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LisaST---0.9.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : LisaST---0.9
% Problem  : NUM503+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:12:57 AM UTC 2026

% Result   : Theorem 6.64s 6.03s
% Output   : CNFRefutation 6.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   83 (  23 unt;   0 def)
%            Number of atoms       :  334 ( 174 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  366 ( 115   ~; 191   |;  47   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   50 (   0 sgn  15   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m_MulZero,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sdtasdt0(X0,sz00) = sz00 ) ) ).

fof(mMulCanc,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( X0 != sz00
       => ! [X1,X2] :
            ( ( aNaturalNumber0(X2)
              & aNaturalNumber0(X1) )
           => ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
                | sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
             => X1 = X2 ) ) ) ) ).

fof(mLETran,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X0,X1) )
       => sdtlseqdt0(X0,X2) ) ) ).

fof(mLETotal,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X0)
          & X1 != X0 )
        | sdtlseqdt0(X0,X1) ) ) ).

fof(mMonMul,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X2)
          & X1 != X2
          & X0 != sz00 )
       => ( 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) ) ) ) ).

fof(mMonMul2,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( X0 != sz00
       => sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ) ).

fof(m__1837,hypothesis,
    ( aNaturalNumber0(xp)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ) ).

fof(m__1860,hypothesis,
    ( doDivides0(xp,sdtasdt0(xn,xm))
    & ? [X0] :
        ( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
        & aNaturalNumber0(X0) )
    & isPrime0(xp)
    & ! [X0] :
        ( ( ( doDivides0(X0,xp)
            | ? [X1] :
                ( xp = sdtasdt0(X0,X1)
                & aNaturalNumber0(X1) ) )
          & aNaturalNumber0(X0) )
       => ( X0 = xp
          | X0 = sz10 ) )
    & xp != sz10
    & xp != sz00 ) ).

fof(m__2075,hypothesis,
    ~ ( sdtlseqdt0(xp,xm)
      | ? [X0] :
          ( sdtpldt0(xp,X0) = xm
          & aNaturalNumber0(X0) ) ) ).

fof(m__2287,hypothesis,
    ( sdtlseqdt0(xm,xp)
    & ? [X0] :
        ( sdtpldt0(xm,X0) = xp
        & aNaturalNumber0(X0) )
    & xm != xp
    & sdtlseqdt0(xn,xp)
    & ? [X0] :
        ( sdtpldt0(xn,X0) = xp
        & aNaturalNumber0(X0) )
    & xn != xp ) ).

fof(m__2306,hypothesis,
    ( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & aNaturalNumber0(xk) ) ).

fof(m__2315,hypothesis,
    ~ ( xk = sz10
      | xk = sz00 ) ).

fof(m__2389,hypothesis,
    ( sdtlseqdt0(xp,xk)
    & ? [X0] :
        ( sdtpldt0(xp,X0) = xk
        & aNaturalNumber0(X0) ) ) ).

fof(m__,conjecture,
    ( ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
      | ? [X0] :
          ( sdtpldt0(sdtasdt0(xp,xm),X0) = sdtasdt0(xp,xk)
          & aNaturalNumber0(X0) ) )
    & sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
    & ( sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
      | ? [X0] :
          ( sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm)
          & aNaturalNumber0(X0) ) )
    & sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ) ).

fof(negated_conjecture,negated_conjecture,
    ~ ( ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
        | ? [X0] :
            ( sdtpldt0(sdtasdt0(xp,xm),X0) = sdtasdt0(xp,xk)
            & aNaturalNumber0(X0) ) )
      & sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
      & ( sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
        | ? [X0] :
            ( sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm)
            & aNaturalNumber0(X0) ) )
      & sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
    inference(negate_conjecture,[status(cth)],[m__]) ).

cnf(c13,plain,
    ( sdtasdt0(X0,sz00) = sz00
    | ~ aNaturalNumber0(X0) ),
    inference(clausification,[status(esa)],[m_MulZero]) ).

