TSTP Solution File: NUM503+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM503+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n003.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 : Thu Aug 31 11:30:58 EDT 2023

% Result   : Theorem 20.17s 3.67s
% Output   : CNFRefutation 20.17s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f246)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).

fof(f3,axiom,
    ( sz00 != sz10
    & aNaturalNumber0(sz10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).

fof(f8,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).

fof(f11,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sdtasdt0(sz10,X0) = X0
        & sdtasdt0(X0,sz10) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).

fof(f12,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).

fof(f15,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sz00 != X0
       => ! [X1,X2] :
            ( ( aNaturalNumber0(X2)
              & aNaturalNumber0(X1) )
           => ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
                | sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
             => X1 = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sz00 = sdtpldt0(X0,X1)
       => ( sz00 = X1
          & sz00 = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sz00 = sdtasdt0(X0,X1)
       => ( sz00 = X1
          | sz00 = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sdtlseqdt0(X0,X1)
       => ! [X2] :
            ( sdtmndt0(X1,X0) = X2
          <=> ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).

fof(f21,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X0)
          & sdtlseqdt0(X0,X1) )
       => X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).

fof(f22,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X0,X1) )
       => sdtlseqdt0(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X0)
          & X0 != X1 )
        | sdtlseqdt0(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).

fof(f25,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X2)
          & X1 != X2
          & sz00 != X0 )
       => ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
          & sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
          & sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
          & sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).

fof(f27,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sz00 != X0
       => sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).

fof(f30,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( doDivides0(X0,X1)
          & sz00 != X0 )
       => ! [X2] :
            ( sdtsldt0(X1,X0) = X2
          <=> ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sz00 != X1
          & doDivides0(X0,X1) )
       => sdtlseqdt0(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).

fof(f37,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( isPrime0(X0)
      <=> ( ! [X1] :
              ( ( doDivides0(X1,X0)
                & aNaturalNumber0(X1) )
             => ( X0 = X1
                | sz10 = X1 ) )
          & sz10 != X0
          & sz00 != X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).

fof(f39,axiom,
    ( aNaturalNumber0(xp)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).

fof(f41,axiom,
    ( doDivides0(xp,sdtasdt0(xn,xm))
    & isPrime0(xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).

fof(f43,axiom,
    ~ sdtlseqdt0(xp,xm),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).

fof(f44,axiom,
    ( sdtlseqdt0(xm,xp)
    & xm != xp
    & sdtlseqdt0(xn,xp)
    & xn != xp ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).

fof(f45,axiom,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).

fof(f47,axiom,
    ( sz10 != xk
    & sz00 != xk ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).

fof(f50,axiom,
    sdtlseqdt0(xp,xk),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2389) ).

fof(f51,conjecture,
    ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    & sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
    & sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    & sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f52,negated_conjecture,
    ~ ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
      & sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
      & sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
      & sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
    inference(negated_conjecture,[],[f51]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f55]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f57]) ).

fof(f63,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f68,plain,
    ! [X0] :
      ( ( sdtasdt0(sz10,X0) = X0
        & sdtasdt0(X0,sz10) = X0 )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f69,plain,
    ! [X0] :
      ( ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( X1 = X2
          | ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
            & sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
          | ~ aNaturalNumber0(X2)
          | ~ aNaturalNumber0(X1) )
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( X1 = X2
          | ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
            & sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
          | ~ aNaturalNumber0(X2)
          | ~ aNaturalNumber0(X1) )
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f74]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( sz00 = X1
        & sz00 = X0 )
      | sz00 != sdtpldt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( sz00 = X1
        & sz00 = X0 )
      | sz00 != sdtpldt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f76]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f78]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f80]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X1,X0) = X2
        <=> ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X1,X0) = X2
        <=> ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f82]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f85]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f87]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X1,X0)
        & X0 != X1 )
      | sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X1,X0)
        & X0 != X1 )
      | sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f89]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        & sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
        & sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
        & sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
      | ~ sdtlseqdt0(X1,X2)
      | X1 = X2
      | sz00 = X0
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        & sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
        & sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
        & sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
      | ~ sdtlseqdt0(X1,X2)
      | X1 = X2
      | sz00 = X0
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f93]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,sdtasdt0(X1,X0))
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,sdtasdt0(X1,X0))
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f97]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f101]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtsldt0(X1,X0) = X2
        <=> ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtsldt0(X1,X0) = X2
        <=> ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f103]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X0,X1)
      | sz00 = X1
      | ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X0,X1)
      | sz00 = X1
      | ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f111]) ).

fof(f115,plain,
    ! [X0] :
      ( ( isPrime0(X0)
      <=> ( ! [X1] :
              ( X0 = X1
              | sz10 = X1
              | ~ doDivides0(X1,X0)
              | ~ aNaturalNumber0(X1) )
          & sz10 != X0
          & sz00 != X0 ) )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f116,plain,
    ! [X0] :
      ( ( isPrime0(X0)
      <=> ( ! [X1] :
              ( X0 = X1
              | sz10 = X1
              | ~ doDivides0(X1,X0)
              | ~ aNaturalNumber0(X1) )
          & sz10 != X0
          & sz00 != X0 ) )
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f115]) ).

