TSTP Solution File: NUM507+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM507+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 : n032.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 10:38:12 EDT 2023

% Result   : Theorem 29.73s 29.84s
% Output   : CNFRefutation 29.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  113 (  23 unt;  31 typ;   0 def)
%            Number of atoms       :  380 ( 135 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  467 ( 169   ~; 182   |;  95   &)
%                                         (   2 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    4 (   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    :   26 (  26 usr;  14 con; 0-3 aty)
%            Number of variables   :   93 (   0 sgn;  52   !;  11   ?;   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 ).

fof(m__,conjecture,
    ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp)
    & ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
      | sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

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(mDefLE,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & sdtpldt0(X1,X3) = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).

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

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(m__2377,hypothesis,
    ( xk != xp
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xk,X1) = xp )
    & sdtlseqdt0(xk,xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2377) ).

fof(m__2362,hypothesis,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xr,X1) = xk )
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
    & doDivides0(xr,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).

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

fof(mMonAdd,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != X2
          & sdtlseqdt0(X1,X2) )
       => ! [X3] :
            ( aNaturalNumber0(X3)
           => ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
              & sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
              & sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
              & sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).

fof(m__2306,hypothesis,
    ( aNaturalNumber0(xk)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).

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

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

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

fof(mDivLE,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( doDivides0(X1,X2)
          & X2 != sz00 )
       => sdtlseqdt0(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).

fof(c_0_18,negated_conjecture,
    ~ ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp)
      & ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
        | sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_19,negated_conjecture,
    ! [X109] :
      ( ( ~ aNaturalNumber0(X109)
        | sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X109) != sdtpldt0(sdtpldt0(xn,xm),xp)
        | sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) )
      & ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
        | sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).

fof(c_0_20,plain,
    ! [X10,X11] :
      ( ~ aNaturalNumber0(X10)
      | ~ aNaturalNumber0(X11)
      | sdtpldt0(X10,X11) = sdtpldt0(X11,X10) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

fof(c_0_21,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_22,plain,
    ! [X36,X37,X39] :
      ( ( aNaturalNumber0(esk1_2(X36,X37))
        | ~ sdtlseqdt0(X36,X37)
        | ~ aNaturalNumber0(X36)
        | ~ aNaturalNumber0(X37) )
      & ( sdtpldt0(X36,esk1_2(X36,X37)) = X37
        | ~ sdtlseqdt0(X36,X37)
        | ~ aNaturalNumber0(X36)
        | ~ aNaturalNumber0(X37) )
      & ( ~ aNaturalNumber0(X39)
        | sdtpldt0(X36,X39) != X37
        | sdtlseqdt0(X36,X37)
        | ~ aNaturalNumber0(X36)
        | ~ aNaturalNumber0(X37) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).

fof(c_0_23,plain,
    ! [X6,X7] :
      ( ~ aNaturalNumber0(X6)
      | ~ aNaturalNumber0(X7)
      | aNaturalNumber0(sdtpldt0(X6,X7)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

cnf(c_0_24,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_27,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])]) ).

fof(c_0_28,hypothesis,
    ( xk != xp
    & aNaturalNumber0(esk15_0)
    & sdtpldt0(xk,esk15_0) = xp
    & sdtlseqdt0(xk,xp) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2377])]) ).

cnf(c_0_29,plain,
    ( sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X2,X1) != X3
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_30,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

fof(c_0_31,hypothesis,
    ( aNaturalNumber0(esk13_0)
    & sdtpldt0(xr,esk13_0) = xk
    & aNaturalNumber0(esk14_0)
    & sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
    & doDivides0(xr,sdtasdt0(xn,xm)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).

cnf(c_0_32,negated_conjecture,
    ( sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).

cnf(c_0_33,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

fof(c_0_34,plain,
    ! [X51,X52,X53] :
      ( ( sdtpldt0(X53,X51) != sdtpldt0(X53,X52)
        | ~ aNaturalNumber0(X53)
        | X51 = X52
        | ~ sdtlseqdt0(X51,X52)
        | ~ aNaturalNumber0(X51)
        | ~ aNaturalNumber0(X52) )
      & ( sdtlseqdt0(sdtpldt0(X53,X51),sdtpldt0(X53,X52))
        | ~ aNaturalNumber0(X53)
        | X51 = X52
        | ~ sdtlseqdt0(X51,X52)
        | ~ aNaturalNumber0(X51)
        | ~ aNaturalNumber0(X52) )
      & ( sdtpldt0(X51,X53) != sdtpldt0(X52,X53)
        | ~ aNaturalNumber0(X53)
        | X51 = X52
        | ~ sdtlseqdt0(X51,X52)
        | ~ aNaturalNumber0(X51)
        | ~ aNaturalNumber0(X52) )
      & ( sdtlseqdt0(sdtpldt0(X51,X53),sdtpldt0(X52,X53))
        | ~ aNaturalNumber0(X53)
        | X51 = X52
        | ~ sdtlseqdt0(X51,X52)
        | ~ aNaturalNumber0(X51)
        | ~ aNaturalNumber0(X52) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).

cnf(c_0_35,plain,
    ( sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_36,hypothesis,
    sdtlseqdt0(xk,xp),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_37,hypothesis,
    aNaturalNumber0(xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_38,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_30]) ).

cnf(c_0_39,hypothesis,
    sdtpldt0(xr,esk13_0) = xk,
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_40,hypothesis,
    aNaturalNumber0(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_41,negated_conjecture,
    ( sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
    | ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm)))
    | ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_33])]) ).

