TSTP Solution File: NUM473+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM473+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n027.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 : Mon Jun 24 12:52:36 EDT 2024

% Result   : Theorem 55.76s 8.28s
% Output   : CNFRefutation 55.97s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f184)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

fof(f8,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
          | sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).

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/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).

fof(f21,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X0)
          & sdtlseqdt0(X0,X1) )
       => X0 = X1 ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mLETran) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X0)
          & X0 != X1 )
        | sdtlseqdt0(X0,X1) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mMonMul) ).

fof(f27,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sz00 != X0
       => sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).

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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).

fof(f34,axiom,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xl) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).

fof(f35,axiom,
    ( doDivides0(xl,sdtpldt0(xm,xn))
    & doDivides0(xl,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).

fof(f36,axiom,
    sz00 != xl,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).

fof(f37,axiom,
    xp = sdtsldt0(xm,xl),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).

fof(f38,axiom,
    xq = sdtsldt0(sdtpldt0(xm,xn),xl),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).

fof(f39,axiom,
    sdtlseqdt0(xm,sdtpldt0(xm,xn)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1409) ).

fof(f40,conjecture,
    sdtlseqdt0(xp,xq),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f41,negated_conjecture,
    ~ sdtlseqdt0(xp,xq),
    inference(negated_conjecture,[],[f40]) ).

fof(f44,plain,
    ~ sdtlseqdt0(xp,xq),
    inference(flattening,[],[f41]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f46]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f50]) ).

fof(f54,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f55]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( X1 = X2
      | ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
        & sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( X1 = X2
      | ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
        & sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f63]) ).

fof(f65,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(f66,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,[],[f65]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f71]) ).

fof(f73,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(f74,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X1,X0) = X2
        <=> ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f73]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f76]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f78]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X1,X0)
        & X0 != X1 )
      | sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f23]) ).

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

fof(f84,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(f85,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,[],[f84]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,sdtasdt0(X1,X0))
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,sdtasdt0(X1,X0))
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f88]) ).

fof(f92,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(f93,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,[],[f92]) ).

fof(f98,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,[],[f72]) ).

fof(f99,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,[],[f98]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtpldt0(X0,X3) = X1
          & aNaturalNumber0(X3) )
     => ( sdtpldt0(X0,sK0(X0,X1)) = X1
        & aNaturalNumber0(sK0(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,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])],[f99,f100]) ).

fof(f102,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,[],[f74]) ).

fof(f103,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,[],[f102]) ).

fof(f108,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,[],[f93]) ).

fof(f109,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,[],[f108]) ).

fof(f110,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f117,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz00) = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f127,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f129,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sK0(X0,X1))
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,sK0(X0,X1)) = X1
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f137,plain,
    ! [X2,X0,X1] :
      ( aNaturalNumber0(X2)
      | sdtmndt0(X1,X0) != X2
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f138,plain,
    ! [X2,X0,X1] :
      ( sdtpldt0(X0,X2) = X1
      | sdtmndt0(X1,X0) != X2
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f142,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f150,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,[],[f85]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,sdtasdt0(X1,X0))
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f159,plain,
    ! [X2,X0,X1] :
      ( aNaturalNumber0(X2)
      | sdtsldt0(X1,X0) != X2
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f160,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(X0,X2) = X1
      | sdtsldt0(X1,X0) != X2
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f164,plain,
    aNaturalNumber0(xl),
    inference(cnf_transformation,[],[f34]) ).

fof(f165,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f34]) ).

fof(f166,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f34]) ).

fof(f167,plain,
    doDivides0(xl,xm),
    inference(cnf_transformation,[],[f35]) ).

fof(f168,plain,
    doDivides0(xl,sdtpldt0(xm,xn)),
    inference(cnf_transformation,[],[f35]) ).

fof(f169,plain,
    sz00 != xl,
    inference(cnf_transformation,[],[f36]) ).

fof(f170,plain,
    xp = sdtsldt0(xm,xl),
    inference(cnf_transformation,[],[f37]) ).

fof(f171,plain,
    xq = sdtsldt0(sdtpldt0(xm,xn),xl),
    inference(cnf_transformation,[],[f38]) ).

