TSTP Solution File: NUM447+5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM447+5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n029.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 May 21 01:14:00 EDT 2024

% Result   : Theorem 6.44s 1.31s
% Output   : CNFRefutation 6.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  115 (  14 unt;   0 def)
%            Number of atoms       :  750 ( 150 equ)
%            Maximal formula atoms :  125 (   6 avg)
%            Number of connectives :  982 ( 347   ~; 406   |; 187   &)
%                                         (   8 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   47 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-3 aty)
%            Number of variables   :  198 (   0 sgn  76   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mAddZero,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).

fof(mAddNeg,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtpldt0(X1,smndt0(X1)) = sz00
        & sz00 = sdtpldt0(smndt0(X1),X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).

fof(mArSeq,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & X2 != sz00 )
     => ! [X3] :
          ( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aInteger0(X4)
                  & sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).

fof(m__2046,hypothesis,
    ( aSet0(xS)
    & ! [X1] :
        ( ( aElementOf0(X1,xS)
         => ? [X2] :
              ( aInteger0(X2)
              & X2 != sz00
              & isPrime0(X2)
              & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
              & ! [X3] :
                  ( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
                   => ( aInteger0(X3)
                      & ? [X4] :
                          ( aInteger0(X4)
                          & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                      & aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                      & sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                  & ( ( aInteger0(X3)
                      & ( ? [X4] :
                            ( aInteger0(X4)
                            & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                        | aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                        | sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                   => aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) )
              & szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
        & ( ? [X2] :
              ( aInteger0(X2)
              & X2 != sz00
              & isPrime0(X2)
              & ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
                  & ! [X3] :
                      ( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
                       => ( aInteger0(X3)
                          & ? [X4] :
                              ( aInteger0(X4)
                              & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                          & aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                          & sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                      & ( ( aInteger0(X3)
                          & ( ? [X4] :
                                ( aInteger0(X4)
                                & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                            | aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                            | sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                       => aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) ) )
               => szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
         => aElementOf0(X1,xS) ) )
    & xS = cS2043 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2046) ).

fof(mIntZero,axiom,
    aInteger0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).

fof(mIntNeg,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => aInteger0(smndt0(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).

fof(m__,conjecture,
    ( ( ( ? [X1] :
            ( aElementOf0(X1,xS)
            & aElementOf0(xn,X1) )
        & aElementOf0(xn,sbsmnsldt0(xS)) )
     => ? [X1] :
          ( ( ( aInteger0(X1)
              & X1 != sz00
              & ? [X2] :
                  ( aInteger0(X2)
                  & sdtasdt0(X1,X2) = xn ) )
            | aDivisorOf0(X1,xn) )
          & isPrime0(X1) ) )
    & ( ? [X1] :
          ( aInteger0(X1)
          & X1 != sz00
          & ? [X2] :
              ( aInteger0(X2)
              & sdtasdt0(X1,X2) = xn )
          & aDivisorOf0(X1,xn)
          & isPrime0(X1) )
     => ( ? [X1] :
            ( aElementOf0(X1,xS)
            & aElementOf0(xn,X1) )
        | aElementOf0(xn,sbsmnsldt0(xS)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mDivisor,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ! [X2] :
          ( aDivisorOf0(X2,X1)
        <=> ( aInteger0(X2)
            & X2 != sz00
            & ? [X3] :
                ( aInteger0(X3)
                & sdtasdt0(X2,X3) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).

fof(mIntMult,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => aInteger0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).

fof(mMulAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3) )
     => sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).

fof(mEquMod,axiom,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3)
        & X3 != sz00 )
     => ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
      <=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).

fof(mMulMinOne,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
        & smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).

fof(mEquModSym,axiom,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3)
        & X3 != sz00 )
     => ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
       => sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).

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

fof(m__2106,hypothesis,
    aInteger0(xn),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2106) ).

fof(c_0_15,plain,
    ! [X78] :
      ( ( sdtpldt0(X78,sz00) = X78
        | ~ aInteger0(X78) )
      & ( X78 = sdtpldt0(sz00,X78)
        | ~ aInteger0(X78) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).

fof(c_0_16,plain,
    ! [X79] :
      ( ( sdtpldt0(X79,smndt0(X79)) = sz00
        | ~ aInteger0(X79) )
      & ( sz00 = sdtpldt0(smndt0(X79),X79)
        | ~ aInteger0(X79) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).

fof(c_0_17,plain,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & X2 != sz00 )
     => ! [X3] :
          ( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aInteger0(X4)
                  & sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[mArSeq]) ).

fof(c_0_18,hypothesis,
    ( aSet0(xS)
    & ! [X1] :
        ( ( aElementOf0(X1,xS)
         => ? [X2] :
              ( aInteger0(X2)
              & X2 != sz00
              & isPrime0(X2)
              & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
              & ! [X3] :
                  ( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
                   => ( aInteger0(X3)
                      & ? [X4] :
                          ( aInteger0(X4)
                          & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                      & aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                      & sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                  & ( ( aInteger0(X3)
                      & ( ? [X4] :
                            ( aInteger0(X4)
                            & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                        | aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                        | sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                   => aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) )
              & szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
        & ( ? [X2] :
              ( aInteger0(X2)
              & X2 != sz00
              & isPrime0(X2)
              & ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
                  & ! [X3] :
                      ( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
                       => ( aInteger0(X3)
                          & ? [X4] :
                              ( aInteger0(X4)
                              & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                          & aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                          & sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                      & ( ( aInteger0(X3)
                          & ( ? [X4] :
                                ( aInteger0(X4)
                                & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                            | aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                            | sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                       => aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) ) )
               => szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
         => aElementOf0(X1,xS) ) )
    & xS = cS2043 ),
    inference(fof_simplification,[status(thm)],[m__2046]) ).

