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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : NUM514+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n003.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 : Fri Sep 25 02:25:47 PM UTC 2026

% Result   : Theorem 3.36s 1.21s
% Output   : CNFRefutation 3.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   89 (  46 unt;   2 def)
%            Number of atoms       :  309 (  99 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  345 ( 140   ~; 133   |;  57   &)
%                                         (   9 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   79 (   0 sgn  71   !;   8   ?;   8   :)

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

fof(f5,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

fof(f30,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( X1 = sdtasdt0(X0,X2)
            & aNaturalNumber0(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( doDivides0(X0,X1)
          & X0 != sz00 )
       => ! [X2] :
            ( X2 = sdtsldt0(X1,X0)
          <=> ( X1 = sdtasdt0(X0,X2)
              & aNaturalNumber0(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).

fof(f37,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( isPrime0(X0)
      <=> ( ! [X1] :
              ( ( doDivides0(X1,X0)
                & aNaturalNumber0(X1) )
             => ( X1 = X0
                | X1 = sz10 ) )
          & X0 != sz10
          & X0 != sz00 ) ) ),
    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(f41,axiom,
    ( doDivides0(xp,sdtasdt0(xn,xm))
    & isPrime0(xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).

fof(f45,axiom,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).

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

fof(f54,axiom,
    ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
    & sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2576) ).

fof(f55,axiom,
    sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2613) ).

fof(f56,conjecture,
    doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f57,negated_conjecture,
    ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
    inference(negated_conjecture,[status(cth)],[f56]) ).

fof(f60,plain,
    ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
    inference(flattening,[],[f57]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | aNaturalNumber0(sdtasdt0(X0,X1)) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | aNaturalNumber0(sdtasdt0(X0,X1)) ),
    inference(flattening,[],[f63]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( X1 = sdtasdt0(X0,X2)
            & aNaturalNumber0(X2) ) ) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( X1 = sdtasdt0(X0,X2)
            & aNaturalNumber0(X2) ) ) ),
    inference(flattening,[],[f107]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ! [X2] :
          ( X2 = sdtsldt0(X1,X0)
        <=> ( X1 = sdtasdt0(X0,X2)
            & aNaturalNumber0(X2) ) ) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ! [X2] :
          ( X2 = sdtsldt0(X1,X0)
        <=> ( X1 = sdtasdt0(X0,X2)
            & aNaturalNumber0(X2) ) ) ),
    inference(flattening,[],[f109]) ).

fof(f121,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | ( isPrime0(X0)
      <=> ( ! [X1] :
              ( ~ doDivides0(X1,X0)
              | ~ aNaturalNumber0(X1)
              | X1 = X0
              | X1 = sz10 )
          & X0 != sz10
          & X0 != sz00 ) ) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f122,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | ( isPrime0(X0)
      <=> ( ! [X1] :
              ( ~ doDivides0(X1,X0)
              | ~ aNaturalNumber0(X1)
              | X1 = X0
              | X1 = sz10 )
          & X0 != sz10
          & X0 != sz00 ) ) ),
    inference(flattening,[],[f121]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ( ( ~ doDivides0(X0,X1)
          | ? [X2] :
              ( X1 = sdtasdt0(X0,X2)
              & aNaturalNumber0(X2) ) )
        & ( ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) )
          | doDivides0(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f108]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ( ( ~ doDivides0(X0,X1)
          | ? [X3] :
              ( sdtasdt0(X0,X3) = X1
              & aNaturalNumber0(X3) ) )
        & ( ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) )
          | doDivides0(X0,X1) ) ) ),
    inference(rectify,[],[f133]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ( ( ~ doDivides0(X0,X1)
          | ( sdtasdt0(X0,sK1(X0,X1)) = X1
            & aNaturalNumber0(sK1(X0,X1)) ) )
        & ( ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) )
          | doDivides0(X0,X1) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f134]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ! [X2] :
          ( ( sdtsldt0(X1,X0) != X2
            | ( X1 = sdtasdt0(X0,X2)
              & aNaturalNumber0(X2) ) )
          & ( sdtasdt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2)
            | X2 = sdtsldt0(X1,X0) ) ) ),
    inference(nnf_transformation,[],[f110]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ! [X2] :
          ( ( sdtsldt0(X1,X0) != X2
            | ( X1 = sdtasdt0(X0,X2)
              & aNaturalNumber0(X2) ) )
          & ( sdtasdt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2)
            | X2 = sdtsldt0(X1,X0) ) ) ),
    inference(flattening,[],[f136]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | ( ( ~ isPrime0(X0)
          | ( ! [X1] :
                ( ~ doDivides0(X1,X0)
                | ~ aNaturalNumber0(X1)
                | X1 = X0
                | X1 = sz10 )
            & X0 != sz10
            & X0 != sz00 ) )
        & ( ? [X1] :
              ( doDivides0(X1,X0)
              & aNaturalNumber0(X1)
              & X0 != X1
              & sz10 != X1 )
          | sz10 = X0
          | sz00 = X0
          | isPrime0(X0) ) ) ),
    inference(nnf_transformation,[],[f122]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | ( ( ~ isPrime0(X0)
          | ( ! [X1] :
                ( ~ doDivides0(X1,X0)
                | ~ aNaturalNumber0(X1)
                | X1 = X0
                | X1 = sz10 )
            & X0 != sz10
            & X0 != sz00 ) )
        & ( ? [X1] :
              ( doDivides0(X1,X0)
              & aNaturalNumber0(X1)
              & X0 != X1
              & sz10 != X1 )
          | sz10 = X0
          | sz00 = X0
          | isPrime0(X0) ) ) ),
    inference(flattening,[],[f138]) ).