cnf(c_0_42,plain,
    ( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X2))
    | X1 = X3
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_43,hypothesis,
    ( sdtlseqdt0(X1,xp)
    | ~ sdtlseqdt0(X1,xk)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33]),c_0_37])]) ).

cnf(c_0_44,hypothesis,
    sdtlseqdt0(xr,xk),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_26]),c_0_40])]) ).

fof(c_0_45,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_46,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])])])]) ).

fof(c_0_47,plain,
    ! [X44,X45] :
      ( ~ aNaturalNumber0(X44)
      | ~ aNaturalNumber0(X45)
      | ~ sdtlseqdt0(X44,X45)
      | ~ sdtlseqdt0(X45,X44)
      | X44 = X45 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).

fof(c_0_48,plain,
    ! [X26,X27,X28] :
      ( ( sdtpldt0(X26,X27) != sdtpldt0(X26,X28)
        | X27 = X28
        | ~ aNaturalNumber0(X26)
        | ~ aNaturalNumber0(X27)
        | ~ aNaturalNumber0(X28) )
      & ( sdtpldt0(X27,X26) != sdtpldt0(X28,X26)
        | X27 = X28
        | ~ aNaturalNumber0(X26)
        | ~ aNaturalNumber0(X27)
        | ~ aNaturalNumber0(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).

cnf(c_0_49,negated_conjecture,
    ( sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
    | xr = xp
    | ~ sdtlseqdt0(xr,xp)
    | ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33]),c_0_26])]) ).

cnf(c_0_50,hypothesis,
    sdtlseqdt0(xr,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_26])]) ).

cnf(c_0_51,hypothesis,
    ( X1 = sz10
    | X1 = xp
    | ~ doDivides0(X1,xp)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_52,plain,
    ( doDivides0(esk4_1(X1),X1)
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_53,hypothesis,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_54,hypothesis,
    xp != sz10,
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

fof(c_0_55,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])])])])]) ).

cnf(c_0_56,plain,
    ( X1 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_57,hypothesis,
    xk != xp,
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_58,plain,
    ( X1 = X3
    | sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_59,negated_conjecture,
    ( sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
    | xr = xp
    | ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).

cnf(c_0_60,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_51,c_0_52]),c_0_33])]),c_0_53]),c_0_54]) ).

cnf(c_0_61,plain,
    ( aNaturalNumber0(esk4_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_62,plain,
    ( X1 != sz10
    | ~ isPrime0(X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_63,plain,
    aNaturalNumber0(sz10),
    inference(split_conjunct,[status(thm)],[mSortsC_01]) ).

cnf(c_0_64,hypothesis,
    ~ sdtlseqdt0(xp,xk),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_36]),c_0_37]),c_0_33])]),c_0_57]) ).

cnf(c_0_65,hypothesis,
    ( sdtlseqdt0(X1,xk)
    | ~ sdtlseqdt0(X1,xr)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_44]),c_0_37]),c_0_26])]) ).

fof(c_0_66,plain,
    ! [X78,X79] :
      ( ~ aNaturalNumber0(X78)
      | ~ aNaturalNumber0(X79)
      | ~ doDivides0(X78,X79)
      | X79 = sz00
      | sdtlseqdt0(X78,X79) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).

cnf(c_0_67,negated_conjecture,
    ( xr = xp
    | X1 = xr
    | sdtpldt0(X1,sdtpldt0(xn,xm)) != sdtpldt0(xp,sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_26])]) ).

cnf(c_0_68,plain,
    ( isPrime0(esk4_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_69,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_60,c_0_61]),c_0_33])]),c_0_53]),c_0_54]) ).

cnf(c_0_70,plain,
    ~ isPrime0(sz10),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_62]),c_0_63])]) ).

cnf(c_0_71,hypothesis,
    ~ sdtlseqdt0(xp,xr),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_33])]) ).

cnf(c_0_72,plain,
    ( X2 = sz00
    | sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_73,hypothesis,
    xr != sz00,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_74,negated_conjecture,
    ( xr = xp
    | ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_67]),c_0_33])]) ).

cnf(c_0_75,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

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

cnf(c_0_77,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_68,c_0_69]),c_0_33])]),c_0_53]),c_0_54]),c_0_70]) ).

cnf(c_0_78,hypothesis,
    ~ doDivides0(xp,xr),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_26]),c_0_33])]),c_0_73]) ).

cnf(c_0_79,negated_conjecture,
    xr = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_30]),c_0_75]),c_0_76])]) ).

cnf(c_0_80,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_52,c_0_77]),c_0_33])]),c_0_53]),c_0_54]) ).

cnf(c_0_81,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_80])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : NUM507+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.30  % Computer : n032.cluster.edu
% 0.08/0.30  % Model    : x86_64 x86_64
% 0.08/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30  % Memory   : 8042.1875MB
% 0.08/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30  % CPULimit   : 300
% 0.08/0.30  % WCLimit    : 300
% 0.08/0.30  % DateTime   : Fri Aug 25 13:39:13 EDT 2023
% 0.08/0.30  % CPUTime  : 
% 0.14/0.45  start to proof: theBenchmark
% 29.73/29.84  % Version  : CSE_E---1.5
% 29.73/29.84  % Problem  : theBenchmark.p
% 29.73/29.84  % Proof found
% 29.73/29.84  % SZS status Theorem for theBenchmark.p
% 29.73/29.84  % SZS output start Proof
% See solution above
% 29.73/29.85  % Total time : 29.379000 s
% 29.73/29.85  % SZS output end Proof
% 29.73/29.85  % Total time : 29.383000 s
%------------------------------------------------------------------------------