TSTP Solution File: NUM494+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM494+1 : TPTP v7.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n138.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.625MB
% OS       : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan  8 15:21:32 EST 2018

% Result   : Theorem 7.28s
% Output   : CNFRefutation 7.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   51
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  208 (  29 unt;   0 def)
%            Number of atoms       :  904 ( 175 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives : 1178 ( 482   ~; 582   |;  96   &)
%                                         (   3 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :  237 (   3 sgn 104   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ( isPrime0(xp)
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__1860) ).

fof(3,axiom,
    equal(xr,sdtmndt0(xn,xp)),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__1883) ).

fof(5,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mAddComm) ).

fof(12,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | ( ~ equal(X2,X1)
          & sdtlseqdt0(X2,X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mLETotal) ).

fof(15,axiom,
    sdtlseqdt0(xp,xn),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__1870) ).

fof(17,axiom,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__1837) ).

fof(19,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( ~ equal(X1,X2)
          & sdtlseqdt0(X1,X2) )
       => ! [X3] :
            ( aNaturalNumber0(X3)
           => ( ~ equal(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
              & sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
              & ~ equal(sdtpldt0(X1,X3),sdtpldt0(X2,X3))
              & sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mMonAdd) ).

fof(23,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & equal(sdtpldt0(X1,X3),X2) ) ) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mDefLE) ).

fof(24,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => equal(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(X1,sdtpldt0(X2,X3))) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mAddAsso) ).

fof(27,axiom,
    ( ~ equal(xr,xn)
    & sdtlseqdt0(xr,xn) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__1894) ).

fof(31,conjecture,
    ( ~ equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    & sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m__) ).

fof(35,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
       => ! [X3] :
            ( equal(X3,sdtmndt0(X2,X1))
          <=> ( aNaturalNumber0(X3)
              & equal(sdtpldt0(X1,X3),X2) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mDefDiff) ).

fof(37,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( isPrime0(X1)
      <=> ( ~ equal(X1,sz00)
          & ~ equal(X1,sz10)
          & ! [X2] :
              ( ( aNaturalNumber0(X2)
                & doDivides0(X2,X1) )
             => ( equal(X2,sz10)
                | equal(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mDefPrime) ).

fof(38,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mSortsC) ).

fof(39,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mSortsB) ).

fof(41,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( equal(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
          | equal(sdtpldt0(X2,X1),sdtpldt0(X3,X1)) )
       => equal(X2,X3) ) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',mAddCanc) ).

fof(45,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1',m_AddZero) ).

fof(47,negated_conjecture,
    ~ ( ~ equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
      & sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(assume_negation,[status(cth)],[31]) ).

cnf(54,plain,
    isPrime0(xp),
    inference(split_conjunct,[status(thm)],[2]) ).

cnf(55,plain,
    xr = sdtmndt0(xn,xp),
    inference(split_conjunct,[status(thm)],[3]) ).

fof(59,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(60,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | equal(sdtpldt0(X3,X4),sdtpldt0(X4,X3)) ),
    inference(variable_rename,[status(thm)],[59]) ).

cnf(61,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[60]) ).

fof(90,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | sdtlseqdt0(X1,X2)
      | ( ~ equal(X2,X1)
        & sdtlseqdt0(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(91,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | sdtlseqdt0(X3,X4)
      | ( ~ equal(X4,X3)
        & sdtlseqdt0(X4,X3) ) ),
    inference(variable_rename,[status(thm)],[90]) ).

fof(92,plain,
    ! [X3,X4] :
      ( ( ~ equal(X4,X3)
        | sdtlseqdt0(X3,X4)
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) )
      & ( sdtlseqdt0(X4,X3)
        | sdtlseqdt0(X3,X4)
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) ) ),
    inference(distribute,[status(thm)],[91]) ).

cnf(93,plain,
    ( sdtlseqdt0(X2,X1)
    | sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[92]) ).

cnf(101,plain,
    sdtlseqdt0(xp,xn),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(105,plain,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[17]) ).