fof(f122,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( ( ( sdtlseqdt0(X0,X1)
          | ! [X2] :
              ( sdtpldt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X2] :
              ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
          | ~ sdtlseqdt0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f81]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ( ( sdtlseqdt0(X0,X1)
          | ! [X2] :
              ( sdtpldt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X3] :
              ( sdtpldt0(X0,X3) = X1
              & aNaturalNumber0(X3) )
          | ~ sdtlseqdt0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f123]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtpldt0(X0,X3) = X1
          & aNaturalNumber0(X3) )
     => ( sdtpldt0(X0,sK0(X0,X1)) = X1
        & aNaturalNumber0(sK0(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( ( ( sdtlseqdt0(X0,X1)
          | ! [X2] :
              ( sdtpldt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ( sdtpldt0(X0,sK0(X0,X1)) = X1
            & aNaturalNumber0(sK0(X0,X1)) )
          | ~ sdtlseqdt0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f124,f125]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X1,X0) = X2
            | sdtpldt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtmndt0(X1,X0) != X2 ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f83]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X1,X0) = X2
            | sdtpldt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtmndt0(X1,X0) != X2 ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f127]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ( ( doDivides0(X0,X1)
          | ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X2] :
              ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
          | ~ doDivides0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f102]) ).

fof(f130,plain,
    ! [X0,X1] :
      ( ( ( doDivides0(X0,X1)
          | ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X3] :
              ( sdtasdt0(X0,X3) = X1
              & aNaturalNumber0(X3) )
          | ~ doDivides0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f129]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtasdt0(X0,X3) = X1
          & aNaturalNumber0(X3) )
     => ( sdtasdt0(X0,sK1(X0,X1)) = X1
        & aNaturalNumber0(sK1(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ( ( doDivides0(X0,X1)
          | ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ( sdtasdt0(X0,sK1(X0,X1)) = X1
            & aNaturalNumber0(sK1(X0,X1)) )
          | ~ doDivides0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f130,f131]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtsldt0(X1,X0) = X2
            | sdtasdt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtsldt0(X1,X0) != X2 ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f104]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtsldt0(X1,X0) = X2
            | sdtasdt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtsldt0(X1,X0) != X2 ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f133]) ).

fof(f135,plain,
    ! [X0] :
      ( ( ( isPrime0(X0)
          | ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 )
        & ( ( ! [X1] :
                ( X0 = X1
                | sz10 = X1
                | ~ doDivides0(X1,X0)
                | ~ aNaturalNumber0(X1) )
            & sz10 != X0
            & sz00 != X0 )
          | ~ isPrime0(X0) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f116]) ).

fof(f136,plain,
    ! [X0] :
      ( ( ( isPrime0(X0)
          | ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 )
        & ( ( ! [X1] :
                ( X0 = X1
                | sz10 = X1
                | ~ doDivides0(X1,X0)
                | ~ aNaturalNumber0(X1) )
            & sz10 != X0
            & sz00 != X0 )
          | ~ isPrime0(X0) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f135]) ).

fof(f137,plain,
    ! [X0] :
      ( ( ( isPrime0(X0)
          | ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 )
        & ( ( ! [X2] :
                ( X0 = X2
                | sz10 = X2
                | ~ doDivides0(X2,X0)
                | ~ aNaturalNumber0(X2) )
            & sz10 != X0
            & sz00 != X0 )
          | ~ isPrime0(X0) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f136]) ).

fof(f138,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 != X1
          & sz10 != X1
          & doDivides0(X1,X0)
          & aNaturalNumber0(X1) )
     => ( sK2(X0) != X0
        & sz10 != sK2(X0)
        & doDivides0(sK2(X0),X0)
        & aNaturalNumber0(sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f139,plain,
    ! [X0] :
      ( ( ( isPrime0(X0)
          | ( sK2(X0) != X0
            & sz10 != sK2(X0)
            & doDivides0(sK2(X0),X0)
            & aNaturalNumber0(sK2(X0)) )
          | sz10 = X0
          | sz00 = X0 )
        & ( ( ! [X2] :
                ( X0 = X2
                | sz10 = X2
                | ~ doDivides0(X2,X0)
                | ~ aNaturalNumber0(X2) )
            & sz10 != X0
            & sz00 != X0 )
          | ~ isPrime0(X0) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f137,f138]) ).

fof(f142,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f143,plain,
    aNaturalNumber0(sz10),
    inference(cnf_transformation,[],[f3]) ).

