)
                                & ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(sz00)) ) )
                            | aDivisorOf0(W1,sdtpldt0(W2,smndt0(sz00)))
                            | sdteqdtlpzmzozddtrp0(W2,sz00,W1) ) )
                       => aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sz00,W1)) ) ) )
               => ( szAzrzSzezqlpdtcmdtrp0(sz00,W1) = W0 ) ) )
         => aElementOf0(W0,xS) ) )
    & ( xS = cS2043 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2046) ).

tff(f_233,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( ? [W1] :
            ( aDivisorOf0(W1,W0)
            & isPrime0(W1) )
      <=> ( ( W0 != sz10 )
          & ( W0 != smndt0(sz10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimeDivisor) ).

tff(f_31,axiom,
    aInteger0(sz10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).

tff(f_35,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => aInteger0(smndt0(W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).

tff(c_338,plain,
    ( ( smndt0(sz10) = '#skF_28' )
    | ( sz10 = '#skF_28' )
    | ( sz10 != '#skF_29' ) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_451,plain,
    sz10 != '#skF_29',
    inference(splitLeft,[status(thm)],[c_338]) ).

tff(c_334,plain,
    ( ( smndt0(sz10) = '#skF_28' )
    | ( sz10 = '#skF_28' )
    | ( smndt0(sz10) != '#skF_29' ) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_498,plain,
    smndt0(sz10) != '#skF_29',
    inference(splitLeft,[status(thm)],[c_334]) ).

tff(c_272,plain,
    xS = cS2043,
    inference(cnfTransformation,[status(thm)],[f_513]) ).

tff(c_342,plain,
    ( ( smndt0(sz10) = '#skF_28' )
    | ( sz10 = '#skF_28' )
    | aElementOf0('#skF_29',stldt0(sbsmnsldt0(xS))) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_400,plain,
    ( ( smndt0(sz10) = '#skF_28' )
    | ( sz10 = '#skF_28' )
    | aElementOf0('#skF_29',stldt0(sbsmnsldt0(cS2043))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_342]) ).

tff(c_1705,plain,
    aElementOf0('#skF_29',stldt0(sbsmnsldt0(cS2043))),
    inference(splitLeft,[status(thm)],[c_400]) ).

tff(c_346,plain,
    ! [W0_239] :
      ( aInteger0(W0_239)
      | ~ aElementOf0(W0_239,stldt0(sbsmnsldt0(xS))) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_396,plain,
    ! [W0_239] :
      ( aInteger0(W0_239)
      | ~ aElementOf0(W0_239,stldt0(sbsmnsldt0(cS2043))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_346]) ).

tff(c_1717,plain,
    aInteger0('#skF_29'),
    inference(resolution,[status(thm)],[c_1705,c_396]) ).

tff(c_74,plain,
    ! [W0_54] :
      ( isPrime0('#skF_2'(W0_54))
      | ( smndt0(sz10) = W0_54 )
      | ( sz10 = W0_54 )
      | ~ aInteger0(W0_54) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_3592,plain,
    ! [W0_351] :
      ( aDivisorOf0('#skF_2'(W0_351),W0_351)
      | ( smndt0(sz10) = W0_351 )
      | ( sz10 = W0_351 )
      | ~ aInteger0(W0_351) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_354,plain,
    ! [W1_232,W0_221] :
      ( ~ aDivisorOf0(W1_232,W0_221)
      | aElementOf0(W0_221,sbsmnsldt0(xS))
      | ~ isPrime0(W1_232)
      | ~ aInteger0(W0_221) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_404,plain,
    ! [W1_232,W0_221] :
      ( ~ aDivisorOf0(W1_232,W0_221)
      | aElementOf0(W0_221,sbsmnsldt0(cS2043))
      | ~ isPrime0(W1_232)
      | ~ aInteger0(W0_221) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_354]) ).

tff(c_58961,plain,
    ! [W0_641] :
      ( aElementOf0(W0_641,sbsmnsldt0(cS2043))
      | ~ isPrime0('#skF_2'(W0_641))
      | ( smndt0(sz10) = W0_641 )
      | ( sz10 = W0_641 )
      | ~ aInteger0(W0_641) ),
    inference(resolution,[status(thm)],[c_3592,c_404]) ).