cnf(106,plain,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[17]) ).

cnf(107,plain,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(109,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(X1,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ! [X3] :
          ( ~ aNaturalNumber0(X3)
          | ( ~ equal(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
            & sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
            & ~ equal(sdtpldt0(X1,X3),sdtpldt0(X2,X3))
            & sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(110,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | equal(X4,X5)
      | ~ sdtlseqdt0(X4,X5)
      | ! [X6] :
          ( ~ aNaturalNumber0(X6)
          | ( ~ equal(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
            & sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
            & ~ equal(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
            & sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6)) ) ) ),
    inference(variable_rename,[status(thm)],[109]) ).

fof(111,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X6)
      | ( ~ equal(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
        & sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
        & ~ equal(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
        & sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6)) )
      | equal(X4,X5)
      | ~ sdtlseqdt0(X4,X5)
      | ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5) ),
    inference(shift_quantors,[status(thm)],[110]) ).

fof(112,plain,
    ! [X4,X5,X6] :
      ( ( ~ equal(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
        | ~ aNaturalNumber0(X6)
        | equal(X4,X5)
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
        | ~ aNaturalNumber0(X6)
        | equal(X4,X5)
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( ~ equal(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
        | ~ aNaturalNumber0(X6)
        | equal(X4,X5)
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
        | ~ aNaturalNumber0(X6)
        | equal(X4,X5)
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) ) ),
    inference(distribute,[status(thm)],[111]) ).

cnf(115,plain,
    ( X2 = X1
    | sdtlseqdt0(sdtpldt0(X3,X2),sdtpldt0(X3,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[112]) ).

fof(130,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ( ( ~ sdtlseqdt0(X1,X2)
          | ? [X3] :
              ( aNaturalNumber0(X3)
              & equal(sdtpldt0(X1,X3),X2) ) )
        & ( ! [X3] :
              ( ~ aNaturalNumber0(X3)
              | ~ equal(sdtpldt0(X1,X3),X2) )
          | sdtlseqdt0(X1,X2) ) ) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(131,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ( ( ~ sdtlseqdt0(X4,X5)
          | ? [X6] :
              ( aNaturalNumber0(X6)
              & equal(sdtpldt0(X4,X6),X5) ) )
        & ( ! [X7] :
              ( ~ aNaturalNumber0(X7)
              | ~ equal(sdtpldt0(X4,X7),X5) )
          | sdtlseqdt0(X4,X5) ) ) ),
    inference(variable_rename,[status(thm)],[130]) ).

fof(132,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ( ( ~ sdtlseqdt0(X4,X5)
          | ( aNaturalNumber0(esk2_2(X4,X5))
            & equal(sdtpldt0(X4,esk2_2(X4,X5)),X5) ) )
        & ( ! [X7] :
              ( ~ aNaturalNumber0(X7)
              | ~ equal(sdtpldt0(X4,X7),X5) )
          | sdtlseqdt0(X4,X5) ) ) ),
    inference(skolemize,[status(esa)],[131]) ).

fof(133,plain,
    ! [X4,X5,X7] :
      ( ( ( ~ aNaturalNumber0(X7)
          | ~ equal(sdtpldt0(X4,X7),X5)
          | sdtlseqdt0(X4,X5) )
        & ( ~ sdtlseqdt0(X4,X5)
          | ( aNaturalNumber0(esk2_2(X4,X5))
            & equal(sdtpldt0(X4,esk2_2(X4,X5)),X5) ) ) )
      | ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5) ),
    inference(shift_quantors,[status(thm)],[132]) ).

fof(134,plain,
    ! [X4,X5,X7] :
      ( ( ~ aNaturalNumber0(X7)
        | ~ equal(sdtpldt0(X4,X7),X5)
        | sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( aNaturalNumber0(esk2_2(X4,X5))
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( equal(sdtpldt0(X4,esk2_2(X4,X5)),X5)
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) ) ),
    inference(distribute,[status(thm)],[133]) ).