fof(f144,plain,
    sz00 != sz10,
    inference(cnf_transformation,[],[f3]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f149,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz00) = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f150,plain,
    ! [X0] :
      ( sdtpldt0(sz00,X0) = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f153,plain,
    ! [X0] :
      ( sdtasdt0(X0,sz10) = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f155,plain,
    ! [X0] :
      ( sz00 = sdtasdt0(X0,sz00)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f161,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f162,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( sz00 = X0
      | sz00 != sdtpldt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,sK0(X0,X1)) = X1
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f168,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(X0,X1)
      | sdtpldt0(X0,X2) != X1
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f171,plain,
    ! [X2,X0,X1] :
      ( sdtmndt0(X1,X0) = X2
      | sdtpldt0(X0,X2) != X1
      | ~ aNaturalNumber0(X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f128]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f174,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f182,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
      | ~ sdtlseqdt0(X1,X2)
      | X1 = X2
      | sz00 = X0
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f184,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
      | ~ sdtlseqdt0(X1,X2)
      | X1 = X2
      | sz00 = X0
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f187,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,sdtasdt0(X1,X0))
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f191,plain,
    ! [X2,X0,X1] :
      ( doDivides0(X0,X1)
      | sdtasdt0(X0,X2) != X1
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f192,plain,
    ! [X2,X0,X1] :
      ( aNaturalNumber0(X2)
      | sdtsldt0(X1,X0) != X2
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f193,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(X0,X2) = X1
      | sdtsldt0(X1,X0) != X2
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X0,X1)
      | sz00 = X1
      | ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f200,plain,
    ! [X0] :
      ( sz00 != X0
      | ~ isPrime0(X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f210,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f39]) ).

fof(f211,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f39]) ).

fof(f212,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f39]) ).

fof(f214,plain,
    isPrime0(xp),
    inference(cnf_transformation,[],[f41]) ).

fof(f215,plain,
    doDivides0(xp,sdtasdt0(xn,xm)),
    inference(cnf_transformation,[],[f41]) ).

fof(f217,plain,
    ~ sdtlseqdt0(xp,xm),
    inference(cnf_transformation,[],[f43]) ).

fof(f218,plain,
    xn != xp,
    inference(cnf_transformation,[],[f44]) ).

fof(f219,plain,
    sdtlseqdt0(xn,xp),
    inference(cnf_transformation,[],[f44]) ).

fof(f222,plain,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    inference(cnf_transformation,[],[f45]) ).

fof(f225,plain,
    sz00 != xk,
    inference(cnf_transformation,[],[f47]) ).

fof(f232,plain,
    sdtlseqdt0(xp,xk),
    inference(cnf_transformation,[],[f50]) ).

fof(f233,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f234,plain,
    ! [X2,X0] :
      ( sdtlseqdt0(X0,sdtpldt0(X0,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(sdtpldt0(X0,X2))
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f168]) ).

fof(f235,plain,
    ! [X2,X0] :
      ( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
      | ~ aNaturalNumber0(X2)
      | ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
      | ~ aNaturalNumber0(sdtpldt0(X0,X2))
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f171]) ).

fof(f240,plain,
    ! [X2,X0] :
      ( doDivides0(X0,sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f191]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f193]) ).

fof(f243,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtsldt0(X1,X0))
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f192]) ).

fof(f245,plain,
    ( ~ isPrime0(sz00)
    | ~ aNaturalNumber0(sz00) ),
    inference(equality_resolution,[],[f200]) ).

cnf(c_49,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_50,negated_conjecture,
    sz00 != sz10,
    inference(cnf_transformation,[],[f144]) ).

cnf(c_51,plain,
    aNaturalNumber0(sz10),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_52,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f145]) ).

cnf(c_53,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_56,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtpldt0(sz00,X0) = X0 ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_57,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_61,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtasdt0(X0,sz10) = X0 ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_63,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtasdt0(X0,sz00) = sz00 ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_68,plain,
    ( sdtasdt0(X0,X1) != sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X0 = X2
    | X1 = sz00 ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_69,plain,
    ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X0 = sz00
    | X1 = X2 ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_71,plain,
    ( sdtpldt0(X0,X1) != sz00
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = sz00 ),
    inference(cnf_transformation,[],[f163]) ).

cnf(c_72,plain,
    ( sdtasdt0(X0,X1) != sz00
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = sz00
    | X1 = sz00 ),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_73,plain,
    ( ~ aNaturalNumber0(sdtpldt0(X0,X1))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f234]) ).

cnf(c_74,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X0,sK0(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_76,plain,
    ( ~ sdtlseqdt0(X0,sdtpldt0(X0,X1))
    | ~ aNaturalNumber0(sdtpldt0(X0,X1))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtmndt0(sdtpldt0(X0,X1),X0) = X1 ),
    inference(cnf_transformation,[],[f235]) ).

cnf(c_80,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ sdtlseqdt0(X1,X0)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_81,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtlseqdt0(X0,X2) ),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_82,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtlseqdt0(X0,X1)
    | sdtlseqdt0(X1,X0) ),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_83,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtlseqdt0(X0,X0) ),
    inference(cnf_transformation,[],[f246]) ).

cnf(c_88,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X0 = X1
    | X2 = sz00
    | sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_90,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X0 = X1
    | X2 = sz00
    | sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X2,X1)) ),
    inference(cnf_transformation,[],[f182]) ).