fof(f172,plain,
    sdtlseqdt0(xm,sdtpldt0(xm,xn)),
    inference(cnf_transformation,[],[f39]) ).

fof(f173,plain,
    ~ sdtlseqdt0(xp,xq),
    inference(cnf_transformation,[],[f44]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f138]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtmndt0(X1,X0))
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f137]) ).

fof(f182,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f160]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtsldt0(X1,X0))
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f159]) ).

cnf(c_49,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f110]) ).

cnf(c_52,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f113]) ).

cnf(c_54,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    inference(cnf_transformation,[],[f115]) ).

cnf(c_57,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_58,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_67,plain,
    ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f127]) ).

cnf(c_69,plain,
    ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X0 = sz00
    | X1 = X2 ),
    inference(cnf_transformation,[],[f129]) ).

cnf(c_74,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X0,sK0(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f135]) ).

cnf(c_75,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sK0(X0,X1)) ),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_77,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_78,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sdtmndt0(X1,X0)) ),
    inference(cnf_transformation,[],[f177]) ).

cnf(c_80,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ sdtlseqdt0(X1,X0)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_81,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtlseqdt0(X0,X2) ),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_82,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtlseqdt0(X0,X1)
    | sdtlseqdt0(X1,X0) ),
    inference(cnf_transformation,[],[f144]) ).

cnf(c_83,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtlseqdt0(X0,X0) ),
    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,[],[f150]) ).

cnf(c_93,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = sz00
    | sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_98,plain,
    ( ~ doDivides0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
    | X0 = sz00 ),
    inference(cnf_transformation,[],[f182]) ).

cnf(c_99,plain,
    ( ~ doDivides0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = sz00
    | aNaturalNumber0(sdtsldt0(X1,X0)) ),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_102,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_103,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_104,plain,
    aNaturalNumber0(xl),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_105,plain,
    doDivides0(xl,sdtpldt0(xm,xn)),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_106,plain,
    doDivides0(xl,xm),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_107,plain,
    sz00 != xl,
    inference(cnf_transformation,[],[f169]) ).

cnf(c_108,plain,
    sdtsldt0(xm,xl) = xp,
    inference(cnf_transformation,[],[f170]) ).

cnf(c_109,plain,
    sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
    inference(cnf_transformation,[],[f171]) ).

cnf(c_110,plain,
    sdtlseqdt0(xm,sdtpldt0(xm,xn)),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_111,negated_conjecture,
    ~ sdtlseqdt0(xp,xq),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_1713,negated_conjecture,
    ~ sdtlseqdt0(xp,xq),
    inference(demodulation,[status(thm)],[c_111]) ).

cnf(c_1714,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_1720,plain,
    ( X0 != X1
    | X2 != X3
    | ~ sdtlseqdt0(X1,X3)
    | sdtlseqdt0(X0,X2) ),
    theory(equality) ).

cnf(c_2629,plain,
    ( xp != X0
    | xq != X1
    | ~ sdtlseqdt0(X0,X1)
    | sdtlseqdt0(xp,xq) ),
    inference(instantiation,[status(thm)],[c_1720]) ).

cnf(c_2704,plain,
    ( xp != X0
    | xq != xq
    | ~ sdtlseqdt0(X0,xq)
    | sdtlseqdt0(xp,xq) ),
    inference(instantiation,[status(thm)],[c_2629]) ).

cnf(c_2705,plain,
    xq = xq,
    inference(instantiation,[status(thm)],[c_1714]) ).

cnf(c_2758,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_3001,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sdtlseqdt0(xq,xp) ),
    inference(superposition,[status(thm)],[c_82,c_1713]) ).

cnf(c_3024,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sdtlseqdt0(xq,xp) ),
    inference(superposition,[status(thm)],[c_82,c_1713]) ).

cnf(c_3608,plain,
    ( xp != xq
    | xq != xq
    | ~ sdtlseqdt0(xq,xq)
    | sdtlseqdt0(xp,xq) ),
    inference(instantiation,[status(thm)],[c_2704]) ).