cnf(137,plain,
    ( sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[134]) ).

fof(138,plain,
    ! [X1,X2,X3] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X3)
      | equal(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(X1,sdtpldt0(X2,X3))) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(139,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | equal(sdtpldt0(sdtpldt0(X4,X5),X6),sdtpldt0(X4,sdtpldt0(X5,X6))) ),
    inference(variable_rename,[status(thm)],[138]) ).

cnf(140,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[139]) ).

cnf(151,plain,
    sdtlseqdt0(xr,xn),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(152,plain,
    xr != xn,
    inference(split_conjunct,[status(thm)],[27]) ).

fof(163,negated_conjecture,
    ( equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(fof_nnf,[status(thm)],[47]) ).

cnf(164,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(split_conjunct,[status(thm)],[163]) ).

fof(176,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ sdtlseqdt0(X1,X2)
      | ! [X3] :
          ( ( ~ equal(X3,sdtmndt0(X2,X1))
            | ( aNaturalNumber0(X3)
              & equal(sdtpldt0(X1,X3),X2) ) )
          & ( ~ aNaturalNumber0(X3)
            | ~ equal(sdtpldt0(X1,X3),X2)
            | equal(X3,sdtmndt0(X2,X1)) ) ) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(177,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ sdtlseqdt0(X4,X5)
      | ! [X6] :
          ( ( ~ equal(X6,sdtmndt0(X5,X4))
            | ( aNaturalNumber0(X6)
              & equal(sdtpldt0(X4,X6),X5) ) )
          & ( ~ aNaturalNumber0(X6)
            | ~ equal(sdtpldt0(X4,X6),X5)
            | equal(X6,sdtmndt0(X5,X4)) ) ) ),
    inference(variable_rename,[status(thm)],[176]) ).

fof(178,plain,
    ! [X4,X5,X6] :
      ( ( ( ~ equal(X6,sdtmndt0(X5,X4))
          | ( aNaturalNumber0(X6)
            & equal(sdtpldt0(X4,X6),X5) ) )
        & ( ~ aNaturalNumber0(X6)
          | ~ equal(sdtpldt0(X4,X6),X5)
          | equal(X6,sdtmndt0(X5,X4)) ) )
      | ~ sdtlseqdt0(X4,X5)
      | ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5) ),
    inference(shift_quantors,[status(thm)],[177]) ).

fof(179,plain,
    ! [X4,X5,X6] :
      ( ( aNaturalNumber0(X6)
        | ~ equal(X6,sdtmndt0(X5,X4))
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( equal(sdtpldt0(X4,X6),X5)
        | ~ equal(X6,sdtmndt0(X5,X4))
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( ~ aNaturalNumber0(X6)
        | ~ equal(sdtpldt0(X4,X6),X5)
        | equal(X6,sdtmndt0(X5,X4))
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) ) ),
    inference(distribute,[status(thm)],[178]) ).

cnf(180,plain,
    ( X3 = sdtmndt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[179]) ).

cnf(181,plain,
    ( sdtpldt0(X2,X3) = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | X3 != sdtmndt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[179]) ).

cnf(182,plain,
    ( aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | X3 != sdtmndt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[179]) ).

fof(186,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( ( ~ isPrime0(X1)
          | ( ~ equal(X1,sz00)
            & ~ equal(X1,sz10)
            & ! [X2] :
                ( ~ aNaturalNumber0(X2)
                | ~ doDivides0(X2,X1)
                | equal(X2,sz10)
                | equal(X2,X1) ) ) )
        & ( equal(X1,sz00)
          | equal(X1,sz10)
          | ? [X2] :
              ( aNaturalNumber0(X2)
              & doDivides0(X2,X1)
              & ~ equal(X2,sz10)
              & ~ equal(X2,X1) )
          | isPrime0(X1) ) ) ),
    inference(fof_nnf,[status(thm)],[37]) ).