cnf(c_93,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = sz00
    | sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
    inference(cnf_transformation,[],[f187]) ).

cnf(c_95,plain,
    ( ~ aNaturalNumber0(sdtasdt0(X0,X1))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | doDivides0(X0,sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f240]) ).

cnf(c_99,plain,
    ( ~ doDivides0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
    | X0 = sz00 ),
    inference(cnf_transformation,[],[f242]) ).

cnf(c_100,plain,
    ( ~ doDivides0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = sz00
    | aNaturalNumber0(sdtsldt0(X1,X0)) ),
    inference(cnf_transformation,[],[f243]) ).

cnf(c_104,plain,
    ( ~ doDivides0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X1 = sz00
    | sdtlseqdt0(X0,X1) ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_112,negated_conjecture,
    ( ~ aNaturalNumber0(sz00)
    | ~ isPrime0(sz00) ),
    inference(cnf_transformation,[],[f245]) ).

cnf(c_116,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f212]) ).

cnf(c_117,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f211]) ).

cnf(c_118,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f210]) ).

cnf(c_120,plain,
    doDivides0(xp,sdtasdt0(xn,xm)),
    inference(cnf_transformation,[],[f215]) ).

cnf(c_121,plain,
    isPrime0(xp),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_123,negated_conjecture,
    ~ sdtlseqdt0(xp,xm),
    inference(cnf_transformation,[],[f217]) ).

cnf(c_126,plain,
    sdtlseqdt0(xn,xp),
    inference(cnf_transformation,[],[f219]) ).

cnf(c_127,negated_conjecture,
    xp != xn,
    inference(cnf_transformation,[],[f218]) ).

cnf(c_128,plain,
    sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
    inference(cnf_transformation,[],[f222]) ).

cnf(c_132,negated_conjecture,
    sz00 != xk,
    inference(cnf_transformation,[],[f225]) ).

cnf(c_138,plain,
    sdtlseqdt0(xp,xk),
    inference(cnf_transformation,[],[f232]) ).

cnf(c_139,negated_conjecture,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
    inference(cnf_transformation,[],[f233]) ).

cnf(c_140,plain,
    ( ~ aNaturalNumber0(sz00)
    | sdtlseqdt0(sz00,sz00) ),
    inference(instantiation,[status(thm)],[c_83]) ).

cnf(c_144,plain,
    ( ~ aNaturalNumber0(sz00)
    | sdtpldt0(sz00,sz00) = sz00 ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_162,plain,
    ( sdtpldt0(sz00,sz00) != sz00
    | ~ aNaturalNumber0(sz00)
    | sz00 = sz00 ),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_187,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | doDivides0(X0,sdtasdt0(X0,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).

cnf(c_190,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).

cnf(c_193,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtmndt0(sdtpldt0(X0,X1),X0) = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_76,c_52,c_76,c_190]) ).

cnf(c_239,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_241,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_242,plain,
    ( X0 != X1
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(X0) ),
    theory(equality) ).

cnf(c_245,plain,
    ( X0 != X1
    | X2 != X3
    | ~ sdtlseqdt0(X1,X3)
    | sdtlseqdt0(X0,X2) ),
    theory(equality) ).

cnf(c_252,plain,
    ( X0 != X1
    | ~ isPrime0(X1)
    | isPrime0(X0) ),
    theory(equality) ).

cnf(c_265,plain,
    ( X0 != xp
    | ~ isPrime0(xp)
    | isPrime0(X0) ),
    inference(instantiation,[status(thm)],[c_252]) ).

cnf(c_266,plain,
    ( sz00 != xp
    | ~ isPrime0(xp)
    | isPrime0(sz00) ),
    inference(instantiation,[status(thm)],[c_265]) ).

cnf(c_308,plain,
    ( xp != X0
    | xm != X1
    | ~ sdtlseqdt0(X0,X1)
    | sdtlseqdt0(xp,xm) ),
    inference(instantiation,[status(thm)],[c_245]) ).

cnf(c_310,plain,
    ( sdtasdt0(xp,xm) != X0
    | sdtasdt0(xn,xm) != X1
    | ~ sdtlseqdt0(X1,X0)
    | sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
    inference(instantiation,[status(thm)],[c_245]) ).

cnf(c_321,plain,
    ( ~ sdtlseqdt0(X0,xm)
    | ~ sdtlseqdt0(xp,X0)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | sdtlseqdt0(xp,xm) ),
    inference(instantiation,[status(thm)],[c_81]) ).

cnf(c_336,plain,
    sdtpldt0(sz00,sz10) = sz10,
    inference(superposition,[status(thm)],[c_51,c_56]) ).

cnf(c_338,plain,
    sdtpldt0(sz00,xm) = xm,
    inference(superposition,[status(thm)],[c_117,c_56]) ).

cnf(c_446,plain,
    ( X0 != X1
    | xp != X1
    | X0 = xp ),
    inference(instantiation,[status(thm)],[c_241]) ).