tff(c_344,plain,
    ! [W0_239] :
      ( ~ aElementOf0(W0_239,sbsmnsldt0(xS))
      | ~ aElementOf0(W0_239,stldt0(sbsmnsldt0(xS))) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_408,plain,
    ! [W0_239] :
      ( ~ aElementOf0(W0_239,sbsmnsldt0(cS2043))
      | ~ aElementOf0(W0_239,stldt0(sbsmnsldt0(cS2043))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_272,c_344]) ).

tff(c_1715,plain,
    ~ aElementOf0('#skF_29',sbsmnsldt0(cS2043)),
    inference(resolution,[status(thm)],[c_1705,c_408]) ).

tff(c_59003,plain,
    ( ~ isPrime0('#skF_2'('#skF_29'))
    | ( smndt0(sz10) = '#skF_29' )
    | ( sz10 = '#skF_29' )
    | ~ aInteger0('#skF_29') ),
    inference(resolution,[status(thm)],[c_58961,c_1715]) ).

tff(c_59054,plain,
    ( ~ isPrime0('#skF_2'('#skF_29'))
    | ( smndt0(sz10) = '#skF_29' )
    | ( sz10 = '#skF_29' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1717,c_59003]) ).

tff(c_59055,plain,
    ~ isPrime0('#skF_2'('#skF_29')),
    inference(negUnitSimplification,[status(thm)],[c_451,c_498,c_59054]) ).

tff(c_59066,plain,
    ( ( smndt0(sz10) = '#skF_29' )
    | ( sz10 = '#skF_29' )
    | ~ aInteger0('#skF_29') ),
    inference(resolution,[status(thm)],[c_74,c_59055]) ).

tff(c_59069,plain,
    ( ( smndt0(sz10) = '#skF_29' )
    | ( sz10 = '#skF_29' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1717,c_59066]) ).

tff(c_59071,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_451,c_498,c_59069]) ).

tff(c_59073,plain,
    ~ aElementOf0('#skF_29',stldt0(sbsmnsldt0(cS2043))),
    inference(splitRight,[status(thm)],[c_400]) ).

tff(c_59072,plain,
    ( ( sz10 = '#skF_28' )
    | ( smndt0(sz10) = '#skF_28' ) ),
    inference(splitRight,[status(thm)],[c_400]) ).

tff(c_59074,plain,
    smndt0(sz10) = '#skF_28',
    inference(splitLeft,[status(thm)],[c_59072]) ).

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

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

tff(c_78,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,smndt0(sz10))
      | ~ aInteger0(smndt0(sz10)) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_1181,plain,
    ~ aInteger0(smndt0(sz10)),
    inference(splitLeft,[status(thm)],[c_78]) ).

tff(c_1184,plain,
    ~ aInteger0(sz10),
    inference(resolution,[status(thm)],[c_8,c_1181]) ).

tff(c_1188,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_1184]) ).

tff(c_1190,plain,
    aInteger0(smndt0(sz10)),
    inference(splitRight,[status(thm)],[c_78]) ).

tff(c_59082,plain,
    aInteger0('#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_59074,c_1190]) ).

tff(c_324,plain,
    ! [W0_239] :
      ( aElementOf0(W0_239,stldt0(sbsmnsldt0(xS)))
      | aElementOf0(W0_239,sbsmnsldt0(xS))
      | ~ aInteger0(W0_239) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_60065,plain,
    ! [W0_664] :
      ( aElementOf0(W0_664,stldt0(sbsmnsldt0(cS2043)))
      | aElementOf0(W0_664,sbsmnsldt0(cS2043))
      | ~ aInteger0(W0_664) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_272,c_324]) ).

tff(c_340,plain,
    ( ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(xS)))
    | aElementOf0('#skF_29',stldt0(sbsmnsldt0(xS))) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_410,plain,
    ( ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(cS2043)))
    | aElementOf0('#skF_29',stldt0(sbsmnsldt0(cS2043))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_272,c_340]) ).

tff(c_59189,plain,
    ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(cS2043))),
    inference(splitLeft,[status(thm)],[c_410]) ).

tff(c_60080,plain,
    ( aElementOf0('#skF_28',sbsmnsldt0(cS2043))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_60065,c_59189]) ).

tff(c_60097,plain,
    aElementOf0('#skF_28',sbsmnsldt0(cS2043)),
    inference(demodulation,[status(thm),theory(equality)],[c_59082,c_60080]) ).