cnf(c_0_19,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,plain,
    ( sz00 = sdtpldt0(smndt0(X1),X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    aInteger0(sz00),
    inference(split_conjunct,[status(thm)],[mIntZero]) ).

fof(c_0_22,plain,
    ! [X83] :
      ( ~ aInteger0(X83)
      | aInteger0(smndt0(X83)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).

fof(c_0_23,plain,
    ! [X30,X31,X32,X33,X34,X35] :
      ( ( aSet0(X32)
        | X32 != szAzrzSzezqlpdtcmdtrp0(X30,X31)
        | ~ aInteger0(X30)
        | ~ aInteger0(X31)
        | X31 = sz00 )
      & ( aInteger0(X33)
        | ~ aElementOf0(X33,X32)
        | X32 != szAzrzSzezqlpdtcmdtrp0(X30,X31)
        | ~ aInteger0(X30)
        | ~ aInteger0(X31)
        | X31 = sz00 )
      & ( sdteqdtlpzmzozddtrp0(X33,X30,X31)
        | ~ aElementOf0(X33,X32)
        | X32 != szAzrzSzezqlpdtcmdtrp0(X30,X31)
        | ~ aInteger0(X30)
        | ~ aInteger0(X31)
        | X31 = sz00 )
      & ( ~ aInteger0(X34)
        | ~ sdteqdtlpzmzozddtrp0(X34,X30,X31)
        | aElementOf0(X34,X32)
        | X32 != szAzrzSzezqlpdtcmdtrp0(X30,X31)
        | ~ aInteger0(X30)
        | ~ aInteger0(X31)
        | X31 = sz00 )
      & ( ~ aElementOf0(esk8_3(X30,X31,X35),X35)
        | ~ aInteger0(esk8_3(X30,X31,X35))
        | ~ sdteqdtlpzmzozddtrp0(esk8_3(X30,X31,X35),X30,X31)
        | ~ aSet0(X35)
        | X35 = szAzrzSzezqlpdtcmdtrp0(X30,X31)
        | ~ aInteger0(X30)
        | ~ aInteger0(X31)
        | X31 = sz00 )
      & ( aInteger0(esk8_3(X30,X31,X35))
        | aElementOf0(esk8_3(X30,X31,X35),X35)
        | ~ aSet0(X35)
        | X35 = szAzrzSzezqlpdtcmdtrp0(X30,X31)
        | ~ aInteger0(X30)
        | ~ aInteger0(X31)
        | X31 = sz00 )
      & ( sdteqdtlpzmzozddtrp0(esk8_3(X30,X31,X35),X30,X31)
        | aElementOf0(esk8_3(X30,X31,X35),X35)
        | ~ aSet0(X35)
        | X35 = szAzrzSzezqlpdtcmdtrp0(X30,X31)
        | ~ aInteger0(X30)
        | ~ aInteger0(X31)
        | X31 = sz00 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])])])]) ).