cnf(c_447,plain,
    ( sz00 != sz00
    | xp != sz00
    | sz00 = xp ),
    inference(instantiation,[status(thm)],[c_446]) ).

cnf(c_456,plain,
    sdtasdt0(xp,sz00) = sz00,
    inference(superposition,[status(thm)],[c_116,c_63]) ).

cnf(c_582,plain,
    ( ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sz10)
    | sdtlseqdt0(sz00,sz10) ),
    inference(superposition,[status(thm)],[c_336,c_190]) ).

cnf(c_584,plain,
    ( ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(xm)
    | sdtlseqdt0(sz00,xm) ),
    inference(superposition,[status(thm)],[c_338,c_190]) ).

cnf(c_610,plain,
    ( X0 != X1
    | xm != X1
    | xm = X0 ),
    inference(instantiation,[status(thm)],[c_241]) ).

cnf(c_686,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
    inference(superposition,[status(thm)],[c_82,c_139]) ).

cnf(c_909,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xm)
    | sdtlseqdt0(X0,xm)
    | sdtlseqdt0(xm,X0) ),
    inference(instantiation,[status(thm)],[c_82]) ).

cnf(c_917,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_1383,plain,
    xm = xm,
    inference(instantiation,[status(thm)],[c_239]) ).

cnf(c_1466,plain,
    ( sdtasdt0(xp,xm) != X0
    | sdtasdt0(xn,xm) != sdtasdt0(xn,xm)
    | ~ sdtlseqdt0(sdtasdt0(xn,xm),X0)
    | sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
    inference(instantiation,[status(thm)],[c_310]) ).

cnf(c_1467,plain,
    sdtasdt0(xn,xm) = sdtasdt0(xn,xm),
    inference(instantiation,[status(thm)],[c_239]) ).

cnf(c_1639,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xp)
    | doDivides0(xp,sdtasdt0(xp,X0)) ),
    inference(instantiation,[status(thm)],[c_187]) ).

cnf(c_1770,plain,
    xp = xp,
    inference(instantiation,[status(thm)],[c_239]) ).

cnf(c_2203,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | aNaturalNumber0(sdtasdt0(xp,xm)) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_2626,plain,
    sdtpldt0(sz00,xm) = xm,
    inference(superposition,[status(thm)],[c_117,c_56]) ).

cnf(c_2725,plain,
    ( ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(xm)
    | sdtlseqdt0(sz00,xm) ),
    inference(superposition,[status(thm)],[c_2626,c_190]) ).

cnf(c_2827,plain,
    sdtlseqdt0(sz00,xm),
    inference(global_subsumption_just,[status(thm)],[c_2725,c_117,c_49,c_584]) ).

cnf(c_3538,plain,
    ( ~ sdtlseqdt0(xm,sz00)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(xm)
    | sz00 = xm ),
    inference(superposition,[status(thm)],[c_2827,c_80]) ).

cnf(c_3551,plain,
    ( sdtasdt0(xp,xm) != sdtasdt0(xn,xm)
    | sdtasdt0(xn,xm) != sdtasdt0(xn,xm)
    | ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xm))
    | sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
    inference(instantiation,[status(thm)],[c_1466]) ).

cnf(c_3552,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xm)) ),
    inference(instantiation,[status(thm)],[c_83]) ).

cnf(c_3844,plain,
    ( xp != xp
    | xm != X0
    | ~ sdtlseqdt0(xp,X0)
    | sdtlseqdt0(xp,xm) ),
    inference(instantiation,[status(thm)],[c_308]) ).

cnf(c_3847,plain,
    ( ~ doDivides0(xp,sdtasdt0(xn,xm))
    | ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | ~ aNaturalNumber0(xp)
    | sz00 = xp
    | aNaturalNumber0(xk) ),
    inference(superposition,[status(thm)],[c_128,c_100]) ).

cnf(c_3884,plain,
    ( ~ sdtlseqdt0(xp,xk)
    | ~ sdtlseqdt0(xk,xm)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xk)
    | sdtlseqdt0(xp,xm) ),
    inference(instantiation,[status(thm)],[c_321]) ).

cnf(c_5771,plain,
    sdtasdt0(xp,sz10) = xp,
    inference(superposition,[status(thm)],[c_116,c_61]) ).

cnf(c_5864,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
    inference(superposition,[status(thm)],[c_82,c_139]) ).

cnf(c_5899,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
    inference(global_subsumption_just,[status(thm)],[c_5864,c_118,c_117,c_116,c_686,c_917,c_2203]) ).

cnf(c_6714,plain,
    ( X0 != X1
    | xm != X2
    | ~ sdtlseqdt0(X2,X1)
    | sdtlseqdt0(xm,X0) ),
    inference(instantiation,[status(thm)],[c_245]) ).

cnf(c_6715,plain,
    ( sz00 != sz00
    | xm != sz00
    | ~ sdtlseqdt0(sz00,sz00)
    | sdtlseqdt0(xm,sz00) ),
    inference(instantiation,[status(thm)],[c_6714]) ).