fof(187,plain,
    ! [X3] :
      ( ~ aNaturalNumber0(X3)
      | ( ( ~ isPrime0(X3)
          | ( ~ equal(X3,sz00)
            & ~ equal(X3,sz10)
            & ! [X4] :
                ( ~ aNaturalNumber0(X4)
                | ~ doDivides0(X4,X3)
                | equal(X4,sz10)
                | equal(X4,X3) ) ) )
        & ( equal(X3,sz00)
          | equal(X3,sz10)
          | ? [X5] :
              ( aNaturalNumber0(X5)
              & doDivides0(X5,X3)
              & ~ equal(X5,sz10)
              & ~ equal(X5,X3) )
          | isPrime0(X3) ) ) ),
    inference(variable_rename,[status(thm)],[186]) ).

fof(188,plain,
    ! [X3] :
      ( ~ aNaturalNumber0(X3)
      | ( ( ~ isPrime0(X3)
          | ( ~ equal(X3,sz00)
            & ~ equal(X3,sz10)
            & ! [X4] :
                ( ~ aNaturalNumber0(X4)
                | ~ doDivides0(X4,X3)
                | equal(X4,sz10)
                | equal(X4,X3) ) ) )
        & ( equal(X3,sz00)
          | equal(X3,sz10)
          | ( aNaturalNumber0(esk3_1(X3))
            & doDivides0(esk3_1(X3),X3)
            & ~ equal(esk3_1(X3),sz10)
            & ~ equal(esk3_1(X3),X3) )
          | isPrime0(X3) ) ) ),
    inference(skolemize,[status(esa)],[187]) ).

fof(189,plain,
    ! [X3,X4] :
      ( ( ( ( ( ~ aNaturalNumber0(X4)
              | ~ doDivides0(X4,X3)
              | equal(X4,sz10)
              | equal(X4,X3) )
            & ~ equal(X3,sz00)
            & ~ equal(X3,sz10) )
          | ~ isPrime0(X3) )
        & ( equal(X3,sz00)
          | equal(X3,sz10)
          | ( aNaturalNumber0(esk3_1(X3))
            & doDivides0(esk3_1(X3),X3)
            & ~ equal(esk3_1(X3),sz10)
            & ~ equal(esk3_1(X3),X3) )
          | isPrime0(X3) ) )
      | ~ aNaturalNumber0(X3) ),
    inference(shift_quantors,[status(thm)],[188]) ).

fof(190,plain,
    ! [X3,X4] :
      ( ( ~ aNaturalNumber0(X4)
        | ~ doDivides0(X4,X3)
        | equal(X4,sz10)
        | equal(X4,X3)
        | ~ isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( ~ equal(X3,sz00)
        | ~ isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( ~ equal(X3,sz10)
        | ~ isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( aNaturalNumber0(esk3_1(X3))
        | equal(X3,sz00)
        | equal(X3,sz10)
        | isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( doDivides0(esk3_1(X3),X3)
        | equal(X3,sz00)
        | equal(X3,sz10)
        | isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( ~ equal(esk3_1(X3),sz10)
        | equal(X3,sz00)
        | equal(X3,sz10)
        | isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( ~ equal(esk3_1(X3),X3)
        | equal(X3,sz00)
        | equal(X3,sz10)
        | isPrime0(X3)
        | ~ aNaturalNumber0(X3) ) ),
    inference(distribute,[status(thm)],[189]) ).

cnf(196,plain,
    ( ~ aNaturalNumber0(X1)
    | ~ isPrime0(X1)
    | X1 != sz00 ),
    inference(split_conjunct,[status(thm)],[190]) ).

cnf(198,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[38]) ).

fof(199,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtpldt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[39]) ).

fof(200,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtpldt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[199]) ).

cnf(201,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[200]) ).

fof(209,plain,
    ! [X1,X2,X3] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X3)
      | ( ~ equal(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
        & ~ equal(sdtpldt0(X2,X1),sdtpldt0(X3,X1)) )
      | equal(X2,X3) ),
    inference(fof_nnf,[status(thm)],[41]) ).