tff(c_366,plain,
    ! [W0_221] :
      ( ~ aElementOf0(W0_221,sbsmnsldt0(xS))
      | isPrime0('#skF_24'(W0_221))
      | ~ aInteger0(W0_221) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_438,plain,
    ! [W0_221] :
      ( ~ aElementOf0(W0_221,sbsmnsldt0(cS2043))
      | isPrime0('#skF_24'(W0_221))
      | ~ aInteger0(W0_221) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_366]) ).

tff(c_60114,plain,
    ( isPrime0('#skF_24'('#skF_28'))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_60097,c_438]) ).

tff(c_60146,plain,
    isPrime0('#skF_24'('#skF_28')),
    inference(demodulation,[status(thm),theory(equality)],[c_59082,c_60114]) ).

tff(c_370,plain,
    ! [W0_221] :
      ( ~ aElementOf0(W0_221,sbsmnsldt0(xS))
      | aDivisorOf0('#skF_24'(W0_221),W0_221)
      | ~ aInteger0(W0_221) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_406,plain,
    ! [W0_221] :
      ( ~ aElementOf0(W0_221,sbsmnsldt0(cS2043))
      | aDivisorOf0('#skF_24'(W0_221),W0_221)
      | ~ aInteger0(W0_221) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_370]) ).

tff(c_60108,plain,
    ( aDivisorOf0('#skF_24'('#skF_28'),'#skF_28')
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_60097,c_406]) ).

tff(c_60140,plain,
    aDivisorOf0('#skF_24'('#skF_28'),'#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_59082,c_60108]) ).

tff(c_1189,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,smndt0(sz10)) ),
    inference(splitRight,[status(thm)],[c_78]) ).

tff(c_59079,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,'#skF_28') ),
    inference(demodulation,[status(thm),theory(equality)],[c_59074,c_1189]) ).

tff(c_60228,plain,
    ~ isPrime0('#skF_24'('#skF_28')),
    inference(resolution,[status(thm)],[c_60140,c_59079]) ).

tff(c_60243,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_60146,c_60228]) ).

tff(c_60244,plain,
    aElementOf0('#skF_29',stldt0(sbsmnsldt0(cS2043))),
    inference(splitRight,[status(thm)],[c_410]) ).

tff(c_60499,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_60244,c_59073]) ).

tff(c_60500,plain,
    sz10 = '#skF_28',
    inference(splitRight,[status(thm)],[c_59072]) ).

tff(c_60526,plain,
    aInteger0('#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_60500,c_6]) ).

tff(c_60913,plain,
    ! [W0_682] :
      ( aElementOf0(W0_682,stldt0(sbsmnsldt0(cS2043)))
      | aElementOf0(W0_682,sbsmnsldt0(cS2043))
      | ~ aInteger0(W0_682) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_272,c_324]) ).

tff(c_60547,plain,
    ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(cS2043))),
    inference(splitLeft,[status(thm)],[c_410]) ).

tff(c_60923,plain,
    ( aElementOf0('#skF_28',sbsmnsldt0(cS2043))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_60913,c_60547]) ).

tff(c_60938,plain,
    aElementOf0('#skF_28',sbsmnsldt0(cS2043)),
    inference(demodulation,[status(thm),theory(equality)],[c_60526,c_60923]) ).

tff(c_60953,plain,
    ( isPrime0('#skF_24'('#skF_28'))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_60938,c_438]) ).

tff(c_60982,plain,
    isPrime0('#skF_24'('#skF_28')),
    inference(demodulation,[status(thm),theory(equality)],[c_60526,c_60953]) ).

tff(c_60947,plain,
    ( aDivisorOf0('#skF_24'('#skF_28'),'#skF_28')
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_60938,c_406]) ).

tff(c_60976,plain,
    aDivisorOf0('#skF_24'('#skF_28'),'#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_60526,c_60947]) ).

tff(c_80,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,sz10)
      | ~ aInteger0(sz10) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_444,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,sz10) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_80]) ).

tff(c_60525,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,'#skF_28') ),
    inference(demodulation,[status(thm),theory(equality)],[c_60500,c_444]) ).

tff(c_61115,plain,
    ~ isPrime0('#skF_24'('#skF_28')),
    inference(resolution,[status(thm)],[c_60976,c_60525]) ).

tff(c_61124,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_60982,c_61115]) ).

tff(c_61125,plain,
    aElementOf0('#skF_29',stldt0(sbsmnsldt0(cS2043))),
    inference(splitRight,[status(thm)],[c_410]) ).

tff(c_61242,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_59073,c_61125]) ).

