TSTP Solution File: NUM516+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n024.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 : Fri May  3 02:49:41 EDT 2024

% Result   : Theorem 17.13s 3.13s
% Output   : CNFRefutation 17.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  114 (  26 unt;   0 def)
%            Number of atoms       :  447 ( 173 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  580 ( 247   ~; 233   |;  77   &)
%                                         (   6 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  128 (   0 sgn  90   !;   4   ?)

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

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(f16,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sz00 = sdtpldt0(X0,X1)
       => ( sz00 = X1
          & sz00 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).

fof(f20,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => sdtlseqdt0(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).

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(f24,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X0,X1)
          & X0 != X1 )
       => ! [X2] :
            ( aNaturalNumber0(X2)
           => ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
              & sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
              & sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
              & sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).

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(f37,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( isPrime0(X0)
      <=> ( ! [X1] :
              ( ( doDivides0(X1,X0)
                & aNaturalNumber0(X1) )
             => ( X0 = X1
                | sz10 = X1 ) )
          & sz10 != X0
          & sz00 != X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).

fof(f39,axiom,
    ( aNaturalNumber0(xp)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).

fof(f48,axiom,
    ( isPrime0(xr)
    & doDivides0(xr,xk)
    & aNaturalNumber0(xr) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).

fof(f52,axiom,
    doDivides0(xr,xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).

fof(f53,axiom,
    ( sdtlseqdt0(sdtsldt0(xn,xr),xn)
    & xn != sdtsldt0(xn,xr) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).

fof(f55,conjecture,
    ( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    & sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f56,negated_conjecture,
    ~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
      & sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ),
    inference(negated_conjecture,[],[f55]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f59]) ).

fof(f67,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f76,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(f77,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,[],[f76]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ( sz00 = X1
        & sz00 = X0 )
      | sz00 != sdtpldt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( sz00 = X1
        & sz00 = X0 )
      | sz00 != sdtpldt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f80]) ).

fof(f88,plain,
    ! [X0] :
      ( sdtlseqdt0(X0,X0)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f21]) ).

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

fof(f95,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
            & sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
            & sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
            & sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
          | ~ aNaturalNumber0(X2) )
      | ~ sdtlseqdt0(X0,X1)
      | X0 = X1
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
            & sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
            & sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
            & sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
          | ~ aNaturalNumber0(X2) )
      | ~ sdtlseqdt0(X0,X1)
      | X0 = X1
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f95]) ).

fof(f107,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(f108,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,[],[f107]) ).

fof(f119,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(f120,plain,
    ! [X0] :
      ( ( isPrime0(X0)
      <=> ( ! [X1] :
              ( X0 = X1
              | sz10 = X1
              | ~ doDivides0(X1,X0)
              | ~ aNaturalNumber0(X1) )
          & sz10 != X0
          & sz00 != X0 ) )
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f119]) ).

fof(f126,plain,
    ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    | sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f137,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,[],[f108]) ).

fof(f138,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,[],[f137]) ).

fof(f139,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,[],[f120]) ).

fof(f140,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,[],[f139]) ).

fof(f141,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,[],[f140]) ).

fof(f142,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(f143,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])],[f141,f142]) ).

fof(f146,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f149,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f153,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz00) = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f164,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( sz00 = X0
      | sz00 != sdtpldt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f176,plain,
    ! [X0] :
      ( sdtlseqdt0(X0,X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f184,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
      | ~ aNaturalNumber0(X2)
      | ~ sdtlseqdt0(X0,X1)
      | X0 = X1
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f196,plain,
    ! [X2,X0,X1] :
      ( aNaturalNumber0(X2)
      | sdtsldt0(X1,X0) != X2
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f204,plain,
    ! [X0] :
      ( sz00 != X0
      | ~ isPrime0(X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f214,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f39]) ).

fof(f215,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f39]) ).

fof(f216,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f39]) ).

fof(f231,plain,
    aNaturalNumber0(xr),
    inference(cnf_transformation,[],[f48]) ).

fof(f233,plain,
    isPrime0(xr),
    inference(cnf_transformation,[],[f48]) ).

fof(f239,plain,
    doDivides0(xr,xn),
    inference(cnf_transformation,[],[f52]) ).

fof(f240,plain,
    xn != sdtsldt0(xn,xr),
    inference(cnf_transformation,[],[f53]) ).

fof(f241,plain,
    sdtlseqdt0(sdtsldt0(xn,xr),xn),
    inference(cnf_transformation,[],[f53]) ).