fof(c_0_24,hypothesis,
    ! [X5,X7,X9,X10,X11,X12,X13,X15,X16] :
      ( aSet0(xS)
      & ( aInteger0(esk1_1(X5))
        | ~ aElementOf0(X5,xS) )
      & ( esk1_1(X5) != sz00
        | ~ aElementOf0(X5,xS) )
      & ( isPrime0(esk1_1(X5))
        | ~ aElementOf0(X5,xS) )
      & ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X5)))
        | ~ aElementOf0(X5,xS) )
      & ( aInteger0(X7)
        | ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X5)))
        | ~ aElementOf0(X5,xS) )
      & ( aInteger0(esk2_2(X5,X7))
        | ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X5)))
        | ~ aElementOf0(X5,xS) )
      & ( sdtasdt0(esk1_1(X5),esk2_2(X5,X7)) = sdtpldt0(X7,smndt0(sz00))
        | ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X5)))
        | ~ aElementOf0(X5,xS) )
      & ( aDivisorOf0(esk1_1(X5),sdtpldt0(X7,smndt0(sz00)))
        | ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X5)))
        | ~ aElementOf0(X5,xS) )
      & ( sdteqdtlpzmzozddtrp0(X7,sz00,esk1_1(X5))
        | ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X5)))
        | ~ aElementOf0(X5,xS) )
      & ( ~ aInteger0(X10)
        | sdtasdt0(esk1_1(X5),X10) != sdtpldt0(X9,smndt0(sz00))
        | ~ aInteger0(X9)
        | aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X5)))
        | ~ aElementOf0(X5,xS) )
      & ( ~ aDivisorOf0(esk1_1(X5),sdtpldt0(X9,smndt0(sz00)))
        | ~ aInteger0(X9)
        | aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X5)))
        | ~ aElementOf0(X5,xS) )
      & ( ~ sdteqdtlpzmzozddtrp0(X9,sz00,esk1_1(X5))
        | ~ aInteger0(X9)
        | aElementOf0(X9,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X5)))
        | ~ aElementOf0(X5,xS) )
      & ( szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X5)) = X5
        | ~ aElementOf0(X5,xS) )
      & ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X12))
        | ~ aInteger0(X12)
        | X12 = sz00
        | ~ isPrime0(X12)
        | aElementOf0(X11,xS) )
      & ( aInteger0(X13)
        | ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(sz00,X12))
        | ~ aInteger0(X12)
        | X12 = sz00
        | ~ isPrime0(X12)
        | aElementOf0(X11,xS) )
      & ( aInteger0(esk3_3(X11,X12,X13))
        | ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(sz00,X12))
        | ~ aInteger0(X12)
        | X12 = sz00
        | ~ isPrime0(X12)
        | aElementOf0(X11,xS) )
      & ( sdtasdt0(X12,esk3_3(X11,X12,X13)) = sdtpldt0(X13,smndt0(sz00))
        | ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(sz00,X12))
        | ~ aInteger0(X12)
        | X12 = sz00
        | ~ isPrime0(X12)
        | aElementOf0(X11,xS) )
      & ( aDivisorOf0(X12,sdtpldt0(X13,smndt0(sz00)))
        | ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(sz00,X12))
        | ~ aInteger0(X12)
        | X12 = sz00
        | ~ isPrime0(X12)
        | aElementOf0(X11,xS) )
      & ( sdteqdtlpzmzozddtrp0(X13,sz00,X12)
        | ~ aElementOf0(X13,szAzrzSzezqlpdtcmdtrp0(sz00,X12))
        | ~ aInteger0(X12)
        | X12 = sz00
        | ~ isPrime0(X12)
        | aElementOf0(X11,xS) )
      & ( ~ aInteger0(X16)
        | sdtasdt0(X12,X16) != sdtpldt0(X15,smndt0(sz00))
        | ~ aInteger0(X15)
        | aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(sz00,X12))
        | ~ aInteger0(X12)
        | X12 = sz00
        | ~ isPrime0(X12)
        | aElementOf0(X11,xS) )
      & ( ~ aDivisorOf0(X12,sdtpldt0(X15,smndt0(sz00)))
        | ~ aInteger0(X15)
        | aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(sz00,X12))
        | ~ aInteger0(X12)
        | X12 = sz00
        | ~ isPrime0(X12)
        | aElementOf0(X11,xS) )
      & ( ~ sdteqdtlpzmzozddtrp0(X15,sz00,X12)
        | ~ aInteger0(X15)
        | aElementOf0(X15,szAzrzSzezqlpdtcmdtrp0(sz00,X12))
        | ~ aInteger0(X12)
        | X12 = sz00
        | ~ isPrime0(X12)
        | aElementOf0(X11,xS) )
      & ( szAzrzSzezqlpdtcmdtrp0(sz00,X12) != X11
        | ~ aInteger0(X12)
        | X12 = sz00
        | ~ isPrime0(X12)
        | aElementOf0(X11,xS) )
      & xS = cS2043 ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])])])]) ).

cnf(c_0_25,plain,
    ( smndt0(sz00) = sz00
    | ~ aInteger0(smndt0(sz00)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_26,plain,
    ( aInteger0(smndt0(X1))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,plain,
    ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
    | X3 = sz00
    | ~ aElementOf0(X1,X4)
    | X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

fof(c_0_28,negated_conjecture,
    ~ ( ( ( ? [X1] :
              ( aElementOf0(X1,xS)
              & aElementOf0(xn,X1) )
          & aElementOf0(xn,sbsmnsldt0(xS)) )
       => ? [X1] :
            ( ( ( aInteger0(X1)
                & X1 != sz00
                & ? [X2] :
                    ( aInteger0(X2)
                    & sdtasdt0(X1,X2) = xn ) )
              | aDivisorOf0(X1,xn) )
            & isPrime0(X1) ) )
      & ( ? [X1] :
            ( aInteger0(X1)
            & X1 != sz00
            & ? [X2] :
                ( aInteger0(X2)
                & sdtasdt0(X1,X2) = xn )
            & aDivisorOf0(X1,xn)
            & isPrime0(X1) )
       => ( ? [X1] :
              ( aElementOf0(X1,xS)
              & aElementOf0(xn,X1) )
          | aElementOf0(xn,sbsmnsldt0(xS)) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_29,hypothesis,
    ( aDivisorOf0(esk1_1(X1),sdtpldt0(X2,smndt0(sz00)))
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X1)))
    | ~ aElementOf0(X1,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_30,plain,
    smndt0(sz00) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_21])]) ).