cnf(c_3609,plain,
    ( ~ aNaturalNumber0(xq)
    | sdtlseqdt0(xq,xq) ),
    inference(instantiation,[status(thm)],[c_83]) ).

cnf(c_4090,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sdtpldt0(xq,sK0(xq,xp)) = xp ),
    inference(superposition,[status(thm)],[c_3024,c_74]) ).

cnf(c_4267,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sdtpldt0(xq,sdtmndt0(xp,xq)) = xp ),
    inference(superposition,[status(thm)],[c_3024,c_77]) ).

cnf(c_5586,plain,
    ( ~ doDivides0(xl,xm)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl)
    | sz00 = xl
    | aNaturalNumber0(xp) ),
    inference(superposition,[status(thm)],[c_108,c_99]) ).

cnf(c_5587,plain,
    ( ~ doDivides0(xl,sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl)
    | sz00 = xl
    | aNaturalNumber0(xq) ),
    inference(superposition,[status(thm)],[c_109,c_99]) ).

cnf(c_5601,plain,
    aNaturalNumber0(xp),
    inference(forward_subsumption_resolution,[status(thm)],[c_5586,c_107,c_104,c_103,c_106]) ).

cnf(c_5602,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | aNaturalNumber0(xq) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5587,c_107,c_104,c_105]) ).

cnf(c_23315,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sdtlseqdt0(xq,xp) ),
    inference(superposition,[status(thm)],[c_82,c_1713]) ).

cnf(c_23326,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtpldt0(X0,xn) = sdtpldt0(xn,X0) ),
    inference(superposition,[status(thm)],[c_102,c_54]) ).

cnf(c_23351,plain,
    sdtlseqdt0(xq,xp),
    inference(global_subsumption_just,[status(thm)],[c_23315,c_103,c_102,c_2758,c_3001,c_5601,c_5602]) ).

cnf(c_23488,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sdtpldt0(xq,sK0(xq,xp)) = xp ),
    inference(superposition,[status(thm)],[c_23351,c_74]) ).

cnf(c_23571,plain,
    sdtpldt0(xq,sK0(xq,xp)) = xp,
    inference(global_subsumption_just,[status(thm)],[c_23488,c_103,c_102,c_2758,c_4090,c_5601,c_5602]) ).

cnf(c_23576,plain,
    ( ~ aNaturalNumber0(sK0(xq,xp))
    | ~ aNaturalNumber0(xq)
    | aNaturalNumber0(xp) ),
    inference(superposition,[status(thm)],[c_23571,c_52]) ).

cnf(c_23583,plain,
    aNaturalNumber0(xp),
    inference(global_subsumption_just,[status(thm)],[c_23576,c_5601]) ).

cnf(c_23586,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtasdt0(X0,xp) = sdtasdt0(xp,X0) ),
    inference(superposition,[status(thm)],[c_23583,c_58]) ).

cnf(c_24099,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl)
    | sdtasdt0(xl,sdtsldt0(xm,xl)) = xm
    | sz00 = xl ),
    inference(superposition,[status(thm)],[c_106,c_98]) ).

cnf(c_24129,plain,
    sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
    inference(forward_subsumption_resolution,[status(thm)],[c_24099,c_107,c_104,c_103]) ).

cnf(c_24425,plain,
    sdtasdt0(xl,xp) = xm,
    inference(light_normalisation,[status(thm)],[c_24129,c_108]) ).

cnf(c_25072,plain,
    sdtasdt0(xl,xp) = sdtasdt0(xp,xl),
    inference(superposition,[status(thm)],[c_104,c_23586]) ).

cnf(c_25929,plain,
    sdtasdt0(xp,xl) = xm,
    inference(light_normalisation,[status(thm)],[c_25072,c_24425]) ).

cnf(c_25935,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xp)
    | sz00 = xl
    | sdtlseqdt0(xp,xm) ),
    inference(superposition,[status(thm)],[c_25929,c_93]) ).

cnf(c_25944,plain,
    sdtlseqdt0(xp,xm),
    inference(forward_subsumption_resolution,[status(thm)],[c_25935,c_107,c_23583,c_104]) ).