fof(210,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | ( ~ equal(sdtpldt0(X4,X5),sdtpldt0(X4,X6))
        & ~ equal(sdtpldt0(X5,X4),sdtpldt0(X6,X4)) )
      | equal(X5,X6) ),
    inference(variable_rename,[status(thm)],[209]) ).

fof(211,plain,
    ! [X4,X5,X6] :
      ( ( ~ equal(sdtpldt0(X4,X5),sdtpldt0(X4,X6))
        | equal(X5,X6)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) )
      & ( ~ equal(sdtpldt0(X5,X4),sdtpldt0(X6,X4))
        | equal(X5,X6)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) ) ),
    inference(distribute,[status(thm)],[210]) ).

cnf(213,plain,
    ( X2 = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtpldt0(X3,X2) != sdtpldt0(X3,X1) ),
    inference(split_conjunct,[status(thm)],[211]) ).

fof(224,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    inference(fof_nnf,[status(thm)],[45]) ).

fof(225,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtpldt0(X2,sz00),X2)
        & equal(X2,sdtpldt0(sz00,X2)) ) ),
    inference(variable_rename,[status(thm)],[224]) ).

fof(226,plain,
    ! [X2] :
      ( ( equal(sdtpldt0(X2,sz00),X2)
        | ~ aNaturalNumber0(X2) )
      & ( equal(X2,sdtpldt0(sz00,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[225]) ).

cnf(227,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[226]) ).

cnf(228,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[226]) ).

cnf(234,plain,
    ( sz00 != xp
    | ~ aNaturalNumber0(xp) ),
    inference(spm,[status(thm)],[196,54,theory(equality)]) ).

cnf(235,plain,
    ( sz00 != xp
    | $false ),
    inference(rw,[status(thm)],[234,105,theory(equality)]) ).

cnf(236,plain,
    sz00 != xp,
    inference(cn,[status(thm)],[235,theory(equality)]) ).

cnf(256,plain,
    ( sdtlseqdt0(X1,xn)
    | sdtlseqdt0(xn,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[93,107,theory(equality)]) ).

cnf(410,plain,
    ( aNaturalNumber0(sdtmndt0(X1,X2))
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[182,theory(equality)]) ).

cnf(411,plain,
    ( aNaturalNumber0(X1)
    | xr != X1
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[182,55,theory(equality)]) ).

cnf(412,plain,
    ( aNaturalNumber0(X1)
    | xr != X1
    | $false
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[411,101,theory(equality)]) ).

cnf(413,plain,
    ( aNaturalNumber0(X1)
    | xr != X1
    | $false
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[412,105,theory(equality)]) ).

cnf(414,plain,
    ( aNaturalNumber0(X1)
    | xr != X1
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[413,107,theory(equality)]) ).

cnf(415,plain,
    ( aNaturalNumber0(X1)
    | xr != X1 ),
    inference(cn,[status(thm)],[414,theory(equality)]) ).

cnf(417,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[213,228,theory(equality)]) ).

cnf(427,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[417,198,theory(equality)]) ).

cnf(428,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[427,theory(equality)]) ).

cnf(488,plain,
    ( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[181,theory(equality)]) ).

cnf(489,plain,
    ( sdtpldt0(xp,X1) = xn
    | xr != X1
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[181,55,theory(equality)]) ).

cnf(490,plain,
    ( sdtpldt0(xp,X1) = xn
    | xr != X1
    | $false
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[489,101,theory(equality)]) ).

cnf(491,plain,
    ( sdtpldt0(xp,X1) = xn
    | xr != X1
    | $false
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[490,105,theory(equality)]) ).

cnf(492,plain,
    ( sdtpldt0(xp,X1) = xn
    | xr != X1
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[491,107,theory(equality)]) ).

cnf(493,plain,
    ( sdtpldt0(xp,X1) = xn
    | xr != X1 ),
    inference(cn,[status(thm)],[492,theory(equality)]) ).