cnf(c_0_31,plain,
    ( X1 = sz00
    | sdteqdtlpzmzozddtrp0(X2,X3,X1)
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
    | ~ aInteger0(X1)
    | ~ aInteger0(X3) ),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_32,hypothesis,
    ( szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X1)) = X1
    | ~ aElementOf0(X1,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,hypothesis,
    ( aInteger0(esk1_1(X1))
    | ~ aElementOf0(X1,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,hypothesis,
    ( esk1_1(X1) != sz00
    | ~ aElementOf0(X1,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_35,hypothesis,
    ( aInteger0(X1)
    | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X2)))
    | ~ aElementOf0(X2,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_36,negated_conjecture,
    ! [X18,X19,X22] :
      ( ( aInteger0(esk5_0)
        | aElementOf0(esk4_0,xS) )
      & ( esk5_0 != sz00
        | aElementOf0(esk4_0,xS) )
      & ( aInteger0(esk6_0)
        | aElementOf0(esk4_0,xS) )
      & ( sdtasdt0(esk5_0,esk6_0) = xn
        | aElementOf0(esk4_0,xS) )
      & ( aDivisorOf0(esk5_0,xn)
        | aElementOf0(esk4_0,xS) )
      & ( isPrime0(esk5_0)
        | aElementOf0(esk4_0,xS) )
      & ( ~ aElementOf0(X22,xS)
        | ~ aElementOf0(xn,X22)
        | aElementOf0(esk4_0,xS) )
      & ( ~ aElementOf0(xn,sbsmnsldt0(xS))
        | aElementOf0(esk4_0,xS) )
      & ( aInteger0(esk5_0)
        | aElementOf0(xn,esk4_0) )
      & ( esk5_0 != sz00
        | aElementOf0(xn,esk4_0) )
      & ( aInteger0(esk6_0)
        | aElementOf0(xn,esk4_0) )
      & ( sdtasdt0(esk5_0,esk6_0) = xn
        | aElementOf0(xn,esk4_0) )
      & ( aDivisorOf0(esk5_0,xn)
        | aElementOf0(xn,esk4_0) )
      & ( isPrime0(esk5_0)
        | aElementOf0(xn,esk4_0) )
      & ( ~ aElementOf0(X22,xS)
        | ~ aElementOf0(xn,X22)
        | aElementOf0(xn,esk4_0) )
      & ( ~ aElementOf0(xn,sbsmnsldt0(xS))
        | aElementOf0(xn,esk4_0) )
      & ( aInteger0(esk5_0)
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( esk5_0 != sz00
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( aInteger0(esk6_0)
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( sdtasdt0(esk5_0,esk6_0) = xn
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( aDivisorOf0(esk5_0,xn)
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( isPrime0(esk5_0)
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( ~ aElementOf0(X22,xS)
        | ~ aElementOf0(xn,X22)
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( ~ aElementOf0(xn,sbsmnsldt0(xS))
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( aInteger0(esk5_0)
        | ~ aInteger0(X18)
        | X18 = sz00
        | ~ aInteger0(X19)
        | sdtasdt0(X18,X19) != xn
        | ~ isPrime0(X18) )
      & ( esk5_0 != sz00
        | ~ aInteger0(X18)
        | X18 = sz00
        | ~ aInteger0(X19)
        | sdtasdt0(X18,X19) != xn
        | ~ isPrime0(X18) )
      & ( aInteger0(esk6_0)
        | ~ aInteger0(X18)
        | X18 = sz00
        | ~ aInteger0(X19)
        | sdtasdt0(X18,X19) != xn
        | ~ isPrime0(X18) )
      & ( sdtasdt0(esk5_0,esk6_0) = xn
        | ~ aInteger0(X18)
        | X18 = sz00
        | ~ aInteger0(X19)
        | sdtasdt0(X18,X19) != xn
        | ~ isPrime0(X18) )
      & ( aDivisorOf0(esk5_0,xn)
        | ~ aInteger0(X18)
        | X18 = sz00
        | ~ aInteger0(X19)
        | sdtasdt0(X18,X19) != xn
        | ~ isPrime0(X18) )
      & ( isPrime0(esk5_0)
        | ~ aInteger0(X18)
        | X18 = sz00
        | ~ aInteger0(X19)
        | sdtasdt0(X18,X19) != xn
        | ~ isPrime0(X18) )
      & ( ~ aElementOf0(X22,xS)
        | ~ aElementOf0(xn,X22)
        | ~ aInteger0(X18)
        | X18 = sz00
        | ~ aInteger0(X19)
        | sdtasdt0(X18,X19) != xn
        | ~ isPrime0(X18) )
      & ( ~ aElementOf0(xn,sbsmnsldt0(xS))
        | ~ aInteger0(X18)
        | X18 = sz00
        | ~ aInteger0(X19)
        | sdtasdt0(X18,X19) != xn
        | ~ isPrime0(X18) )
      & ( aInteger0(esk5_0)
        | ~ aDivisorOf0(X18,xn)
        | ~ isPrime0(X18) )
      & ( esk5_0 != sz00
        | ~ aDivisorOf0(X18,xn)
        | ~ isPrime0(X18) )
      & ( aInteger0(esk6_0)
        | ~ aDivisorOf0(X18,xn)
        | ~ isPrime0(X18) )
      & ( sdtasdt0(esk5_0,esk6_0) = xn
        | ~ aDivisorOf0(X18,xn)
        | ~ isPrime0(X18) )
      & ( aDivisorOf0(esk5_0,xn)
        | ~ aDivisorOf0(X18,xn)
        | ~ isPrime0(X18) )
      & ( isPrime0(esk5_0)
        | ~ aDivisorOf0(X18,xn)
        | ~ isPrime0(X18) )
      & ( ~ aElementOf0(X22,xS)
        | ~ aElementOf0(xn,X22)
        | ~ aDivisorOf0(X18,xn)
        | ~ isPrime0(X18) )
      & ( ~ aElementOf0(xn,sbsmnsldt0(xS))
        | ~ aDivisorOf0(X18,xn)
        | ~ isPrime0(X18) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])])]) ).