cnf(c_25988,plain,
    ( ~ sdtlseqdt0(xm,X0)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xp)
    | sdtlseqdt0(xp,X0) ),
    inference(superposition,[status(thm)],[c_25944,c_81]) ).

cnf(c_25999,plain,
    ( ~ sdtlseqdt0(xm,X0)
    | ~ aNaturalNumber0(X0)
    | sdtlseqdt0(xp,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_25988,c_23583,c_103]) ).

cnf(c_26596,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | sdtlseqdt0(xp,sdtpldt0(xm,xn)) ),
    inference(superposition,[status(thm)],[c_110,c_25999]) ).

cnf(c_27119,plain,
    sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
    inference(superposition,[status(thm)],[c_103,c_23326]) ).

cnf(c_42561,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(superposition,[status(thm)],[c_27119,c_52]) ).

cnf(c_42573,plain,
    aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(forward_subsumption_resolution,[status(thm)],[c_42561,c_103,c_102]) ).

cnf(c_42587,plain,
    sdtlseqdt0(xp,sdtpldt0(xm,xn)),
    inference(backward_subsumption_resolution,[status(thm)],[c_26596,c_42573]) ).

cnf(c_43762,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xp)
    | sdtpldt0(xp,sK0(xp,sdtpldt0(xm,xn))) = sdtpldt0(xm,xn) ),
    inference(superposition,[status(thm)],[c_42587,c_74]) ).

cnf(c_43774,plain,
    sdtpldt0(xp,sK0(xp,sdtpldt0(xm,xn))) = sdtpldt0(xm,xn),
    inference(forward_subsumption_resolution,[status(thm)],[c_43762,c_23583,c_42573]) ).

cnf(c_44739,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sdtlseqdt0(xq,xp) ),
    inference(superposition,[status(thm)],[c_82,c_1713]) ).

cnf(c_44775,plain,
    sdtlseqdt0(xq,xp),
    inference(global_subsumption_just,[status(thm)],[c_44739,c_103,c_102,c_2758,c_3001,c_5601,c_5602]) ).

cnf(c_44929,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sdtpldt0(xq,sK0(xq,xp)) = xp ),
    inference(superposition,[status(thm)],[c_44775,c_74]) ).

cnf(c_44967,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sdtpldt0(xq,sdtmndt0(xp,xq)) = xp ),
    inference(superposition,[status(thm)],[c_44775,c_77]) ).

cnf(c_45012,plain,
    sdtpldt0(xq,sK0(xq,xp)) = xp,
    inference(global_subsumption_just,[status(thm)],[c_44929,c_103,c_102,c_2758,c_4090,c_5601,c_5602]) ).

cnf(c_45017,plain,
    ( ~ aNaturalNumber0(sK0(xq,xp))
    | ~ aNaturalNumber0(xq)
    | aNaturalNumber0(xp) ),
    inference(superposition,[status(thm)],[c_45012,c_52]) ).

cnf(c_45018,plain,
    sdtpldt0(xq,sdtmndt0(xp,xq)) = xp,
    inference(global_subsumption_just,[status(thm)],[c_44967,c_103,c_102,c_2758,c_4267,c_5601,c_5602]) ).

cnf(c_45024,plain,
    aNaturalNumber0(xp),
    inference(global_subsumption_just,[status(thm)],[c_45017,c_5601]) ).

cnf(c_45027,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtasdt0(X0,xp) = sdtasdt0(xp,X0) ),
    inference(superposition,[status(thm)],[c_45024,c_58]) ).

cnf(c_45059,plain,
    ( ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xm)
    | sdtpldt0(xm,xn) = xm ),
    inference(superposition,[status(thm)],[c_110,c_80]) ).

cnf(c_45081,plain,
    ( ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | sdtpldt0(xm,xn) = xm ),
    inference(forward_subsumption_resolution,[status(thm)],[c_45059,c_103]) ).

cnf(c_45123,plain,
    ( ~ doDivides0(xl,sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl)
    | sz00 = xl
    | aNaturalNumber0(xq) ),
    inference(superposition,[status(thm)],[c_109,c_99]) ).