fof(f140,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | ( ( ~ isPrime0(X0)
          | ( ! [X2] :
                ( ~ doDivides0(X2,X0)
                | ~ aNaturalNumber0(X2)
                | X0 = X2
                | sz10 = X2 )
            & X0 != sz10
            & X0 != sz00 ) )
        & ( ? [X1] :
              ( doDivides0(X1,X0)
              & aNaturalNumber0(X1)
              & X0 != X1
              & sz10 != X1 )
          | sz10 = X0
          | sz00 = X0
          | isPrime0(X0) ) ) ),
    inference(rectify,[],[f139]) ).

fof(f141,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | ( ( ~ isPrime0(X0)
          | ( ! [X2] :
                ( ~ doDivides0(X2,X0)
                | ~ aNaturalNumber0(X2)
                | X0 = X2
                | sz10 = X2 )
            & X0 != sz10
            & X0 != sz00 ) )
        & ( ( doDivides0(sK2(X0),X0)
            & aNaturalNumber0(sK2(X0))
            & sK2(X0) != X0
            & sz10 != sK2(X0) )
          | sz10 = X0
          | sz00 = X0
          | isPrime0(X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f140]) ).

fof(f143,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | aNaturalNumber0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f192,plain,
    ! [X2,X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | sdtasdt0(X0,X2) != X1
      | ~ aNaturalNumber0(X2)
      | doDivides0(X0,X1) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f194,plain,
    ! [X2,X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | sdtsldt0(X1,X0) != X2
      | aNaturalNumber0(X2) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f203,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | ~ isPrime0(X0)
      | sz00 != X0 ),
    inference(cnf_transformation,[],[f141]) ).

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

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

fof(f213,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f39]) ).

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

fof(f216,plain,
    isPrime0(xp),
    inference(cnf_transformation,[],[f41]) ).

fof(f223,plain,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    inference(cnf_transformation,[],[f45]) ).

fof(f228,plain,
    isPrime0(xr),
    inference(cnf_transformation,[],[f48]) ).

fof(f229,plain,
    doDivides0(xr,xk),
    inference(cnf_transformation,[],[f48]) ).

fof(f230,plain,
    aNaturalNumber0(xr),
    inference(cnf_transformation,[],[f48]) ).

fof(f240,plain,
    sdtasdt0(xn,xm) = sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr),
    inference(cnf_transformation,[],[f54]) ).

fof(f241,plain,
    sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sdtsldt0(xk,xr)),
    inference(cnf_transformation,[],[f55]) ).

fof(f242,plain,
    ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
    inference(cnf_transformation,[],[f60]) ).

fof(f249,plain,
    ! [X2,X0] :
      ( ~ aNaturalNumber0(sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X2)
      | doDivides0(X0,sdtasdt0(X0,X2)) ),
    inference(equality_resolution,[],[f192]) ).

fof(f251,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | aNaturalNumber0(sdtsldt0(X1,X0)) ),
    inference(equality_resolution,[],[f194]) ).

fof(f253,plain,
    ( ~ aNaturalNumber0(sz00)
    | ~ isPrime0(sz00) ),
    inference(equality_resolution,[],[f203]) ).