cnf(c20,plain,
    ( sdtasdt0(X2,X0) != sdtasdt0(X1,X0)
    | X2 = X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X0)
    | X0 = sz00 ),
    inference(clausification,[status(esa)],[mMulCanc]) ).

cnf(c32,plain,
    ( ~ aNaturalNumber0(X1)
    | ~ sdtlseqdt0(X0,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X0)
    | ~ sdtlseqdt0(X2,X1)
    | sdtlseqdt0(X0,X1) ),
    inference(clausification,[status(esa)],[mLETran]) ).

cnf(c34,plain,
    ( sdtlseqdt0(X1,X0)
    | sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X0) ),
    inference(clausification,[status(esa)],[mLETotal]) ).

cnf(c40,plain,
    ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X2,X0))
    | ~ aNaturalNumber0(X1)
    | ~ sdtlseqdt0(X1,X0)
    | ~ aNaturalNumber0(X2)
    | X2 = sz00
    | X1 = X0
    | ~ aNaturalNumber0(X0) ),
    inference(clausification,[status(esa)],[mMonMul]) ).

cnf(c42,plain,
    ( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X0,X2))
    | ~ aNaturalNumber0(X1)
    | ~ sdtlseqdt0(X1,X0)
    | ~ aNaturalNumber0(X2)
    | X2 = sz00
    | X1 = X0
    | ~ aNaturalNumber0(X0) ),
    inference(clausification,[status(esa)],[mMonMul]) ).

cnf(c45,plain,
    ( sdtlseqdt0(X1,sdtasdt0(X1,X0))
    | X0 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X0) ),
    inference(clausification,[status(esa)],[mMonMul2]) ).

cnf(c70,plain,
    aNaturalNumber0(xn),
    inference(clausification,[status(esa)],[m__1837]) ).

cnf(c71,plain,
    aNaturalNumber0(xm),
    inference(clausification,[status(esa)],[m__1837]) ).

cnf(c72,plain,
    aNaturalNumber0(xp),
    inference(clausification,[status(esa)],[m__1837]) ).

cnf(c89,plain,
    xp != sz00,
    inference(clausification,[status(esa)],[m__1860]) ).

cnf(c95,plain,
    sdtasdt0(xn,xm) = sdtasdt0(xp,sK99),
    inference(clausification,[status(esa)],[m__1860]) ).

cnf(c99,plain,
    ( sdtpldt0(xp,X0) != xm
    | ~ aNaturalNumber0(X0) ),
    inference(clausification,[status(esa)],[m__2075]) ).

cnf(c100,plain,
    ~ sdtlseqdt0(xp,xm),
    inference(clausification,[status(esa)],[m__2075]) ).

cnf(c101,plain,
    xn != xp,
    inference(clausification,[status(esa)],[m__2287]) ).

cnf(c104,plain,
    sdtlseqdt0(xn,xp),
    inference(clausification,[status(esa)],[m__2287]) ).

cnf(c109,plain,
    aNaturalNumber0(xk),
    inference(clausification,[status(esa)],[m__2306]) ).

cnf(c110,plain,
    sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
    inference(clausification,[status(esa)],[m__2306]) ).

cnf(c112,plain,
    xk != sz00,
    inference(clausification,[status(esa)],[m__2315]) ).

cnf(c130,plain,
    aNaturalNumber0(sK109),
    inference(clausification,[status(esa)],[m__2389]) ).

cnf(c131,plain,
    sdtpldt0(xp,sK109) = xk,
    inference(clausification,[status(esa)],[m__2389]) ).

cnf(c132,plain,
    sdtlseqdt0(xp,xk),
    inference(clausification,[status(esa)],[m__2389]) ).

cnf(c136,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(clausification,[status(esa)],[negated_conjecture]) ).

cnf(d0,plain,
    sdtasdt0(xn,sz00) = sz00,
    inference(resolution,[status(thm)],[c13,c70]) ).

cnf(d1,plain,
    ( ~ aNaturalNumber0(sK109)
    | xk != xm ),
    inference(superposition,[status(thm)],[c131,c99]) ).

cnf(d2,plain,
    xk != xm,
    inference(resolution,[status(thm)],[c130,d1]) ).