cnf(c_45134,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | aNaturalNumber0(xq) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_45123,c_107,c_104,c_105]) ).

cnf(c_45161,plain,
    aNaturalNumber0(xq),
    inference(global_subsumption_just,[status(thm)],[c_45134,c_103,c_102,c_2758,c_5602]) ).

cnf(c_45172,plain,
    sdtpldt0(xq,sz00) = xq,
    inference(superposition,[status(thm)],[c_45161,c_57]) ).

cnf(c_45526,plain,
    ( sdtpldt0(xq,X0) != xp
    | ~ aNaturalNumber0(sdtmndt0(xp,xq))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xq)
    | sdtmndt0(xp,xq) = X0 ),
    inference(superposition,[status(thm)],[c_45018,c_67]) ).

cnf(c_45554,plain,
    ( sdtpldt0(xq,X0) != xp
    | ~ aNaturalNumber0(sdtmndt0(xp,xq))
    | ~ aNaturalNumber0(X0)
    | sdtmndt0(xp,xq) = X0 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_45526,c_45161]) ).

cnf(c_45562,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl)
    | sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtpldt0(xm,xn)
    | sz00 = xl ),
    inference(superposition,[status(thm)],[c_105,c_98]) ).

cnf(c_45563,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl)
    | sdtasdt0(xl,sdtsldt0(xm,xl)) = xm
    | sz00 = xl ),
    inference(superposition,[status(thm)],[c_106,c_98]) ).

cnf(c_45593,plain,
    sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
    inference(forward_subsumption_resolution,[status(thm)],[c_45563,c_107,c_104,c_103]) ).

cnf(c_45594,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtpldt0(xm,xn) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_45562,c_107,c_104]) ).

cnf(c_45603,plain,
    sdtasdt0(xl,xp) = xm,
    inference(light_normalisation,[status(thm)],[c_45593,c_108]) ).

cnf(c_46284,plain,
    ( sdtasdt0(xl,X0) != xm
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xp)
    | X0 = xp
    | sz00 = xl ),
    inference(superposition,[status(thm)],[c_45603,c_69]) ).

cnf(c_46287,plain,
    ( sdtasdt0(xl,X0) != xm
    | ~ aNaturalNumber0(X0)
    | X0 = xp ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46284,c_107,c_45024,c_104]) ).

cnf(c_46456,plain,
    sdtasdt0(xl,xp) = sdtasdt0(xp,xl),
    inference(superposition,[status(thm)],[c_104,c_45027]) ).

cnf(c_46611,plain,
    ( ~ sdtlseqdt0(X0,xp)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xp)
    | X0 = xp
    | sz00 = xl
    | sdtlseqdt0(sdtasdt0(xl,X0),xm) ),
    inference(superposition,[status(thm)],[c_45603,c_90]) ).

cnf(c_46618,plain,
    ( ~ sdtlseqdt0(X0,xp)
    | ~ aNaturalNumber0(X0)
    | X0 = xp
    | sdtlseqdt0(sdtasdt0(xl,X0),xm) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46611,c_107,c_45024,c_104]) ).

cnf(c_46700,plain,
    sdtasdt0(xp,xl) = xm,
    inference(light_normalisation,[status(thm)],[c_46456,c_45603]) ).

cnf(c_46706,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xp)
    | sz00 = xl
    | sdtlseqdt0(xp,xm) ),
    inference(superposition,[status(thm)],[c_46700,c_93]) ).

cnf(c_46714,plain,
    sdtlseqdt0(xp,xm),
    inference(forward_subsumption_resolution,[status(thm)],[c_46706,c_107,c_45024,c_104]) ).

cnf(c_46728,plain,
    ( ~ sdtlseqdt0(xm,X0)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xp)
    | sdtlseqdt0(xp,X0) ),
    inference(superposition,[status(thm)],[c_46714,c_81]) ).

cnf(c_46739,plain,
    ( ~ sdtlseqdt0(xm,X0)
    | ~ aNaturalNumber0(X0)
    | sdtlseqdt0(xp,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46728,c_45024,c_103]) ).