fof(f243,plain,
    ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    | sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f253,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtsldt0(X1,X0))
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f196]) ).

fof(f255,plain,
    ( ~ isPrime0(sz00)
    | ~ aNaturalNumber0(sz00) ),
    inference(equality_resolution,[],[f204]) ).

cnf(c_49,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_52,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_57,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_66,plain,
    ( sdtpldt0(X0,X1) != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X0 = X2 ),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_71,plain,
    ( sdtpldt0(X0,X1) != sz00
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = sz00 ),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_79,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtlseqdt0(X0,X0) ),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_80,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ sdtlseqdt0(X1,X0)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f177]) ).

cnf(c_84,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X0 = X1
    | sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_100,plain,
    ( ~ doDivides0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = sz00
    | aNaturalNumber0(sdtsldt0(X1,X0)) ),
    inference(cnf_transformation,[],[f253]) ).

cnf(c_112,plain,
    ( ~ aNaturalNumber0(sz00)
    | ~ isPrime0(sz00) ),
    inference(cnf_transformation,[],[f255]) ).

cnf(c_116,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f216]) ).

cnf(c_117,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f215]) ).

cnf(c_118,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_133,plain,
    isPrime0(xr),
    inference(cnf_transformation,[],[f233]) ).

cnf(c_135,plain,
    aNaturalNumber0(xr),
    inference(cnf_transformation,[],[f231]) ).

cnf(c_141,plain,
    doDivides0(xr,xn),
    inference(cnf_transformation,[],[f239]) ).

cnf(c_142,plain,
    sdtlseqdt0(sdtsldt0(xn,xr),xn),
    inference(cnf_transformation,[],[f241]) ).

cnf(c_143,plain,
    sdtsldt0(xn,xr) != xn,
    inference(cnf_transformation,[],[f240]) ).

cnf(c_145,negated_conjecture,
    ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    | sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
    inference(cnf_transformation,[],[f243]) ).

cnf(c_150,plain,
    ( ~ aNaturalNumber0(sz00)
    | sdtpldt0(sz00,sz00) = sz00 ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_168,plain,
    ( sdtpldt0(sz00,sz00) != sz00
    | ~ aNaturalNumber0(sz00)
    | sz00 = sz00 ),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_191,plain,
    ~ isPrime0(sz00),
    inference(global_subsumption_just,[status(thm)],[c_112,c_49,c_112]) ).

cnf(c_1192,plain,
    sz00 != xr,
    inference(resolution_lifted,[status(thm)],[c_191,c_133]) ).

cnf(c_2556,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_2558,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_2560,plain,
    ( X0 != X1
    | X2 != X3
    | sdtpldt0(X0,X2) = sdtpldt0(X1,X3) ),
    theory(equality) ).

cnf(c_2562,plain,
    ( X0 != X1
    | X2 != X3
    | ~ sdtlseqdt0(X1,X3)
    | sdtlseqdt0(X0,X2) ),
    theory(equality) ).

cnf(c_3851,plain,
    ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != X0
    | sdtpldt0(sdtpldt0(xn,xm),xp) != X1
    | ~ sdtlseqdt0(X0,X1)
    | sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(instantiation,[status(thm)],[c_2562]) ).

cnf(c_3854,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(xp)
    | aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_3869,plain,
    ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),X0)
    | ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ aNaturalNumber0(X0)
    | sdtpldt0(sdtpldt0(xn,xm),xp) = X0 ),
    inference(instantiation,[status(thm)],[c_80]) ).

cnf(c_3884,plain,
    ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != X0
    | sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
    | sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(instantiation,[status(thm)],[c_3851]) ).

cnf(c_3889,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | aNaturalNumber0(sdtpldt0(xn,xm)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_3969,plain,
    ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
    | sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    | sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(instantiation,[status(thm)],[c_3884]) ).

cnf(c_3976,plain,
    ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
    | sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
    inference(instantiation,[status(thm)],[c_3869]) ).

cnf(c_4127,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
    | sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(instantiation,[status(thm)],[c_79]) ).

cnf(c_4218,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(xm)
    | aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_4508,plain,
    ( sdtpldt0(sdtsldt0(xn,xr),xm) != sdtpldt0(xn,xm)
    | xp != xp
    | sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
    inference(instantiation,[status(thm)],[c_2560]) ).

cnf(c_4940,plain,
    xp = xp,
    inference(instantiation,[status(thm)],[c_2556]) ).

cnf(c_9176,plain,
    ( X0 != X1
    | xr != X1
    | X0 = xr ),
    inference(instantiation,[status(thm)],[c_2558]) ).