cnf(c_0_37,hypothesis,
    ( aDivisorOf0(esk1_1(X1),sdtpldt0(X2,sz00))
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X1)))
    | ~ aElementOf0(X1,xS) ),
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_38,hypothesis,
    ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X2)))
    | ~ sdteqdtlpzmzozddtrp0(X1,sz00,esk1_1(X2))
    | ~ aInteger0(X1)
    | ~ aElementOf0(X2,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_39,hypothesis,
    ( sdteqdtlpzmzozddtrp0(X1,sz00,esk1_1(X2))
    | ~ aElementOf0(X2,xS)
    | ~ aElementOf0(X1,X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_21])]),c_0_33]),c_0_34]) ).

cnf(c_0_40,hypothesis,
    ( aInteger0(X1)
    | ~ aElementOf0(X2,xS)
    | ~ aElementOf0(X1,X2) ),
    inference(spm,[status(thm)],[c_0_35,c_0_32]) ).

fof(c_0_41,plain,
    ! [X1] :
      ( aInteger0(X1)
     => ! [X2] :
          ( aDivisorOf0(X2,X1)
        <=> ( aInteger0(X2)
            & X2 != sz00
            & ? [X3] :
                ( aInteger0(X3)
                & sdtasdt0(X2,X3) = X1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mDivisor]) ).

cnf(c_0_42,negated_conjecture,
    ( ~ aElementOf0(xn,sbsmnsldt0(xS))
    | ~ aDivisorOf0(X1,xn)
    | ~ isPrime0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_43,negated_conjecture,
    ( aDivisorOf0(esk5_0,xn)
    | aElementOf0(xn,sbsmnsldt0(xS)) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_44,hypothesis,
    ( aDivisorOf0(esk1_1(X1),X2)
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X1)))
    | ~ aElementOf0(X1,xS) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_19]),c_0_35]) ).

cnf(c_0_45,hypothesis,
    ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk1_1(X2)))
    | ~ aElementOf0(X2,xS)
    | ~ aElementOf0(X1,X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).

fof(c_0_46,plain,
    ! [X63,X64,X66,X67] :
      ( ( aInteger0(X64)
        | ~ aDivisorOf0(X64,X63)
        | ~ aInteger0(X63) )
      & ( X64 != sz00
        | ~ aDivisorOf0(X64,X63)
        | ~ aInteger0(X63) )
      & ( aInteger0(esk11_2(X63,X64))
        | ~ aDivisorOf0(X64,X63)
        | ~ aInteger0(X63) )
      & ( sdtasdt0(X64,esk11_2(X63,X64)) = X63
        | ~ aDivisorOf0(X64,X63)
        | ~ aInteger0(X63) )
      & ( ~ aInteger0(X66)
        | X66 = sz00
        | ~ aInteger0(X67)
        | sdtasdt0(X66,X67) != X63
        | aDivisorOf0(X66,X63)
        | ~ aInteger0(X63) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])])])])]) ).

fof(c_0_47,plain,
    ! [X85,X86] :
      ( ~ aInteger0(X85)
      | ~ aInteger0(X86)
      | aInteger0(sdtasdt0(X85,X86)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])])]) ).

cnf(c_0_48,negated_conjecture,
    ( aDivisorOf0(esk5_0,xn)
    | ~ isPrime0(X1)
    | ~ aDivisorOf0(X1,xn) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_49,hypothesis,
    ( aDivisorOf0(esk1_1(X1),X2)
    | ~ aElementOf0(X1,xS)
    | ~ aElementOf0(X2,X1) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_50,hypothesis,
    ( isPrime0(esk1_1(X1))
    | ~ aElementOf0(X1,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_51,negated_conjecture,
    ( isPrime0(esk5_0)
    | ~ aDivisorOf0(X1,xn)
    | ~ isPrime0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_52,plain,
    ( X1 = sz00
    | aDivisorOf0(X1,X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | sdtasdt0(X1,X2) != X3
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_53,plain,
    ( aInteger0(sdtasdt0(X1,X2))
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_54,negated_conjecture,
    ( aInteger0(esk5_0)
    | ~ aDivisorOf0(X1,xn)
    | ~ isPrime0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_55,negated_conjecture,
    ( aDivisorOf0(esk5_0,xn)
    | ~ aElementOf0(X1,xS)
    | ~ aElementOf0(xn,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).

cnf(c_0_56,negated_conjecture,
    ( aElementOf0(esk4_0,xS)
    | esk5_0 != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_57,negated_conjecture,
    ( aDivisorOf0(esk5_0,xn)
    | aElementOf0(xn,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_58,negated_conjecture,
    ( isPrime0(esk5_0)
    | ~ aElementOf0(X1,xS)
    | ~ aElementOf0(xn,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_49]),c_0_50]) ).

cnf(c_0_59,negated_conjecture,
    ( isPrime0(esk5_0)
    | aElementOf0(xn,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_60,plain,
    ( X1 = sz00
    | aDivisorOf0(X1,sdtasdt0(X1,X2))
    | ~ aInteger0(X2)
    | ~ aInteger0(X1) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_52]),c_0_53]) ).

cnf(c_0_61,negated_conjecture,
    ( aInteger0(esk5_0)
    | ~ aElementOf0(X1,xS)
    | ~ aElementOf0(xn,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_49]),c_0_50]) ).