cnf(c_46915,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | sdtlseqdt0(xp,sdtpldt0(xm,xn)) ),
    inference(superposition,[status(thm)],[c_110,c_46739]) ).

cnf(c_48112,plain,
    sdtlseqdt0(xp,sdtpldt0(xm,xn)),
    inference(global_subsumption_just,[status(thm)],[c_46915,c_103,c_102,c_2758,c_26596]) ).

cnf(c_48117,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xp)
    | sdtpldt0(xp,sK0(xp,sdtpldt0(xm,xn))) = sdtpldt0(xm,xn) ),
    inference(superposition,[status(thm)],[c_48112,c_74]) ).

cnf(c_48122,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | sdtpldt0(xp,sK0(xp,sdtpldt0(xm,xn))) = sdtpldt0(xm,xn) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_48117,c_45024]) ).

cnf(c_49442,plain,
    sdtpldt0(xp,sK0(xp,sdtpldt0(xm,xn))) = sdtpldt0(xm,xn),
    inference(global_subsumption_just,[status(thm)],[c_48122,c_43774]) ).

cnf(c_49449,plain,
    ( ~ aNaturalNumber0(sK0(xp,sdtpldt0(xm,xn)))
    | ~ aNaturalNumber0(xp)
    | aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(superposition,[status(thm)],[c_49442,c_52]) ).

cnf(c_49463,plain,
    ( ~ aNaturalNumber0(sK0(xp,sdtpldt0(xm,xn)))
    | aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_49449,c_45024]) ).

cnf(c_49478,plain,
    aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(global_subsumption_just,[status(thm)],[c_49463,c_103,c_102,c_2758]) ).

cnf(c_49497,plain,
    sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtpldt0(xm,xn),
    inference(backward_subsumption_resolution,[status(thm)],[c_45594,c_49478]) ).

cnf(c_49501,plain,
    ( ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | sdtpldt0(xm,xn) = xm ),
    inference(backward_subsumption_resolution,[status(thm)],[c_45081,c_49478]) ).

cnf(c_62053,plain,
    ( xp != xq
    | ~ aNaturalNumber0(sdtmndt0(xp,xq))
    | ~ aNaturalNumber0(sz00)
    | sdtmndt0(xp,xq) = sz00 ),
    inference(superposition,[status(thm)],[c_45172,c_45554]) ).

cnf(c_62054,plain,
    ( ~ aNaturalNumber0(sK0(xq,xp))
    | ~ aNaturalNumber0(sdtmndt0(xp,xq))
    | sK0(xq,xp) = sdtmndt0(xp,xq) ),
    inference(superposition,[status(thm)],[c_45012,c_45554]) ).

cnf(c_62060,plain,
    ( xp != xq
    | ~ aNaturalNumber0(sdtmndt0(xp,xq))
    | sdtmndt0(xp,xq) = sz00 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_62053,c_49]) ).

cnf(c_62064,plain,
    ( ~ aNaturalNumber0(sdtmndt0(xp,xq))
    | ~ sdtlseqdt0(xq,xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sK0(xq,xp) = sdtmndt0(xp,xq) ),
    inference(superposition,[status(thm)],[c_75,c_62054]) ).

cnf(c_62065,plain,
    ( ~ aNaturalNumber0(sdtmndt0(xp,xq))
    | sK0(xq,xp) = sdtmndt0(xp,xq) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_62064,c_45161,c_45024,c_44775]) ).

cnf(c_62068,plain,
    ( ~ sdtlseqdt0(xq,xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | sK0(xq,xp) = sdtmndt0(xp,xq) ),
    inference(superposition,[status(thm)],[c_78,c_62065]) ).

cnf(c_62069,plain,
    sK0(xq,xp) = sdtmndt0(xp,xq),
    inference(forward_subsumption_resolution,[status(thm)],[c_62068,c_45161,c_45024,c_44775]) ).

cnf(c_62072,plain,
    ( ~ sdtlseqdt0(xq,xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | aNaturalNumber0(sdtmndt0(xp,xq)) ),
    inference(superposition,[status(thm)],[c_62069,c_75]) ).