tff(c_61244,plain,
    smndt0(sz10) = '#skF_29',
    inference(splitRight,[status(thm)],[c_334]) ).

tff(c_61243,plain,
    ( ( sz10 = '#skF_28' )
    | ( smndt0(sz10) = '#skF_28' ) ),
    inference(splitRight,[status(thm)],[c_334]) ).

tff(c_61254,plain,
    ( ( sz10 = '#skF_28' )
    | ( '#skF_29' = '#skF_28' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_61244,c_61243]) ).

tff(c_61255,plain,
    '#skF_29' = '#skF_28',
    inference(splitLeft,[status(thm)],[c_61254]) ).

tff(c_61248,plain,
    ( aInteger0('#skF_29')
    | ~ aInteger0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_61244,c_8]) ).

tff(c_61252,plain,
    aInteger0('#skF_29'),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_61248]) ).

tff(c_61262,plain,
    aInteger0('#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_61255,c_61252]) ).

tff(c_62929,plain,
    ! [W0_749] :
      ( aElementOf0(W0_749,stldt0(sbsmnsldt0(cS2043)))
      | aElementOf0(W0_749,sbsmnsldt0(cS2043))
      | ~ aInteger0(W0_749) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_272,c_324]) ).

tff(c_61256,plain,
    smndt0(sz10) = '#skF_28',
    inference(demodulation,[status(thm),theory(equality)],[c_61255,c_61244]) ).

tff(c_332,plain,
    ( ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(xS)))
    | ( smndt0(sz10) != '#skF_29' ) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_414,plain,
    ( ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(cS2043)))
    | ( smndt0(sz10) != '#skF_29' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_332]) ).

tff(c_61594,plain,
    ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(cS2043))),
    inference(demodulation,[status(thm),theory(equality)],[c_61256,c_61255,c_414]) ).

tff(c_62938,plain,
    ( aElementOf0('#skF_28',sbsmnsldt0(cS2043))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_62929,c_61594]) ).

tff(c_62946,plain,
    aElementOf0('#skF_28',sbsmnsldt0(cS2043)),
    inference(demodulation,[status(thm),theory(equality)],[c_61262,c_62938]) ).

tff(c_62961,plain,
    ( isPrime0('#skF_24'('#skF_28'))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_62946,c_438]) ).

tff(c_62982,plain,
    isPrime0('#skF_24'('#skF_28')),
    inference(demodulation,[status(thm),theory(equality)],[c_61262,c_62961]) ).

tff(c_62949,plain,
    ( aDivisorOf0('#skF_24'('#skF_28'),'#skF_28')
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_62946,c_406]) ).

tff(c_62972,plain,
    aDivisorOf0('#skF_24'('#skF_28'),'#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_61262,c_62949]) ).

tff(c_62532,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,'#skF_28') ),
    inference(demodulation,[status(thm),theory(equality)],[c_61262,c_61256,c_61256,c_78]) ).

tff(c_63092,plain,
    ~ isPrime0('#skF_24'('#skF_28')),
    inference(resolution,[status(thm)],[c_62972,c_62532]) ).

tff(c_63101,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_62982,c_63092]) ).

tff(c_63102,plain,
    sz10 = '#skF_28',
    inference(splitRight,[status(thm)],[c_61254]) ).

tff(c_63109,plain,
    aInteger0('#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_63102,c_6]) ).

tff(c_67175,plain,
    ! [W0_871] :
      ( aElementOf0(W0_871,stldt0(sbsmnsldt0(cS2043)))
      | aElementOf0(W0_871,sbsmnsldt0(cS2043))
      | ~ aInteger0(W0_871) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_272,c_324]) ).

tff(c_63105,plain,
    smndt0('#skF_28') = '#skF_29',
    inference(demodulation,[status(thm),theory(equality)],[c_63102,c_61244]) ).

tff(c_63463,plain,
    ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(cS2043))),
    inference(demodulation,[status(thm),theory(equality)],[c_63105,c_63102,c_414]) ).

tff(c_67195,plain,
    ( aElementOf0('#skF_28',sbsmnsldt0(cS2043))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_67175,c_63463]) ).

tff(c_67208,plain,
    aElementOf0('#skF_28',sbsmnsldt0(cS2043)),
    inference(demodulation,[status(thm),theory(equality)],[c_63109,c_67195]) ).

tff(c_67222,plain,
    ( isPrime0('#skF_24'('#skF_28'))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_67208,c_438]) ).

