TSTP Solution File: NUM518+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM518+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 10:38:19 EDT 2023

% Result   : Theorem 0.20s 0.67s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   58
% Syntax   : Number of formulae    :  134 (  36 unt;  38 typ;   0 def)
%            Number of atoms       :  412 ( 160 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  461 ( 145   ~; 179   |; 114   &)
%                                         (   2 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  17   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   33 (  33 usr;  21 con; 0-3 aty)
%            Number of variables   :   93 (   0 sgn;  50   !;  15   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aNaturalNumber0: $i > $o ).

tff(decl_23,type,
    sz00: $i ).

tff(decl_24,type,
    sz10: $i ).

tff(decl_25,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_26,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_27,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(decl_28,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(decl_29,type,
    iLess0: ( $i * $i ) > $o ).

tff(decl_30,type,
    doDivides0: ( $i * $i ) > $o ).

tff(decl_31,type,
    sdtsldt0: ( $i * $i ) > $i ).

tff(decl_32,type,
    isPrime0: $i > $o ).

tff(decl_33,type,
    xn: $i ).

tff(decl_34,type,
    xm: $i ).

tff(decl_35,type,
    xp: $i ).

tff(decl_36,type,
    xk: $i ).

tff(decl_37,type,
    xr: $i ).

tff(decl_38,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk3_1: $i > $i ).

tff(decl_41,type,
    esk4_1: $i > $i ).

tff(decl_42,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    esk9_0: $i ).

tff(decl_47,type,
    esk10_0: $i ).

tff(decl_48,type,
    esk11_0: $i ).

tff(decl_49,type,
    esk12_0: $i ).

tff(decl_50,type,
    esk13_0: $i ).

tff(decl_51,type,
    esk14_0: $i ).

tff(decl_52,type,
    esk15_0: $i ).

tff(decl_53,type,
    esk16_0: $i ).

tff(decl_54,type,
    esk17_0: $i ).

tff(decl_55,type,
    esk18_0: $i ).

tff(decl_56,type,
    esk19_0: $i ).

tff(decl_57,type,
    esk20_0: $i ).

tff(decl_58,type,
    esk21_0: $i ).

tff(decl_59,type,
    esk22_0: $i ).

fof(m__1860,hypothesis,
    ( xp != sz00
    & xp != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xp = sdtasdt0(X1,X2) )
            | doDivides0(X1,xp) ) )
       => ( X1 = sz10
          | X1 = xp ) )
    & isPrime0(xp)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).

fof(mPrimDiv,axiom,
    ! [X1] :
      ( ( aNaturalNumber0(X1)
        & X1 != sz00
        & X1 != sz10 )
     => ? [X2] :
          ( aNaturalNumber0(X2)
          & doDivides0(X2,X1)
          & isPrime0(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).

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

fof(mDefPrime,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( isPrime0(X1)
      <=> ( X1 != sz00
          & X1 != sz10
          & ! [X2] :
              ( ( aNaturalNumber0(X2)
                & doDivides0(X2,X1) )
             => ( X2 = sz10
                | X2 = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).

fof(m__,conjecture,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & xn = sdtasdt0(xp,X1) )
    | doDivides0(xp,xn)
    | ? [X1] :
        ( aNaturalNumber0(X1)
        & xm = sdtasdt0(xp,X1) )
    | doDivides0(xp,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(mSortsC_01,axiom,
    ( aNaturalNumber0(sz10)
    & sz10 != sz00 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).

fof(m__2645,hypothesis,
    ( ( aNaturalNumber0(sdtsldt0(xn,xr))
      & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
      & ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtsldt0(xn,xr) = sdtasdt0(xp,X1) )
      & doDivides0(xp,sdtsldt0(xn,xr)) )
    | ( ? [X1] :
          ( aNaturalNumber0(X1)
          & xm = sdtasdt0(xp,X1) )
      & doDivides0(xp,xm) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2645) ).

fof(mMulCanc,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( X1 != sz00
       => ! [X2,X3] :
            ( ( aNaturalNumber0(X2)
              & aNaturalNumber0(X3) )
           => ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
                | sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
             => X2 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).

fof(m__2487,hypothesis,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & xn = sdtasdt0(xr,X1) )
    & doDivides0(xr,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).