cnf(c_6811,plain,
    ( X0 != xm
    | xm != xm
    | xm = X0 ),
    inference(instantiation,[status(thm)],[c_610]) ).

cnf(c_6812,plain,
    ( sz00 != xm
    | xm != xm
    | xm = sz00 ),
    inference(instantiation,[status(thm)],[c_6811]) ).

cnf(c_7251,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xk)
    | sdtlseqdt0(xm,xk)
    | sdtlseqdt0(xk,xm) ),
    inference(instantiation,[status(thm)],[c_909]) ).

cnf(c_8010,plain,
    ( sdtasdt0(xp,X0) != X1
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sdtasdt0(xp,X0)) ),
    inference(instantiation,[status(thm)],[c_242]) ).

cnf(c_8011,plain,
    ( sdtasdt0(xp,sz00) != sz00
    | ~ aNaturalNumber0(sz00)
    | aNaturalNumber0(sdtasdt0(xp,sz00)) ),
    inference(instantiation,[status(thm)],[c_8010]) ).

cnf(c_9549,plain,
    ( xp != xp
    | xm != xk
    | ~ sdtlseqdt0(xp,xk)
    | sdtlseqdt0(xp,xm) ),
    inference(instantiation,[status(thm)],[c_3844]) ).

cnf(c_10621,plain,
    ( sdtasdt0(xp,X0) != xp
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xp)
    | X0 = sz10
    | sz00 = xp ),
    inference(superposition,[status(thm)],[c_5771,c_69]) ).

cnf(c_10650,plain,
    ( sdtasdt0(xp,sz00) != xp
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xp)
    | sz00 = sz10
    | sz00 = xp ),
    inference(instantiation,[status(thm)],[c_10621]) ).

cnf(c_10951,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | ~ sdtlseqdt0(xn,xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sz00 = xm
    | xp = xn ),
    inference(superposition,[status(thm)],[c_88,c_139]) ).

cnf(c_11376,plain,
    ( sz00 = xm
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
    inference(global_subsumption_just,[status(thm)],[c_10951,c_118,c_117,c_116,c_126,c_127,c_10951]) ).

cnf(c_11377,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sz00 = xm ),
    inference(renaming,[status(thm)],[c_11376]) ).

cnf(c_11609,plain,
    ( ~ sdtlseqdt0(X0,sz10)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xp)
    | X0 = sz10
    | sz00 = xp
    | sdtlseqdt0(sdtasdt0(xp,X0),xp) ),
    inference(superposition,[status(thm)],[c_5771,c_90]) ).

cnf(c_11638,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sz00 = xp
    | sz00 = xm
    | xm = xk ),
    inference(superposition,[status(thm)],[c_90,c_11377]) ).

cnf(c_11639,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sz00 = xp
    | xm = xk
    | sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
    inference(superposition,[status(thm)],[c_90,c_5899]) ).

cnf(c_11654,plain,
    ( ~ sdtlseqdt0(sz00,sz10)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xp)
    | sz00 = sz10
    | sz00 = xp
    | sdtlseqdt0(sdtasdt0(xp,sz00),xp) ),
    inference(instantiation,[status(thm)],[c_11609]) ).

cnf(c_12447,plain,
    sdtasdt0(xp,sz00) = sz00,
    inference(superposition,[status(thm)],[c_116,c_63]) ).

cnf(c_12449,plain,
    sdtasdt0(xn,sz00) = sz00,
    inference(superposition,[status(thm)],[c_118,c_63]) ).

cnf(c_12524,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
    inference(superposition,[status(thm)],[c_82,c_139]) ).

cnf(c_12559,plain,
    ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
    inference(global_subsumption_just,[status(thm)],[c_12524,c_121,c_118,c_117,c_116,c_49,c_138,c_123,c_120,c_112,c_266,c_917,c_1770,c_3847,c_3884,c_7251,c_9549,c_11639]) ).

cnf(c_12806,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | sdtpldt0(sdtasdt0(xp,xm),sK0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))) = sdtasdt0(xn,xm)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_12559,c_74]) ).

cnf(c_12875,plain,
    ( sdtpldt0(sdtasdt0(xp,xm),sK0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))) = sdtasdt0(xn,xm)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
    inference(global_subsumption_just,[status(thm)],[c_12806,c_118,c_117,c_116,c_917,c_2203,c_12806]) ).

cnf(c_12880,plain,
    ( ~ aNaturalNumber0(sK0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(superposition,[status(thm)],[c_12875,c_52]) ).

cnf(c_12887,plain,
    aNaturalNumber0(sdtasdt0(xn,xm)),
    inference(global_subsumption_just,[status(thm)],[c_12880,c_118,c_117,c_917]) ).

cnf(c_12889,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtmndt0(sdtpldt0(X0,sdtasdt0(xn,xm)),X0) = sdtasdt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_12887,c_193]) ).

cnf(c_12920,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_12559,c_80]) ).