cnf(c_0_62,negated_conjecture,
    ( aInteger0(esk5_0)
    | aElementOf0(esk4_0,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_63,negated_conjecture,
    ( aInteger0(esk5_0)
    | aElementOf0(xn,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_64,negated_conjecture,
    ( esk5_0 != sz00
    | ~ aDivisorOf0(X1,xn)
    | ~ isPrime0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_65,negated_conjecture,
    ( aDivisorOf0(esk5_0,xn)
    | esk5_0 != sz00 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).

cnf(c_0_66,negated_conjecture,
    ( isPrime0(esk5_0)
    | esk5_0 != sz00 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_56]),c_0_59]) ).

fof(c_0_67,plain,
    ! [X87,X88,X89] :
      ( ~ aInteger0(X87)
      | ~ aInteger0(X88)
      | ~ aInteger0(X89)
      | sdtasdt0(X87,sdtasdt0(X88,X89)) = sdtasdt0(sdtasdt0(X87,X88),X89) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).

fof(c_0_68,plain,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3)
        & X3 != sz00 )
     => ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
      <=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
    inference(fof_simplification,[status(thm)],[mEquMod]) ).

cnf(c_0_69,plain,
    ( X1 = sz00
    | aDivisorOf0(X1,sdtasdt0(X1,sdtasdt0(X2,X3)))
    | ~ aInteger0(X1)
    | ~ aInteger0(X3)
    | ~ aInteger0(X2) ),
    inference(spm,[status(thm)],[c_0_60,c_0_53]) ).

cnf(c_0_70,negated_conjecture,
    aInteger0(esk5_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).

cnf(c_0_71,negated_conjecture,
    esk5_0 != sz00,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).

cnf(c_0_72,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_73,plain,
    ( sdtasdt0(X1,esk11_2(X2,X1)) = X2
    | ~ aDivisorOf0(X1,X2)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_74,plain,
    ( aInteger0(X1)
    | ~ aDivisorOf0(X1,X2)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_75,plain,
    ( aInteger0(esk11_2(X1,X2))
    | ~ aDivisorOf0(X2,X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

fof(c_0_76,plain,
    ! [X47,X48,X49] :
      ( ( ~ sdteqdtlpzmzozddtrp0(X47,X48,X49)
        | aDivisorOf0(X49,sdtpldt0(X47,smndt0(X48)))
        | ~ aInteger0(X47)
        | ~ aInteger0(X48)
        | ~ aInteger0(X49)
        | X49 = sz00 )
      & ( ~ aDivisorOf0(X49,sdtpldt0(X47,smndt0(X48)))
        | sdteqdtlpzmzozddtrp0(X47,X48,X49)
        | ~ aInteger0(X47)
        | ~ aInteger0(X48)
        | ~ aInteger0(X49)
        | X49 = sz00 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])])]) ).

cnf(c_0_77,negated_conjecture,
    ( aDivisorOf0(esk5_0,sdtasdt0(esk5_0,sdtasdt0(X1,X2)))
    | ~ aInteger0(X2)
    | ~ aInteger0(X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).

cnf(c_0_78,plain,
    ( sdtasdt0(X1,sdtasdt0(esk11_2(X2,X1),X3)) = sdtasdt0(X2,X3)
    | ~ aDivisorOf0(X1,X2)
    | ~ aInteger0(X3)
    | ~ aInteger0(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_75]) ).

fof(c_0_79,plain,
    ! [X84] :
      ( ( sdtasdt0(smndt0(sz10),X84) = smndt0(X84)
        | ~ aInteger0(X84) )
      & ( smndt0(X84) = sdtasdt0(X84,smndt0(sz10))
        | ~ aInteger0(X84) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])])]) ).

fof(c_0_80,plain,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3)
        & X3 != sz00 )
     => ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
       => sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
    inference(fof_simplification,[status(thm)],[mEquModSym]) ).

cnf(c_0_81,plain,
    ( sdteqdtlpzmzozddtrp0(X2,X3,X1)
    | X1 = sz00
    | ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
    | ~ aInteger0(X2)
    | ~ aInteger0(X3)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

cnf(c_0_82,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_83,negated_conjecture,
    ( aDivisorOf0(esk5_0,sdtasdt0(X1,X2))
    | ~ aDivisorOf0(esk5_0,X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_75]) ).

cnf(c_0_84,plain,
    ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_79]) ).

fof(c_0_85,plain,
    ! [X52,X53,X54] :
      ( ~ aInteger0(X52)
      | ~ aInteger0(X53)
      | ~ aInteger0(X54)
      | X54 = sz00
      | ~ sdteqdtlpzmzozddtrp0(X52,X53,X54)
      | sdteqdtlpzmzozddtrp0(X53,X52,X54) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])])]) ).

cnf(c_0_86,plain,
    ( X1 = sz00
    | sdteqdtlpzmzozddtrp0(sz00,X2,X1)
    | ~ aDivisorOf0(X1,smndt0(X2))
    | ~ aInteger0(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_21])]),c_0_74]),c_0_26]) ).