tff(c_67257,plain,
    isPrime0('#skF_24'('#skF_28')),
    inference(demodulation,[status(thm),theory(equality)],[c_63109,c_67222]) ).

tff(c_67219,plain,
    ( aDivisorOf0('#skF_24'('#skF_28'),'#skF_28')
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_67208,c_406]) ).

tff(c_67254,plain,
    aDivisorOf0('#skF_24'('#skF_28'),'#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_63109,c_67219]) ).

tff(c_63108,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,'#skF_28') ),
    inference(demodulation,[status(thm),theory(equality)],[c_63102,c_444]) ).

tff(c_67427,plain,
    ~ isPrime0('#skF_24'('#skF_28')),
    inference(resolution,[status(thm)],[c_67254,c_63108]) ).

tff(c_67442,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_67257,c_67427]) ).

tff(c_67444,plain,
    sz10 = '#skF_29',
    inference(splitRight,[status(thm)],[c_338]) ).

tff(c_67446,plain,
    aInteger0('#skF_29'),
    inference(demodulation,[status(thm),theory(equality)],[c_67444,c_6]) ).

tff(c_67443,plain,
    ( ( sz10 = '#skF_28' )
    | ( smndt0(sz10) = '#skF_28' ) ),
    inference(splitRight,[status(thm)],[c_338]) ).

tff(c_67453,plain,
    ( ( '#skF_29' = '#skF_28' )
    | ( smndt0('#skF_29') = '#skF_28' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_67444,c_67444,c_67443]) ).

tff(c_67454,plain,
    smndt0('#skF_29') = '#skF_28',
    inference(splitLeft,[status(thm)],[c_67453]) ).

tff(c_67459,plain,
    ( aInteger0('#skF_28')
    | ~ aInteger0('#skF_29') ),
    inference(superposition,[status(thm),theory(equality)],[c_67454,c_8]) ).

tff(c_67463,plain,
    aInteger0('#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_67446,c_67459]) ).

tff(c_70164,plain,
    ! [W0_973] :
      ( aElementOf0(W0_973,stldt0(sbsmnsldt0(cS2043)))
      | aElementOf0(W0_973,sbsmnsldt0(cS2043))
      | ~ aInteger0(W0_973) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_272,c_324]) ).

tff(c_336,plain,
    ( ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(xS)))
    | ( sz10 != '#skF_29' ) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_439,plain,
    ( ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(cS2043)))
    | ( sz10 != '#skF_29' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_336]) ).

tff(c_67701,plain,
    ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(cS2043))),
    inference(demodulation,[status(thm),theory(equality)],[c_67444,c_439]) ).

tff(c_70183,plain,
    ( aElementOf0('#skF_28',sbsmnsldt0(cS2043))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_70164,c_67701]) ).

tff(c_70192,plain,
    aElementOf0('#skF_28',sbsmnsldt0(cS2043)),
    inference(demodulation,[status(thm),theory(equality)],[c_67463,c_70183]) ).

tff(c_70201,plain,
    ( isPrime0('#skF_24'('#skF_28'))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_70192,c_438]) ).

tff(c_70230,plain,
    isPrime0('#skF_24'('#skF_28')),
    inference(demodulation,[status(thm),theory(equality)],[c_67463,c_70201]) ).

tff(c_70198,plain,
    ( aDivisorOf0('#skF_24'('#skF_28'),'#skF_28')
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_70192,c_406]) ).

tff(c_70227,plain,
    aDivisorOf0('#skF_24'('#skF_28'),'#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_67463,c_70198]) ).

tff(c_68986,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,'#skF_28') ),
    inference(demodulation,[status(thm),theory(equality)],[c_67463,c_67454,c_67444,c_67454,c_67444,c_78]) ).

tff(c_70407,plain,
    ~ isPrime0('#skF_24'('#skF_28')),
    inference(resolution,[status(thm)],[c_70227,c_68986]) ).

tff(c_70422,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_70230,c_70407]) ).

tff(c_70423,plain,
    '#skF_29' = '#skF_28',
    inference(splitRight,[status(thm)],[c_67453]) ).

tff(c_70426,plain,
    aInteger0('#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_70423,c_67446]) ).

tff(c_74199,plain,
    ! [W0_1100] :
      ( aElementOf0(W0_1100,stldt0(sbsmnsldt0(cS2043)))
      | aElementOf0(W0_1100,sbsmnsldt0(cS2043))
      | ~ aInteger0(W0_1100) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_272,c_324]) ).