cnf(d3,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | xn = X0
    | xm = sz00
    | sdtasdt0(xp,xk) != sdtasdt0(X0,xm) ),
    inference(superposition,[status(thm)],[c110,c20]) ).

cnf(d4,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X0)
    | xm = sz00
    | xn = X0
    | sdtasdt0(xp,xk) != sdtasdt0(X0,xm) ),
    inference(resolution,[status(thm)],[c70,d3]) ).

cnf(d5,plain,
    ( ~ aNaturalNumber0(X0)
    | xm = sz00
    | xn = X0
    | sdtasdt0(xp,xk) != sdtasdt0(X0,xm) ),
    inference(resolution,[status(thm)],[c71,d4]) ).

cnf(d6,plain,
    sdtasdt0(xp,xk) = sdtasdt0(xp,sK99),
    inference(demodulation,[status(thm)],[c95,c110]) ).

cnf(d7,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
    | ~ sdtlseqdt0(xm,xk)
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xp)
    | xm = xk
    | xp = sz00 ),
    inference(resolution,[status(thm)],[c40,c136]) ).

cnf(d8,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(xp)
    | xp = sz00
    | xm = xk
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c71,d7]) ).

cnf(d9,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(xk)
    | xp = sz00
    | xm = xk
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c72,d8]) ).

cnf(d10,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | xp = sz00
    | xm = xk
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c109,d9]) ).

cnf(d11,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | xm = xk
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c89,d10]) ).

cnf(d12,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | xm = xk
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
    | ~ sdtlseqdt0(xn,xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | xn = xp
    | xm = sz00 ),
    inference(resolution,[status(thm)],[c42,d11]) ).

cnf(d13,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ sdtlseqdt0(xn,xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | xm = xk
    | xm = sz00
    | xn = xp
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c70,d12]) ).

cnf(d14,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ sdtlseqdt0(xn,xp)
    | ~ aNaturalNumber0(xp)
    | xm = xk
    | xm = sz00
    | xn = xp
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c71,d13]) ).

cnf(d15,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ sdtlseqdt0(xn,xp)
    | xm = xk
    | xm = sz00
    | xn = xp
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c72,d14]) ).

cnf(d16,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | ~ sdtlseqdt0(xn,xp)
    | xm = xk
    | xm = sz00
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c101,d15]) ).

cnf(d17,plain,
    ( ~ sdtlseqdt0(xm,xk)
    | xm = xk
    | xm = sz00
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c104,d16]) ).

cnf(d18,plain,
    ( sdtlseqdt0(xk,xm)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xk)
    | xm = xk
    | xm = sz00
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[d17,c34]) ).

cnf(d19,plain,
    ( sdtlseqdt0(xk,xm)
    | ~ aNaturalNumber0(xk)
    | xm = xk
    | xm = sz00
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c71,d18]) ).

cnf(d20,plain,
    ( sdtlseqdt0(xk,xm)
    | xm = xk
    | xm = sz00
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
    inference(resolution,[status(thm)],[c109,d19]) ).

cnf(d21,plain,
    ( sdtlseqdt0(xk,xm)
    | xm = xk
    | xm = sz00
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtasdt0(xp,sK99) = sdtasdt0(xp,xm) ),
    inference(demodulation,[status(thm)],[d20,c95]) ).

cnf(d22,plain,
    ( sdtlseqdt0(xp,X0)
    | ~ sdtlseqdt0(xk,X0)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xk) ),
    inference(resolution,[status(thm)],[c32,c132]) ).

cnf(d23,plain,
    ( ~ sdtlseqdt0(xk,X0)
    | sdtlseqdt0(xp,X0)
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(X0) ),
    inference(resolution,[status(thm)],[c72,d22]) ).

cnf(d24,plain,
    ( ~ sdtlseqdt0(xk,X0)
    | sdtlseqdt0(xp,X0)
    | ~ aNaturalNumber0(X0) ),
    inference(resolution,[status(thm)],[c109,d23]) ).