cnf(c_0_87,negated_conjecture,
    ( aDivisorOf0(esk5_0,smndt0(X1))
    | ~ aDivisorOf0(esk5_0,X1)
    | ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(X1) ),
    inference(spm,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_88,hypothesis,
    ( X1 = sz00
    | aElementOf0(X2,xS)
    | szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X2
    | ~ aInteger0(X1)
    | ~ isPrime0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_89,plain,
    ( aElementOf0(X1,X4)
    | X3 = sz00
    | ~ aInteger0(X1)
    | ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
    | X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_90,plain,
    ( X3 = sz00
    | sdteqdtlpzmzozddtrp0(X2,X1,X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3)
    | ~ sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_91,negated_conjecture,
    ( sdteqdtlpzmzozddtrp0(sz00,X1,esk5_0)
    | ~ aDivisorOf0(esk5_0,X1)
    | ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_71]) ).

cnf(c_0_92,hypothesis,
    ( X1 = sz00
    | aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X1),xS)
    | ~ isPrime0(X1)
    | ~ aInteger0(X1) ),
    inference(er,[status(thm)],[c_0_88]) ).

cnf(c_0_93,negated_conjecture,
    ( isPrime0(esk5_0)
    | aElementOf0(esk4_0,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_94,plain,
    ( X1 = sz00
    | aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
    | ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
    | ~ aInteger0(X1)
    | ~ aInteger0(X3)
    | ~ aInteger0(X2) ),
    inference(er,[status(thm)],[c_0_89]) ).

cnf(c_0_95,negated_conjecture,
    ( sdteqdtlpzmzozddtrp0(X1,sz00,esk5_0)
    | ~ aDivisorOf0(esk5_0,X1)
    | ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_70]),c_0_21])]),c_0_71]) ).

cnf(c_0_96,negated_conjecture,
    ( aElementOf0(xn,esk4_0)
    | esk5_0 != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_97,negated_conjecture,
    ( aElementOf0(esk4_0,xS)
    | ~ aElementOf0(X1,xS)
    | ~ aElementOf0(xn,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_98,negated_conjecture,
    ( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk5_0),xS)
    | aElementOf0(esk4_0,xS) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_62]),c_0_56]) ).

cnf(c_0_99,negated_conjecture,
    ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk5_0))
    | ~ aDivisorOf0(esk5_0,X1)
    | ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_70]),c_0_21])]),c_0_71]) ).

cnf(c_0_100,plain,
    aInteger0(sz10),
    inference(split_conjunct,[status(thm)],[mIntOne]) ).

cnf(c_0_101,negated_conjecture,
    ( aElementOf0(xn,esk4_0)
    | ~ aElementOf0(X1,xS)
    | ~ aElementOf0(xn,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_102,negated_conjecture,
    ( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk5_0),xS)
    | aElementOf0(xn,esk4_0) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_59]),c_0_63]),c_0_96]) ).

cnf(c_0_103,negated_conjecture,
    ( aElementOf0(esk4_0,xS)
    | ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk5_0)) ),
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_104,negated_conjecture,
    ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk5_0))
    | ~ aDivisorOf0(esk5_0,X1)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_26]),c_0_100])]) ).

cnf(c_0_105,hypothesis,
    aInteger0(xn),
    inference(split_conjunct,[status(thm)],[m__2106]) ).

cnf(c_0_106,negated_conjecture,
    ( aDivisorOf0(esk5_0,xn)
    | aElementOf0(esk4_0,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_107,negated_conjecture,
    ( aElementOf0(xn,esk4_0)
    | ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk5_0)) ),
    inference(spm,[status(thm)],[c_0_101,c_0_102]) ).

cnf(c_0_108,negated_conjecture,
    ( ~ aElementOf0(X1,xS)
    | ~ aElementOf0(xn,X1)
    | ~ aDivisorOf0(X2,xn)
    | ~ isPrime0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_109,negated_conjecture,
    aElementOf0(esk4_0,xS),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105])]),c_0_106]) ).

cnf(c_0_110,negated_conjecture,
    aElementOf0(xn,esk4_0),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_104]),c_0_105])]),c_0_57]) ).

cnf(c_0_111,negated_conjecture,
    ( ~ isPrime0(X1)
    | ~ aDivisorOf0(X1,xn) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110])]) ).

cnf(c_0_112,negated_conjecture,
    aDivisorOf0(esk5_0,xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_109]),c_0_110])]) ).

cnf(c_0_113,negated_conjecture,
    isPrime0(esk5_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_109]),c_0_110])]) ).