fof(m__2342,hypothesis,
    ( aNaturalNumber0(xr)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xk = sdtasdt0(xr,X1) )
    & doDivides0(xr,xk)
    & xr != sz00
    & xr != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xr = sdtasdt0(X1,X2) )
            | doDivides0(X1,xr) ) )
       => ( X1 = sz10
          | X1 = xr ) )
    & isPrime0(xr) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).

fof(m__2504,hypothesis,
    ( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
          & xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
       => sdtsldt0(xn,xr) = xn )
    & aNaturalNumber0(sdtsldt0(xn,xr))
    & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(sdtsldt0(xn,xr),X1) = xn )
    & sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).

fof(mDivMin,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( doDivides0(X1,X2)
          & doDivides0(X1,sdtpldt0(X2,X3)) )
       => doDivides0(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivMin) ).

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

fof(mDefDiv,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & X2 = sdtasdt0(X1,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).

fof(mSortsC,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

fof(mLETran,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X3) )
       => sdtlseqdt0(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).

fof(mMonMul2,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( X1 != sz00
       => sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).

fof(mZeroMul,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtasdt0(X1,X2) = sz00
       => ( X1 = sz00
          | X2 = sz00 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).

fof(m__1870,hypothesis,
    ~ ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xp,X1) = xn )
      | sdtlseqdt0(xp,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).

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

fof(c_0_20,hypothesis,
    ! [X96,X97] :
      ( xp != sz00
      & xp != sz10
      & ( ~ aNaturalNumber0(X97)
        | xp != sdtasdt0(X96,X97)
        | ~ aNaturalNumber0(X96)
        | X96 = sz10
        | X96 = xp )
      & ( ~ doDivides0(X96,xp)
        | ~ aNaturalNumber0(X96)
        | X96 = sz10
        | X96 = xp )
      & isPrime0(xp)
      & aNaturalNumber0(esk9_0)
      & sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
      & doDivides0(xp,sdtasdt0(xn,xm)) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).

fof(c_0_21,plain,
    ! [X86] :
      ( ( aNaturalNumber0(esk4_1(X86))
        | ~ aNaturalNumber0(X86)
        | X86 = sz00
        | X86 = sz10 )
      & ( doDivides0(esk4_1(X86),X86)
        | ~ aNaturalNumber0(X86)
        | X86 = sz00
        | X86 = sz10 )
      & ( isPrime0(esk4_1(X86))
        | ~ aNaturalNumber0(X86)
        | X86 = sz00
        | X86 = sz10 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrimDiv])])])]) ).

cnf(c_0_22,hypothesis,
    ( X1 = sz10
    | X1 = xp
    | ~ doDivides0(X1,xp)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_23,plain,
    ( doDivides0(esk4_1(X1),X1)
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_24,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_25,hypothesis,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,hypothesis,
    xp != sz10,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_27,plain,
    ! [X83,X84] :
      ( ( X83 != sz00
        | ~ isPrime0(X83)
        | ~ aNaturalNumber0(X83) )
      & ( X83 != sz10
        | ~ isPrime0(X83)
        | ~ aNaturalNumber0(X83) )
      & ( ~ aNaturalNumber0(X84)
        | ~ doDivides0(X84,X83)
        | X84 = sz10
        | X84 = X83
        | ~ isPrime0(X83)
        | ~ aNaturalNumber0(X83) )
      & ( aNaturalNumber0(esk3_1(X83))
        | X83 = sz00
        | X83 = sz10
        | isPrime0(X83)
        | ~ aNaturalNumber0(X83) )
      & ( doDivides0(esk3_1(X83),X83)
        | X83 = sz00
        | X83 = sz10
        | isPrime0(X83)
        | ~ aNaturalNumber0(X83) )
      & ( esk3_1(X83) != sz10
        | X83 = sz00
        | X83 = sz10
        | isPrime0(X83)
        | ~ aNaturalNumber0(X83) )
      & ( esk3_1(X83) != X83
        | X83 = sz00
        | X83 = sz10
        | isPrime0(X83)
        | ~ aNaturalNumber0(X83) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).

fof(c_0_28,negated_conjecture,
    ~ ( ? [X1] :
          ( aNaturalNumber0(X1)
          & xn = sdtasdt0(xp,X1) )
      | doDivides0(xp,xn)
      | ? [X1] :
          ( aNaturalNumber0(X1)
          & xm = sdtasdt0(xp,X1) )
      | doDivides0(xp,xm) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_29,hypothesis,
    ( esk4_1(xp) = xp
    | esk4_1(xp) = sz10
    | ~ aNaturalNumber0(esk4_1(xp)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_25]),c_0_26]) ).