tcf(c_49,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f143]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f147]) ).

tcf(c_95,plain,
    ! [X0: $i,X1: $i] :
      ( doDivides0(X0,sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f249]) ).

tcf(c_99,plain,
    ! [X0: $i,X1: $i] :
      ( aNaturalNumber0(sdtsldt0(X1,X0))
      | ( X0 = sz00 )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | ~ doDivides0(X0,X1) ),
    inference(cnf_transformation,[],[f251]) ).

tcf(c_110,plain,
    ( ~ isPrime0(sz00)
    | ~ aNaturalNumber0(sz00) ),
    inference(cnf_transformation,[],[f253]) ).

tcf(c_116,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f213]) ).

tcf(c_117,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f212]) ).

tcf(c_118,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f211]) ).

tcf(c_120,plain,
    isPrime0(xp),
    inference(cnf_transformation,[],[f216]) ).

tcf(c_121,plain,
    doDivides0(xp,sdtasdt0(xn,xm)),
    inference(cnf_transformation,[],[f215]) ).

tcf(c_128,plain,
    sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
    inference(cnf_transformation,[],[f223]) ).

tcf(c_133,plain,
    aNaturalNumber0(xr),
    inference(cnf_transformation,[],[f230]) ).

tcf(c_134,plain,
    doDivides0(xr,xk),
    inference(cnf_transformation,[],[f229]) ).

tcf(c_135,plain,
    isPrime0(xr),
    inference(cnf_transformation,[],[f228]) ).

tcf(c_144,plain,
    sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm),
    inference(cnf_transformation,[],[f240]) ).

tcf(c_146,plain,
    sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sdtsldt0(xk,xr)),
    inference(cnf_transformation,[],[f241]) ).

tcf(c_147,negated_conjecture,
    ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
    inference(cnf_transformation,[],[f242]) ).

tcf(c_195,plain,
    ~ isPrime0(sz00),
    inference(global_subsumption_just,[status(thm)],[c_110,c_49,c_110]) ).

tcf(c_197,plain,
    ! [X0: $i,X1: $i] :
      ( doDivides0(X0,sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).

tcf(c_839,plain,
    ~ doDivides0(xp,sdtasdt0(xp,sdtsldt0(xk,xr))),
    inference(demodulation,[status(thm)],[c_147,c_146]) ).

tcf(c_840,plain,
    sdtasdt0(sdtasdt0(xp,sdtsldt0(xk,xr)),xr) = sdtasdt0(xn,xm),
    inference(light_normalisation,[status(thm)],[c_144,c_146]) ).

tcf(c_1612,plain,
    sz00 != xp,
    inference(resolution_lifted,[status(thm)],[c_195,c_120]) ).

tcf(c_1616,plain,
    sz00 != xr,
    inference(resolution_lifted,[status(thm)],[c_195,c_135]) ).

tcf(c_3572,definition,
    iPr_def_10 = sdtsldt0(xk,xr),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_3573,definition,
    iPr_def_11 = sdtasdt0(xp,iPr_def_10),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_3574,plain,
    ~ doDivides0(xp,iPr_def_11),
    inference(demodulation,[status(thm)],[c_839,c_3572,c_3573]) ).

tcf(c_5055,plain,
    ( doDivides0(xp,iPr_def_11)
    | ~ aNaturalNumber0(iPr_def_10)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm)],[c_3573,c_197]) ).

tcf(c_5068,plain,
    ~ aNaturalNumber0(iPr_def_10),
    inference(forward_subsumption_resolution,[status(thm)],[c_5055,c_3574,c_118]) ).

tcf(c_5105,plain,
    sdtasdt0(xn,xm) = sdtasdt0(iPr_def_11,xr),
    inference(light_normalisation,[status(thm)],[c_840,c_3572,c_3573]) ).

tcf(c_5108,plain,
    sdtsldt0(sdtasdt0(iPr_def_11,xr),xp) = xk,
    inference(demodulation,[status(thm)],[c_128,c_5105]) ).

tcf(c_5109,plain,
    doDivides0(xp,sdtasdt0(iPr_def_11,xr)),
    inference(demodulation,[status(thm)],[c_121,c_5105]) ).

tcf(c_5111,plain,
    ( aNaturalNumber0(sdtasdt0(iPr_def_11,xr))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm)],[c_5105,c_53]) ).