cnf(c_0_114,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : NUM447+5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.11  % Command    : run_E %s %d THM
% 0.11/0.31  % Computer : n029.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon May 20 06:40:22 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.17/0.45  Running first-order theorem proving
% 0.17/0.45  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.44/1.31  # Version: 3.1.0
% 6.44/1.31  # Preprocessing class: FSLSSMSSSSSNFFN.
% 6.44/1.31  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.44/1.31  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.44/1.31  # Starting new_bool_3 with 300s (1) cores
% 6.44/1.31  # Starting new_bool_1 with 300s (1) cores
% 6.44/1.31  # Starting sh5l with 300s (1) cores
% 6.44/1.31  # new_bool_3 with pid 1334 completed with status 0
% 6.44/1.31  # Result found by new_bool_3
% 6.44/1.31  # Preprocessing class: FSLSSMSSSSSNFFN.
% 6.44/1.31  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.44/1.31  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.44/1.31  # Starting new_bool_3 with 300s (1) cores
% 6.44/1.31  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.44/1.31  # Search class: FGHSF-FSLM31-SFFFFFNN
% 6.44/1.31  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 6.44/1.31  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 148s (1) cores
% 6.44/1.31  # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1337 completed with status 0
% 6.44/1.31  # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 6.44/1.31  # Preprocessing class: FSLSSMSSSSSNFFN.
% 6.44/1.31  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.44/1.31  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.44/1.31  # Starting new_bool_3 with 300s (1) cores
% 6.44/1.31  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.44/1.31  # Search class: FGHSF-FSLM31-SFFFFFNN
% 6.44/1.31  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 6.44/1.31  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 148s (1) cores
% 6.44/1.31  # Preprocessing time       : 0.003 s
% 6.44/1.31  # Presaturation interreduction done
% 6.44/1.31  
% 6.44/1.31  # Proof found!
% 6.44/1.31  # SZS status Theorem
% 6.44/1.31  # SZS output start CNFRefutation
% See solution above
% 6.44/1.31  # Parsed axioms                        : 44
% 6.44/1.31  # Removed by relevancy pruning/SinE    : 8
% 6.44/1.31  # Initial clauses                      : 146
% 6.44/1.31  # Removed in clause preprocessing      : 5
% 6.44/1.31  # Initial clauses in saturation        : 141
% 6.44/1.31  # Processed clauses                    : 4804
% 6.44/1.31  # ...of these trivial                  : 43
% 6.44/1.31  # ...subsumed                          : 2797
% 6.44/1.31  # ...remaining for further processing  : 1964
% 6.44/1.31  # Other redundant clauses eliminated   : 106
% 6.44/1.31  # Clauses deleted for lack of memory   : 0
% 6.44/1.31  # Backward-subsumed                    : 197
% 6.44/1.31  # Backward-rewritten                   : 845
% 6.44/1.31  # Generated clauses                    : 71527
% 6.44/1.31  # ...of the previous two non-redundant : 68586
% 6.44/1.31  # ...aggressively subsumed             : 0
% 6.44/1.31  # Contextual simplify-reflections      : 336
% 6.44/1.31  # Paramodulations                      : 71412
% 6.44/1.31  # Factorizations                       : 0
% 6.44/1.31  # NegExts                              : 0
% 6.44/1.31  # Equation resolutions                 : 106
% 6.44/1.31  # Disequality decompositions           : 0
% 6.44/1.31  # Total rewrite steps                  : 31709
% 6.44/1.31  # ...of those cached                   : 31658
% 6.44/1.31  # Propositional unsat checks           : 0
% 6.44/1.31  #    Propositional check models        : 0
% 6.44/1.31  #    Propositional check unsatisfiable : 0
% 6.44/1.31  #    Propositional clauses             : 0
% 6.44/1.31  #    Propositional clauses after purity: 0
% 6.44/1.31  #    Propositional unsat core size     : 0
% 6.44/1.31  #    Propositional preprocessing time  : 0.000
% 6.44/1.31  #    Propositional encoding time       : 0.000
% 6.44/1.31  #    Propositional solver time         : 0.000
% 6.44/1.31  #    Success case prop preproc time    : 0.000
% 6.44/1.31  #    Success case prop encoding time   : 0.000
% 6.44/1.31  #    Success case prop solver time     : 0.000
% 6.44/1.31  # Current number of processed clauses  : 753
% 6.44/1.31  #    Positive orientable unit clauses  : 71
% 6.44/1.31  #    Positive unorientable unit clauses: 0
% 6.44/1.31  #    Negative unit clauses             : 3
% 6.44/1.31  #    Non-unit-clauses                  : 679
% 6.44/1.31  # Current number of unprocessed clauses: 63768
% 6.44/1.31  # ...number of literals in the above   : 262596
% 6.87/1.31  # Current number of archived formulas  : 0
% 6.87/1.31  # Current number of archived clauses   : 1192
% 6.87/1.31  # Clause-clause subsumption calls (NU) : 264972
% 6.87/1.31  # Rec. Clause-clause subsumption calls : 124102
% 6.87/1.31  # Non-unit clause-clause subsumptions  : 3213
% 6.87/1.31  # Unit Clause-clause subsumption calls : 11631
% 6.87/1.31  # Rewrite failures with RHS unbound    : 0
% 6.87/1.31  # BW rewrite match attempts            : 34
% 6.87/1.31  # BW rewrite match successes           : 18
% 6.87/1.31  # Condensation attempts                : 0
% 6.87/1.31  # Condensation successes               : 0
% 6.87/1.31  # Termbank termtop insertions          : 1434805
% 6.87/1.31  # Search garbage collected termcells   : 2327
% 6.87/1.31  
% 6.87/1.31  # -------------------------------------------------
% 6.87/1.31  # User time                : 0.769 s
% 6.87/1.31  # System time              : 0.030 s
% 6.87/1.31  # Total time               : 0.800 s
% 6.87/1.31  # Maximum resident set size: 2164 pages
% 6.87/1.31  
% 6.87/1.31  # -------------------------------------------------
% 6.87/1.31  # User time                : 0.772 s
% 6.87/1.31  # System time              : 0.033 s
% 6.87/1.31  # Total time               : 0.804 s
% 6.87/1.31  # Maximum resident set size: 1752 pages
% 6.87/1.31  % E---3.1 exiting
% 6.87/1.31  % E exiting
%------------------------------------------------------------------------------