cnf(c_9177,plain,
    ( sz00 != sz00
    | xr != sz00
    | sz00 = xr ),
    inference(instantiation,[status(thm)],[c_9176]) ).

cnf(c_25443,plain,
    ( ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
    | ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(xp)
    | sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_84,c_145]) ).

cnf(c_29201,plain,
    ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
    | ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm)) ),
    inference(global_subsumption_just,[status(thm)],[c_25443,c_118,c_117,c_116,c_3889,c_4508,c_4940,c_25443]) ).

cnf(c_29202,plain,
    ( ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
    | sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
    inference(renaming,[status(thm)],[c_29201]) ).

cnf(c_29205,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
    | ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
    | ~ aNaturalNumber0(sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | sdtsldt0(xn,xr) = xn ),
    inference(superposition,[status(thm)],[c_84,c_29202]) ).

cnf(c_29479,plain,
    ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
    inference(global_subsumption_just,[status(thm)],[c_29205,c_118,c_117,c_142,c_143,c_4218,c_29205]) ).

cnf(c_29480,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xr))
    | sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
    inference(renaming,[status(thm)],[c_29479]) ).

cnf(c_29481,plain,
    ( ~ doDivides0(xr,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xr)
    | sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | sz00 = xr ),
    inference(superposition,[status(thm)],[c_100,c_29480]) ).

cnf(c_33613,plain,
    ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
    | ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(xp)
    | sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ),
    inference(resolution,[status(thm)],[c_66,c_145]) ).

cnf(c_34050,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
    | sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ),
    inference(global_subsumption_just,[status(thm)],[c_33613,c_135,c_118,c_117,c_116,c_141,c_1192,c_3854,c_3889,c_3969,c_3976,c_4127,c_29481,c_33613]) ).

cnf(c_34060,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
    | ~ aNaturalNumber0(sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | sdtsldt0(xn,xr) = xn ),
    inference(resolution,[status(thm)],[c_34050,c_66]) ).

cnf(c_35285,plain,
    ~ aNaturalNumber0(sdtsldt0(xn,xr)),
    inference(global_subsumption_just,[status(thm)],[c_34060,c_118,c_117,c_143,c_4218,c_34060]) ).

cnf(c_35291,plain,
    ( ~ doDivides0(xr,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xr)
    | xr = sz00 ),
    inference(resolution,[status(thm)],[c_35285,c_100]) ).

cnf(c_35292,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_35291,c_9177,c_1192,c_168,c_150,c_141,c_49,c_118,c_135]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.31  % Computer : n024.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu May  2 19:42:35 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.17/0.42  Running first-order theorem proving
% 0.17/0.42  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
% 17.13/3.13  % SZS status Started for theBenchmark.p
% 17.13/3.13  % SZS status Theorem for theBenchmark.p
% 17.13/3.13  
% 17.13/3.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.13/3.13  
% 17.13/3.13  ------  iProver source info
% 17.13/3.13  
% 17.13/3.13  git: date: 2024-05-02 19:28:25 +0000
% 17.13/3.13  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.13/3.13  git: non_committed_changes: false
% 17.13/3.13  
% 17.13/3.13  ------ Parsing...
% 17.13/3.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 17.13/3.13  
% 17.13/3.13  ------ 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 
% 17.13/3.13  
% 17.13/3.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 17.13/3.13  
% 17.13/3.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 17.13/3.13  ------ Proving...
% 17.13/3.13  ------ Problem Properties 
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  clauses                                 89
% 17.13/3.13  conjectures                             1
% 17.13/3.13  EPR                                     33
% 17.13/3.13  Horn                                    64
% 17.13/3.13  unary                                   30
% 17.13/3.13  binary                                  8
% 17.13/3.13  lits                                    285
% 17.13/3.13  lits eq                                 79
% 17.13/3.13  fd_pure                                 0
% 17.13/3.13  fd_pseudo                               0
% 17.13/3.13  fd_cond                                 15
% 17.13/3.13  fd_pseudo_cond                          11
% 17.13/3.13  AC symbols                              0
% 17.13/3.13  
% 17.13/3.13  ------ Input Options Time Limit: Unbounded
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  ------ 
% 17.13/3.13  Current options:
% 17.13/3.13  ------ 
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  ------ Proving...
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  % SZS status Theorem for theBenchmark.p
% 17.13/3.13  
% 17.13/3.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.13/3.13  
% 17.13/3.13  
%------------------------------------------------------------------------------