cnf(d25,plain,
    ( xm = xk
    | xm = sz00
    | sdtasdt0(xp,sK99) = sdtasdt0(xp,xm)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
    | sdtlseqdt0(xp,xm)
    | ~ aNaturalNumber0(xm) ),
    inference(resolution,[status(thm)],[d24,d21]) ).

cnf(d26,plain,
    ( sdtlseqdt0(xp,xm)
    | xm = xk
    | xm = sz00
    | sdtasdt0(xp,sK99) = sdtasdt0(xp,xm)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
    inference(resolution,[status(thm)],[c71,d25]) ).

cnf(d27,plain,
    ( xm = xk
    | xm = sz00
    | sdtasdt0(xp,sK99) = sdtasdt0(xp,xm)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
    inference(resolution,[status(thm)],[c100,d26]) ).

cnf(d28,plain,
    ( xm = xk
    | xm = sz00
    | sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
    inference(demodulation,[status(thm)],[d27,d6]) ).

cnf(d29,plain,
    ( xm = xk
    | xm = sz00
    | sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
    | sdtasdt0(xp,xm) != sdtasdt0(xp,xm) ),
    inference(equality_factoring,[status(thm)],[d28]) ).

cnf(d30,plain,
    ( xm = xk
    | xm = sz00
    | sdtasdt0(xp,xk) = sdtasdt0(xp,xm) ),
    inference(equality_resolution,[status(thm)],[d29]) ).

cnf(d31,plain,
    ( xm = xk
    | xm = sz00
    | ~ aNaturalNumber0(X0)
    | xm = sz00
    | xn = X0
    | sdtasdt0(xp,xm) != sdtasdt0(X0,xm) ),
    inference(superposition,[status(thm)],[d30,d5]) ).

cnf(d32,plain,
    ( ~ aNaturalNumber0(xp)
    | xm = xk
    | xm = sz00
    | xn = xp ),
    inference(equality_resolution,[status(thm)],[d31]) ).

cnf(d33,plain,
    ( xm = xk
    | xm = sz00
    | xn = xp ),
    inference(resolution,[status(thm)],[c72,d32]) ).

cnf(d34,plain,
    ( xm = xk
    | xm = sz00 ),
    inference(resolution,[status(thm)],[c101,d33]) ).

cnf(d35,plain,
    ( xm = sz00
    | xm != xm ),
    inference(superposition,[status(thm)],[d34,d2]) ).

cnf(d36,plain,
    xm = sz00,
    inference(equality_resolution,[status(thm)],[d35]) ).

cnf(d37,plain,
    sdtasdt0(xn,sz00) = sdtasdt0(xp,xk),
    inference(demodulation,[status(thm)],[c110,d36]) ).

cnf(d38,plain,
    sz00 = sdtasdt0(xp,xk),
    inference(demodulation,[status(thm)],[d37,d0]) ).

cnf(d39,plain,
    ( ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(xp)
    | xk = sz00
    | sdtlseqdt0(xp,sz00) ),
    inference(superposition,[status(thm)],[d38,c45]) ).

cnf(d40,plain,
    ( sdtlseqdt0(xp,sz00)
    | ~ aNaturalNumber0(xk)
    | xk = sz00 ),
    inference(resolution,[status(thm)],[c72,d39]) ).

cnf(d41,plain,
    ( sdtlseqdt0(xp,sz00)
    | xk = sz00 ),
    inference(resolution,[status(thm)],[c109,d40]) ).

cnf(d42,plain,
    sdtlseqdt0(xp,sz00),
    inference(resolution,[status(thm)],[c112,d41]) ).

cnf(d43,plain,
    ~ sdtlseqdt0(xp,sz00),
    inference(demodulation,[status(thm)],[c100,d36]) ).

cnf(d44,plain,
    $false,
    inference(resolution,[status(thm)],[d43,d42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM503+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37  % Computer : n009.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Sat Sep 26 03:00:59 UTC 2026
% 0.10/0.38  % CPUTime  : 
% 0.10/0.38  Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.64/6.03  % SZS status Theorem for theBenchmark.p
% 6.64/6.03  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------