tcf(c_5112,plain,
    aNaturalNumber0(sdtasdt0(iPr_def_11,xr)),
    inference(forward_subsumption_resolution,[status(thm)],[c_5111,c_117,c_116]) ).

tcf(c_7126,plain,
    ( aNaturalNumber0(iPr_def_10)
    | ( sz00 = xr )
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xk)
    | ~ doDivides0(xr,xk) ),
    inference(superposition,[status(thm)],[c_3572,c_99]) ).

tcf(c_7127,plain,
    ( aNaturalNumber0(xk)
    | ( sz00 = xp )
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtasdt0(iPr_def_11,xr))
    | ~ doDivides0(xp,sdtasdt0(iPr_def_11,xr)) ),
    inference(superposition,[status(thm)],[c_5108,c_99]) ).

tcf(c_7143,plain,
    ( ( sz00 = xr )
    | ~ aNaturalNumber0(xk) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7126,c_5068,c_133,c_134]) ).

tcf(c_7146,plain,
    ( aNaturalNumber0(xk)
    | ( sz00 = xp ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7127,c_118,c_5112,c_5109]) ).

tcf(c_7207,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_7143,c_7146,c_1616,c_1612]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM514+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38  % Computer : n003.cluster.edu
% 0.10/0.38  % Model    : x86_64 x86_64
% 0.10/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38  % Memory   : 8046.5625MB
% 0.10/0.38  % OS       : Linux 6.8.0-71-generic
% 0.10/0.38  % CPULimit : 300
% 0.10/0.38  % WCLimit  : 300
% 0.10/0.38  % DateTime : Thu Sep 24 04:24:35 UTC 2026
% 0.10/0.39  % CPUTime  : 
% 0.10/0.39  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.43  Running first-order theorem proving
% 0.10/0.43  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.44  
% 0.10/0.44  % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.44  
% 0.10/0.44  % Detected problem language: tptp
% 0.10/0.45  % Proving...
% 3.36/1.21  % SZS status Started for theBenchmark.p
% 3.36/1.21  % SZS status Theorem for theBenchmark.p
% 3.36/1.21  
% 3.36/1.21  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.36/1.21  
% 3.36/1.21  % ------  iProver source info
% 3.36/1.21  
% 3.36/1.21  % git: date: 2026-07-19 20:42:38 +0200
% 3.36/1.21  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.36/1.21  % git: non_committed_changes: false
% 3.36/1.21  
% 3.36/1.21  % ------ Parsing...
% 3.36/1.21  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 3.36/1.21  
% 3.36/1.21  % ------ Preprocessing... sup_sim: 2  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 % 
% 3.36/1.21  
% 3.36/1.21  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 3.36/1.21  
% 3.36/1.21  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.36/1.21  % ------ Proving...
% 3.36/1.21  % ------ Problem Properties 
% 3.36/1.21  
% 3.36/1.21  % 
% 3.36/1.21  % clauses                               93
% 3.36/1.21  % conjectures                           0
% 3.36/1.21  % EPR                                   34
% 3.36/1.21  % Horn                                  68
% 3.36/1.21  % unary                                 35
% 3.36/1.21  % binary                                7
% 3.36/1.21  % lits                                  288
% 3.36/1.21  % lits eq                               83
% 3.36/1.21  % fd_pure                               0
% 3.36/1.21  % fd_pseudo                             0
% 3.36/1.21  % fd_cond                               15
% 3.36/1.21  % fd_pseudo_cond                        11
% 3.36/1.21  % AC symbols                            0
% 3.36/1.21  
% 3.36/1.21  % ------ Schedule dynamic 5 is on 
% 3.36/1.21  
% 3.36/1.21  % ------ no conjectures: strip conj schedule 
% 3.36/1.21  
% 3.36/1.21  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.36/1.21  
% 3.36/1.21  
% 3.36/1.21  % ------ 
% 3.36/1.21  % Current options:
% 3.36/1.21  % ------ 
% 3.36/1.21  
% 3.36/1.21  
% 3.36/1.21  % 
% 3.36/1.21  
% 3.36/1.21  % ------ Proving...
% 3.36/1.21  % 
% 3.36/1.21  
% 3.36/1.21  % SZS status Theorem for theBenchmark.p
% 3.36/1.21  
% 3.36/1.21  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.36/1.21  
%------------------------------------------------------------------------------