cnf(c_0_30,plain,
    ( aNaturalNumber0(esk4_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_31,plain,
    ( X1 != sz10
    | ~ isPrime0(X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_32,plain,
    aNaturalNumber0(sz10),
    inference(split_conjunct,[status(thm)],[mSortsC_01]) ).

fof(c_0_33,hypothesis,
    ( ( aNaturalNumber0(esk22_0)
      | aNaturalNumber0(sdtsldt0(xn,xr)) )
    & ( xm = sdtasdt0(xp,esk22_0)
      | aNaturalNumber0(sdtsldt0(xn,xr)) )
    & ( doDivides0(xp,xm)
      | aNaturalNumber0(sdtsldt0(xn,xr)) )
    & ( aNaturalNumber0(esk22_0)
      | xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
    & ( xm = sdtasdt0(xp,esk22_0)
      | xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
    & ( doDivides0(xp,xm)
      | xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
    & ( aNaturalNumber0(esk22_0)
      | aNaturalNumber0(esk21_0) )
    & ( xm = sdtasdt0(xp,esk22_0)
      | aNaturalNumber0(esk21_0) )
    & ( doDivides0(xp,xm)
      | aNaturalNumber0(esk21_0) )
    & ( aNaturalNumber0(esk22_0)
      | sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0) )
    & ( xm = sdtasdt0(xp,esk22_0)
      | sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0) )
    & ( doDivides0(xp,xm)
      | sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0) )
    & ( aNaturalNumber0(esk22_0)
      | doDivides0(xp,sdtsldt0(xn,xr)) )
    & ( xm = sdtasdt0(xp,esk22_0)
      | doDivides0(xp,sdtsldt0(xn,xr)) )
    & ( doDivides0(xp,xm)
      | doDivides0(xp,sdtsldt0(xn,xr)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2645])])]) ).

fof(c_0_34,negated_conjecture,
    ! [X116,X117] :
      ( ( ~ aNaturalNumber0(X116)
        | xn != sdtasdt0(xp,X116) )
      & ~ doDivides0(xp,xn)
      & ( ~ aNaturalNumber0(X117)
        | xm != sdtasdt0(xp,X117) )
      & ~ doDivides0(xp,xm) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).

cnf(c_0_35,plain,
    ( isPrime0(esk4_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_36,hypothesis,
    ( esk4_1(xp) = sz10
    | esk4_1(xp) = xp ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24])]),c_0_25]),c_0_26]) ).

cnf(c_0_37,plain,
    ~ isPrime0(sz10),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_31]),c_0_32])]) ).

fof(c_0_38,plain,
    ! [X29,X30,X31] :
      ( ( sdtasdt0(X29,X30) != sdtasdt0(X29,X31)
        | X30 = X31
        | ~ aNaturalNumber0(X30)
        | ~ aNaturalNumber0(X31)
        | X29 = sz00
        | ~ aNaturalNumber0(X29) )
      & ( sdtasdt0(X30,X29) != sdtasdt0(X31,X29)
        | X30 = X31
        | ~ aNaturalNumber0(X30)
        | ~ aNaturalNumber0(X31)
        | X29 = sz00
        | ~ aNaturalNumber0(X29) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).

fof(c_0_39,hypothesis,
    ( aNaturalNumber0(esk18_0)
    & xn = sdtasdt0(xr,esk18_0)
    & doDivides0(xr,xn) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2487])]) ).

fof(c_0_40,hypothesis,
    ! [X104,X105] :
      ( aNaturalNumber0(xr)
      & aNaturalNumber0(esk12_0)
      & xk = sdtasdt0(xr,esk12_0)
      & doDivides0(xr,xk)
      & xr != sz00
      & xr != sz10
      & ( ~ aNaturalNumber0(X105)
        | xr != sdtasdt0(X104,X105)
        | ~ aNaturalNumber0(X104)
        | X104 = sz10
        | X104 = xr )
      & ( ~ doDivides0(X104,xr)
        | ~ aNaturalNumber0(X104)
        | X104 = sz10
        | X104 = xr )
      & isPrime0(xr) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).