cnf(c_13017,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
    inference(global_subsumption_just,[status(thm)],[c_12920,c_118,c_117,c_116,c_917,c_2203,c_12920]) ).

cnf(c_13223,plain,
    sdtmndt0(sdtpldt0(sdtasdt0(xn,xm),sdtasdt0(xn,xm)),sdtasdt0(xn,xm)) = sdtasdt0(xn,xm),
    inference(superposition,[status(thm)],[c_12887,c_12889]) ).

cnf(c_14310,plain,
    ( ~ sdtlseqdt0(xn,xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sz00 = xm
    | xp = xn ),
    inference(superposition,[status(thm)],[c_88,c_13017]) ).

cnf(c_14563,plain,
    ( sz00 = xm
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
    inference(global_subsumption_just,[status(thm)],[c_14310,c_121,c_118,c_117,c_116,c_49,c_138,c_123,c_120,c_112,c_266,c_917,c_1770,c_3847,c_3884,c_7251,c_9549,c_11638]) ).

cnf(c_14564,plain,
    ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
    | sz00 = xm ),
    inference(renaming,[status(thm)],[c_14563]) ).

cnf(c_14590,plain,
    ( sdtmndt0(sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xp,xm)),sdtasdt0(xp,xm)) = sdtasdt0(xp,xm)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sz00 = xm ),
    inference(superposition,[status(thm)],[c_14564,c_13223]) ).

cnf(c_16174,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | xp = xn
    | xm = sz00 ),
    inference(resolution,[status(thm)],[c_68,c_139]) ).

cnf(c_16785,plain,
    ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | xm = sz00 ),
    inference(global_subsumption_just,[status(thm)],[c_16174,c_118,c_117,c_116,c_127,c_917,c_1383,c_1467,c_3551,c_3552,c_6812,c_11377,c_16174]) ).

cnf(c_16786,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | xm = sz00 ),
    inference(renaming,[status(thm)],[c_16785]) ).

cnf(c_16812,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xk)
    | xp = sz00
    | xm = sz00
    | xm = xk ),
    inference(resolution,[status(thm)],[c_16786,c_69]) ).

cnf(c_16814,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | ~ isPrime0(sdtasdt0(xp,xk))
    | xm = sz00
    | isPrime0(sdtasdt0(xp,xm)) ),
    inference(resolution,[status(thm)],[c_16786,c_252]) ).

cnf(c_16824,plain,
    ( xm = sz00
    | ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
    inference(global_subsumption_just,[status(thm)],[c_16814,c_121,c_118,c_117,c_116,c_49,c_138,c_123,c_120,c_112,c_144,c_162,c_266,c_447,c_917,c_1770,c_3847,c_9549,c_16812]) ).

cnf(c_16825,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | xm = sz00 ),
    inference(renaming,[status(thm)],[c_16824]) ).

cnf(c_16836,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xk)
    | xp = sz00
    | xm = sz00
    | xm = xk ),
    inference(resolution,[status(thm)],[c_16825,c_90]) ).

cnf(c_17153,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | doDivides0(xp,sdtasdt0(xp,xm)) ),
    inference(instantiation,[status(thm)],[c_1639]) ).

cnf(c_18895,plain,
    sz00 = xm,
    inference(global_subsumption_just,[status(thm)],[c_14590,c_121,c_118,c_117,c_116,c_49,c_138,c_123,c_120,c_112,c_140,c_144,c_162,c_266,c_447,c_917,c_1770,c_3538,c_3847,c_3884,c_6715,c_7251,c_9549,c_16836]) ).

cnf(c_18954,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xn,sz00),sdtasdt0(xp,sz00))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_18895,c_13017]) ).

cnf(c_20091,plain,
    ( ~ sdtlseqdt0(sz00,sdtasdt0(xp,sz00))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_12449,c_18954]) ).

cnf(c_21020,plain,
    ( ~ sdtlseqdt0(sz00,sz00)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_12447,c_20091]) ).

cnf(c_25495,negated_conjecture,
    ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
    inference(global_subsumption_just,[status(thm)],[c_139,c_49,c_140,c_21020]) ).

cnf(c_25497,plain,
    ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | doDivides0(xp,sdtasdt0(xp,xm)) ),
    inference(superposition,[status(thm)],[c_25495,c_120]) ).

cnf(c_25499,plain,
    ( sdtsldt0(sdtasdt0(xp,xm),xp) = xk
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
    inference(superposition,[status(thm)],[c_25495,c_128]) ).

cnf(c_25500,plain,
    doDivides0(xp,sdtasdt0(xp,xm)),
    inference(global_subsumption_just,[status(thm)],[c_25497,c_117,c_116,c_17153]) ).

cnf(c_25769,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sz00 = xm
    | sdtlseqdt0(xn,sdtasdt0(xp,xm)) ),
    inference(superposition,[status(thm)],[c_25495,c_93]) ).