tff(c_70427,plain,
    sz10 = '#skF_28',
    inference(demodulation,[status(thm),theory(equality)],[c_70423,c_67444]) ).

tff(c_70573,plain,
    ~ aElementOf0('#skF_28',stldt0(sbsmnsldt0(cS2043))),
    inference(demodulation,[status(thm),theory(equality)],[c_70427,c_70423,c_439]) ).

tff(c_74222,plain,
    ( aElementOf0('#skF_28',sbsmnsldt0(cS2043))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_74199,c_70573]) ).

tff(c_74233,plain,
    aElementOf0('#skF_28',sbsmnsldt0(cS2043)),
    inference(demodulation,[status(thm),theory(equality)],[c_70426,c_74222]) ).

tff(c_74249,plain,
    ( isPrime0('#skF_24'('#skF_28'))
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_74233,c_438]) ).

tff(c_74284,plain,
    isPrime0('#skF_24'('#skF_28')),
    inference(demodulation,[status(thm),theory(equality)],[c_70426,c_74249]) ).

tff(c_74243,plain,
    ( aDivisorOf0('#skF_24'('#skF_28'),'#skF_28')
    | ~ aInteger0('#skF_28') ),
    inference(resolution,[status(thm)],[c_74233,c_406]) ).

tff(c_74278,plain,
    aDivisorOf0('#skF_24'('#skF_28'),'#skF_28'),
    inference(demodulation,[status(thm),theory(equality)],[c_70426,c_74243]) ).

tff(c_67445,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,'#skF_29') ),
    inference(demodulation,[status(thm),theory(equality)],[c_67444,c_444]) ).

tff(c_70439,plain,
    ! [W1_57] :
      ( ~ isPrime0(W1_57)
      | ~ aDivisorOf0(W1_57,'#skF_28') ),
    inference(demodulation,[status(thm),theory(equality)],[c_70423,c_67445]) ).

tff(c_74419,plain,
    ~ isPrime0('#skF_24'('#skF_28')),
    inference(resolution,[status(thm)],[c_74278,c_70439]) ).

tff(c_74434,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_74284,c_74419]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUM448+5 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15  % 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
% 0.14/0.36  % Computer : n007.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 14:25:24 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 30.90/15.97  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.90/15.99  
% 30.90/15.99  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 31.22/16.03  
% 31.22/16.03  Inference rules
% 31.22/16.03  ----------------------
% 31.22/16.03  #Ref     : 0
% 31.22/16.03  #Sup     : 15091
% 31.22/16.03  #Fact    : 0
% 31.22/16.03  #Define  : 0
% 31.22/16.03  #Split   : 82
% 31.22/16.03  #Chain   : 0
% 31.22/16.03  #Close   : 0
% 31.22/16.03  
% 31.22/16.03  Ordering : KBO
% 31.22/16.03  
% 31.22/16.03  Simplification rules
% 31.22/16.03  ----------------------
% 31.22/16.03  #Subsume      : 2081
% 31.22/16.03  #Demod        : 36211
% 31.22/16.03  #Tautology    : 6544
% 31.22/16.03  #SimpNegUnit  : 911
% 31.22/16.03  #BackRed      : 477
% 31.22/16.03  
% 31.22/16.03  #Partial instantiations: 0
% 31.22/16.03  #Strategies tried      : 1
% 31.22/16.03  
% 31.22/16.03  Timing (in seconds)
% 31.22/16.03  ----------------------
% 31.22/16.04  Preprocessing        : 0.78
% 31.22/16.04  Parsing              : 0.36
% 31.22/16.04  CNF conversion       : 0.08
% 31.22/16.04  Main loop            : 14.15
% 31.22/16.04  Inferencing          : 1.95
% 31.22/16.04  Reduction            : 8.45
% 31.22/16.04  Demodulation         : 7.55
% 31.22/16.04  BG Simplification    : 0.18
% 31.22/16.04  Subsumption          : 2.97
% 31.22/16.04  Abstraction          : 0.24
% 31.22/16.04  MUC search           : 0.00
% 31.22/16.04  Cooper               : 0.00
% 31.22/16.04  Total                : 15.01
% 31.22/16.04  Index Insertion      : 0.00
% 31.22/16.04  Index Deletion       : 0.00
% 31.22/16.04  Index Matching       : 0.00
% 31.22/16.04  BG Taut test         : 0.00
%------------------------------------------------------------------------------