cnf(c_62073,plain,
    aNaturalNumber0(sdtmndt0(xp,xq)),
    inference(forward_subsumption_resolution,[status(thm)],[c_62072,c_45161,c_45024,c_44775]) ).

cnf(c_62074,plain,
    ( xp != xq
    | sdtmndt0(xp,xq) = sz00 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_62060,c_62073]) ).

cnf(c_64699,plain,
    xp != xq,
    inference(global_subsumption_just,[status(thm)],[c_62074,c_103,c_102,c_111,c_2705,c_2758,c_3608,c_3609,c_5602]) ).

cnf(c_75485,plain,
    sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
    inference(light_normalisation,[status(thm)],[c_49497,c_109]) ).

cnf(c_75499,plain,
    ( ~ sdtlseqdt0(xq,xp)
    | ~ aNaturalNumber0(xq)
    | xp = xq
    | sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
    inference(superposition,[status(thm)],[c_75485,c_46618]) ).

cnf(c_75500,plain,
    ( sdtpldt0(xm,xn) != xm
    | ~ aNaturalNumber0(xq)
    | xp = xq ),
    inference(superposition,[status(thm)],[c_75485,c_46287]) ).

cnf(c_75501,plain,
    sdtpldt0(xm,xn) != xm,
    inference(forward_subsumption_resolution,[status(thm)],[c_75500,c_64699,c_45161]) ).

cnf(c_75502,plain,
    sdtlseqdt0(sdtpldt0(xm,xn),xm),
    inference(forward_subsumption_resolution,[status(thm)],[c_75499,c_64699,c_45161,c_44775]) ).

cnf(c_75509,plain,
    ~ sdtlseqdt0(sdtpldt0(xm,xn),xm),
    inference(backward_subsumption_resolution,[status(thm)],[c_49501,c_75501]) ).

cnf(c_75510,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_75509,c_75502]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : NUM473+1 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.12  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sat Jun 22 19:02:24 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 55.76/8.28  % SZS status Started for theBenchmark.p
% 55.76/8.28  % SZS status Theorem for theBenchmark.p
% 55.76/8.28  
% 55.76/8.28  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 55.76/8.28  
% 55.76/8.28  ------  iProver source info
% 55.76/8.28  
% 55.76/8.28  git: date: 2024-06-12 09:56:46 +0000
% 55.76/8.28  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 55.76/8.28  git: non_committed_changes: false
% 55.76/8.28  
% 55.76/8.28  ------ Parsing...
% 55.76/8.28  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 55.76/8.28  
% 55.76/8.28  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 55.76/8.28  
% 55.76/8.28  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 55.76/8.28  
% 55.76/8.28  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 55.76/8.28  ------ Proving...
% 55.76/8.28  ------ Problem Properties 
% 55.76/8.28  
% 55.76/8.28  
% 55.76/8.28  clauses                                 58
% 55.76/8.28  conjectures                             1
% 55.76/8.28  EPR                                     15
% 55.76/8.28  Horn                                    45
% 55.76/8.28  unary                                   13
% 55.76/8.28  binary                                  7
% 55.76/8.28  lits                                    198
% 55.76/8.28  lits eq                                 52
% 55.76/8.28  fd_pure                                 0
% 55.76/8.28  fd_pseudo                               0
% 55.76/8.28  fd_cond                                 6
% 55.76/8.28  fd_pseudo_cond                          9
% 55.76/8.28  AC symbols                              0
% 55.76/8.28  
% 55.76/8.28  ------ Input Options Time Limit: Unbounded
% 55.76/8.28  
% 55.76/8.28  
% 55.76/8.28  ------ 
% 55.76/8.28  Current options:
% 55.76/8.28  ------ 
% 55.76/8.28  
% 55.76/8.28  
% 55.76/8.28  
% 55.76/8.28  
% 55.76/8.28  ------ Proving...
% 55.76/8.28  
% 55.76/8.28  
% 55.76/8.28  % SZS status Theorem for theBenchmark.p
% 55.76/8.28  
% 55.76/8.28  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 55.97/8.28  
% 55.97/8.29  
%------------------------------------------------------------------------------