cnf(c_25828,plain,
    sz00 = xm,
    inference(global_subsumption_just,[status(thm)],[c_25769,c_121,c_118,c_117,c_116,c_49,c_138,c_123,c_120,c_112,c_140,c_144,c_162,c_266,c_447,c_917,c_1770,c_3538,c_3847,c_3884,c_6715,c_7251,c_9549,c_16836]) ).

cnf(c_25955,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(xp)
    | sdtasdt0(xp,xm) = sz00
    | sdtlseqdt0(xp,sdtasdt0(xp,xm)) ),
    inference(superposition,[status(thm)],[c_25500,c_104]) ).

cnf(c_26447,plain,
    ( sdtasdt0(xp,xm) = sz00
    | sdtlseqdt0(xp,sdtasdt0(xp,xm)) ),
    inference(global_subsumption_just,[status(thm)],[c_25955,c_117,c_116,c_2203,c_25955]) ).

cnf(c_26449,plain,
    ( sdtasdt0(xp,xm) = sz00
    | sdtlseqdt0(xp,sdtasdt0(xp,sz00)) ),
    inference(superposition,[status(thm)],[c_25828,c_26447]) ).

cnf(c_26457,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,sz00),xp)
    | ~ aNaturalNumber0(sdtasdt0(xp,sz00))
    | ~ aNaturalNumber0(xp)
    | sdtasdt0(xp,sz00) = xp
    | sdtasdt0(xp,xm) = sz00 ),
    inference(superposition,[status(thm)],[c_26449,c_80]) ).

cnf(c_26646,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(xp)
    | sdtasdt0(xp,sdtsldt0(sdtasdt0(xp,xm),xp)) = sdtasdt0(xp,xm)
    | sz00 = xp ),
    inference(superposition,[status(thm)],[c_25500,c_99]) ).

cnf(c_27004,plain,
    sdtasdt0(xp,sdtsldt0(sdtasdt0(xp,xm),xp)) = sdtasdt0(xp,xm),
    inference(global_subsumption_just,[status(thm)],[c_26646,c_121,c_117,c_116,c_49,c_112,c_266,c_2203,c_26646]) ).

cnf(c_27006,plain,
    sdtasdt0(xp,xm) = sdtasdt0(xp,xk),
    inference(superposition,[status(thm)],[c_25499,c_27004]) ).

cnf(c_27013,plain,
    ( sdtasdt0(xp,xm) != sz00
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xk)
    | sz00 = xp
    | sz00 = xk ),
    inference(superposition,[status(thm)],[c_27006,c_72]) ).

cnf(c_27017,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_27013,c_26457,c_11654,c_10650,c_8011,c_3847,c_917,c_582,c_456,c_266,c_112,c_120,c_50,c_132,c_49,c_51,c_116,c_117,c_118,c_121]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM503+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Aug 25 09:56:53 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 20.17/3.67  % SZS status Started for theBenchmark.p
% 20.17/3.67  % SZS status Theorem for theBenchmark.p
% 20.17/3.67  
% 20.17/3.67  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 20.17/3.67  
% 20.17/3.67  ------  iProver source info
% 20.17/3.67  
% 20.17/3.67  git: date: 2023-05-31 18:12:56 +0000
% 20.17/3.67  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 20.17/3.67  git: non_committed_changes: false
% 20.17/3.67  git: last_make_outside_of_git: false
% 20.17/3.67  
% 20.17/3.67  ------ Parsing...
% 20.17/3.67  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 20.17/3.67  
% 20.17/3.67  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e 
% 20.17/3.67  
% 20.17/3.67  ------ Preprocessing...
% 20.17/3.67  
% 20.17/3.67  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 20.17/3.67  ------ Proving...
% 20.17/3.67  ------ Problem Properties 
% 20.17/3.67  
% 20.17/3.67  
% 20.17/3.67  clauses                                 84
% 20.17/3.67  conjectures                             10
% 20.17/3.67  EPR                                     31
% 20.17/3.67  Horn                                    58
% 20.17/3.67  unary                                   25
% 20.17/3.67  binary                                  7
% 20.17/3.67  lits                                    282
% 20.17/3.67  lits eq                                 78
% 20.17/3.67  fd_pure                                 0
% 20.17/3.67  fd_pseudo                               0
% 20.17/3.67  fd_cond                                 15
% 20.17/3.67  fd_pseudo_cond                          11
% 20.17/3.67  AC symbols                              0
% 20.17/3.67  
% 20.17/3.67  ------ Input Options Time Limit: Unbounded
% 20.17/3.67  
% 20.17/3.67  
% 20.17/3.67  ------ 
% 20.17/3.67  Current options:
% 20.17/3.67  ------ 
% 20.17/3.67  
% 20.17/3.67  
% 20.17/3.67  
% 20.17/3.67  
% 20.17/3.67  ------ Proving...
% 20.17/3.67  
% 20.17/3.67  
% 20.17/3.67  % SZS status Theorem for theBenchmark.p
% 20.17/3.67  
% 20.17/3.67  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.17/3.67  
% 20.17/3.67  
%------------------------------------------------------------------------------