fof(c_0_41,hypothesis,
    ( aNaturalNumber0(sdtsldt0(xn,xr))
    & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
    & sdtsldt0(xn,xr) != xn
    & aNaturalNumber0(sdtsldt0(xn,xr))
    & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
    & aNaturalNumber0(esk19_0)
    & sdtpldt0(sdtsldt0(xn,xr),esk19_0) = xn
    & sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2504])])]) ).

cnf(c_0_42,hypothesis,
    ( doDivides0(xp,xm)
    | sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_43,negated_conjecture,
    ~ doDivides0(xp,xm),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

fof(c_0_44,plain,
    ! [X75,X76,X77] :
      ( ~ aNaturalNumber0(X75)
      | ~ aNaturalNumber0(X76)
      | ~ aNaturalNumber0(X77)
      | ~ doDivides0(X75,X76)
      | ~ doDivides0(X75,sdtpldt0(X76,X77))
      | doDivides0(X75,X77) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).

cnf(c_0_45,hypothesis,
    esk4_1(xp) = xp,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_24])]),c_0_25]),c_0_26]),c_0_37]) ).

cnf(c_0_46,plain,
    ( X2 = X3
    | X1 = sz00
    | sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_47,hypothesis,
    xn = sdtasdt0(xr,esk18_0),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_48,hypothesis,
    aNaturalNumber0(esk18_0),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_49,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_50,hypothesis,
    xr != sz00,
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_51,hypothesis,
    xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_52,hypothesis,
    sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0),
    inference(sr,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_53,hypothesis,
    aNaturalNumber0(sdtsldt0(xn,xr)),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_54,plain,
    ( doDivides0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ doDivides0(X1,X2)
    | ~ doDivides0(X1,sdtpldt0(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_55,hypothesis,
    doDivides0(xp,xp),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_45]),c_0_24])]),c_0_25]),c_0_26]) ).

fof(c_0_56,plain,
    ! [X15] :
      ( ( sdtpldt0(X15,sz00) = X15
        | ~ aNaturalNumber0(X15) )
      & ( X15 = sdtpldt0(sz00,X15)
        | ~ aNaturalNumber0(X15) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).

cnf(c_0_57,hypothesis,
    sdtlseqdt0(sdtsldt0(xn,xr),xn),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_58,hypothesis,
    ( X1 = esk18_0
    | sdtasdt0(xr,X1) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49])]),c_0_50]) ).

cnf(c_0_59,hypothesis,
    sdtasdt0(xr,sdtasdt0(xp,esk21_0)) = xn,
    inference(rw,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_60,hypothesis,
    aNaturalNumber0(sdtasdt0(xp,esk21_0)),
    inference(rw,[status(thm)],[c_0_53,c_0_52]) ).

fof(c_0_61,plain,
    ! [X62,X63,X65] :
      ( ( aNaturalNumber0(esk2_2(X62,X63))
        | ~ doDivides0(X62,X63)
        | ~ aNaturalNumber0(X62)
        | ~ aNaturalNumber0(X63) )
      & ( X63 = sdtasdt0(X62,esk2_2(X62,X63))
        | ~ doDivides0(X62,X63)
        | ~ aNaturalNumber0(X62)
        | ~ aNaturalNumber0(X63) )
      & ( ~ aNaturalNumber0(X65)
        | X63 != sdtasdt0(X62,X65)
        | doDivides0(X62,X63)
        | ~ aNaturalNumber0(X62)
        | ~ aNaturalNumber0(X63) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).

cnf(c_0_62,hypothesis,
    ( doDivides0(xp,X1)
    | ~ doDivides0(xp,sdtpldt0(xp,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_24])]) ).

cnf(c_0_63,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_64,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

fof(c_0_65,plain,
    ! [X46,X47,X48] :
      ( ~ aNaturalNumber0(X46)
      | ~ aNaturalNumber0(X47)
      | ~ aNaturalNumber0(X48)
      | ~ sdtlseqdt0(X46,X47)
      | ~ sdtlseqdt0(X47,X48)
      | sdtlseqdt0(X46,X48) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).

cnf(c_0_66,hypothesis,
    sdtlseqdt0(sdtasdt0(xp,esk21_0),xn),
    inference(rw,[status(thm)],[c_0_57,c_0_52]) ).

cnf(c_0_67,hypothesis,
    sdtasdt0(xp,esk21_0) = esk18_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).

fof(c_0_68,plain,
    ! [X58,X59] :
      ( ~ aNaturalNumber0(X58)
      | ~ aNaturalNumber0(X59)
      | X58 = sz00
      | sdtlseqdt0(X59,sdtasdt0(X59,X58)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).

cnf(c_0_69,hypothesis,
    ( doDivides0(xp,xm)
    | aNaturalNumber0(esk21_0) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

fof(c_0_70,plain,
    ! [X34,X35] :
      ( ~ aNaturalNumber0(X34)
      | ~ aNaturalNumber0(X35)
      | sdtasdt0(X34,X35) != sz00
      | X34 = sz00
      | X35 = sz00 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).

cnf(c_0_71,plain,
    ( X1 = sdtasdt0(X2,esk2_2(X2,X1))
    | ~ doDivides0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_72,hypothesis,
    doDivides0(xp,sz00),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_55]),c_0_64]),c_0_24])]) ).

cnf(c_0_73,plain,
    ( aNaturalNumber0(esk2_2(X1,X2))
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_74,plain,
    ( sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_75,hypothesis,
    sdtlseqdt0(esk18_0,xn),
    inference(rw,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_76,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_77,plain,
    ( X1 = sz00
    | sdtlseqdt0(X2,sdtasdt0(X2,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_78,hypothesis,
    aNaturalNumber0(esk21_0),
    inference(sr,[status(thm)],[c_0_69,c_0_43]) ).

fof(c_0_79,hypothesis,
    ! [X99] :
      ( ( ~ aNaturalNumber0(X99)
        | sdtpldt0(xp,X99) != xn )
      & ~ sdtlseqdt0(xp,xn) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1870])])]) ).

cnf(c_0_80,plain,
    ( X1 = sz00
    | X2 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtasdt0(X1,X2) != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_70]) ).

cnf(c_0_81,hypothesis,
    sdtasdt0(xp,esk2_2(xp,sz00)) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_24]),c_0_64])]) ).

cnf(c_0_82,hypothesis,
    aNaturalNumber0(esk2_2(xp,sz00)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_72]),c_0_64]),c_0_24])]) ).

cnf(c_0_83,hypothesis,
    ( sdtlseqdt0(X1,xn)
    | ~ sdtlseqdt0(X1,esk18_0)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_48])]) ).

cnf(c_0_84,hypothesis,
    ( esk21_0 = sz00
    | sdtlseqdt0(xp,esk18_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_67]),c_0_24]),c_0_78])]) ).

cnf(c_0_85,hypothesis,
    ~ sdtlseqdt0(xp,xn),
    inference(split_conjunct,[status(thm)],[c_0_79]) ).

cnf(c_0_86,hypothesis,
    esk2_2(xp,sz00) = sz00,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_24])]),c_0_25]) ).

cnf(c_0_87,hypothesis,
    esk21_0 = sz00,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_24])]),c_0_85]) ).

cnf(c_0_88,hypothesis,
    sdtasdt0(xp,sz00) = sz00,
    inference(rw,[status(thm)],[c_0_81,c_0_86]) ).

fof(c_0_89,plain,
    ! [X22] :
      ( ( sdtasdt0(X22,sz00) = sz00
        | ~ aNaturalNumber0(X22) )
      & ( sz00 = sdtasdt0(sz00,X22)
        | ~ aNaturalNumber0(X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).

cnf(c_0_90,hypothesis,
    esk18_0 = sz00,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_87]),c_0_88]) ).

cnf(c_0_91,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | xn != sdtasdt0(xp,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_92,plain,
    ( sdtasdt0(X1,sz00) = sz00
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_89]) ).

cnf(c_0_93,hypothesis,
    sdtasdt0(xr,sz00) = xn,
    inference(rw,[status(thm)],[c_0_47,c_0_90]) ).

cnf(c_0_94,negated_conjecture,
    sz00 != xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_64]),c_0_24])]) ).

cnf(c_0_95,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_49])]),c_0_94]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM518+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n007.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Fri Aug 25 14:18:26 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.67  % Version  : CSE_E---1.5
% 0.20/0.67  % Problem  : theBenchmark.p
% 0.20/0.67  % Proof found
% 0.20/0.67  % SZS status Theorem for theBenchmark.p
% 0.20/0.67  % SZS output start Proof
% See solution above
% 0.20/0.68  % Total time : 0.103000 s
% 0.20/0.68  % SZS output end Proof
% 0.20/0.68  % Total time : 0.107000 s
%------------------------------------------------------------------------------