cnf(505,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[228,140,theory(equality)]) ).

cnf(507,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[140,227,theory(equality)]) ).

cnf(509,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[164,140,theory(equality)]) ).

cnf(511,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[61,140,theory(equality)]) ).

cnf(513,plain,
    ( sdtpldt0(sdtpldt0(X2,X1),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[140,61,theory(equality)]) ).

cnf(526,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2))
    | $false
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[505,198,theory(equality)]) ).

cnf(527,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[526,theory(equality)]) ).

cnf(530,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[507,198,theory(equality)]) ).

cnf(531,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[530,theory(equality)]) ).

cnf(535,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
    | $false
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[509,105,theory(equality)]) ).

cnf(536,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
    | $false
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[535,106,theory(equality)]) ).

cnf(537,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[536,107,theory(equality)]) ).

cnf(538,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
    inference(cn,[status(thm)],[537,theory(equality)]) ).

cnf(597,plain,
    ( sdtmndt0(X1,X2) = X3
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[180,137]) ).

cnf(598,plain,
    ( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2)) ),
    inference(er,[status(thm)],[597,theory(equality)]) ).

cnf(975,plain,
    ( xn = sdtpldt0(X1,xp)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xp)
    | xr != X1 ),
    inference(spm,[status(thm)],[61,493,theory(equality)]) ).

cnf(985,plain,
    ( sdtpldt0(xn,X2) = sdtpldt0(xp,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xp)
    | xr != X1 ),
    inference(spm,[status(thm)],[140,493,theory(equality)]) ).

cnf(986,plain,
    ( X1 = X2
    | sdtlseqdt0(xn,sdtpldt0(xp,X1))
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | xr != X2 ),
    inference(spm,[status(thm)],[115,493,theory(equality)]) ).

cnf(999,plain,
    ( xn = sdtpldt0(X1,xp)
    | ~ aNaturalNumber0(X1)
    | $false
    | xr != X1 ),
    inference(rw,[status(thm)],[975,105,theory(equality)]) ).

cnf(1000,plain,
    ( xn = sdtpldt0(X1,xp)
    | ~ aNaturalNumber0(X1)
    | xr != X1 ),
    inference(cn,[status(thm)],[999,theory(equality)]) ).

cnf(1020,plain,
    ( sdtpldt0(xn,X2) = sdtpldt0(xp,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false
    | xr != X1 ),
    inference(rw,[status(thm)],[985,105,theory(equality)]) ).

cnf(1021,plain,
    ( sdtpldt0(xn,X2) = sdtpldt0(xp,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | xr != X1 ),
    inference(cn,[status(thm)],[1020,theory(equality)]) ).

cnf(1022,plain,
    ( X1 = X2
    | sdtlseqdt0(xn,sdtpldt0(xp,X1))
    | ~ sdtlseqdt0(X2,X1)
    | $false
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | xr != X2 ),
    inference(rw,[status(thm)],[986,105,theory(equality)]) ).

cnf(1023,plain,
    ( X1 = X2
    | sdtlseqdt0(xn,sdtpldt0(xp,X1))
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | xr != X2 ),
    inference(cn,[status(thm)],[1022,theory(equality)]) ).

cnf(1081,plain,
    sdtlseqdt0(xn,xn),
    inference(spm,[status(thm)],[256,107,theory(equality)]) ).

cnf(1401,plain,
    ( sdtpldt0(X1,xp) = xn
    | xr != X1 ),
    inference(csr,[status(thm)],[1000,415]) ).

cnf(3594,plain,
    ( aNaturalNumber0(xr)
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[410,55,theory(equality)]) ).

cnf(3606,plain,
    ( aNaturalNumber0(xr)
    | $false
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[3594,101,theory(equality)]) ).

cnf(3607,plain,
    ( aNaturalNumber0(xr)
    | $false
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[3606,105,theory(equality)]) ).

cnf(3608,plain,
    ( aNaturalNumber0(xr)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[3607,107,theory(equality)]) ).

cnf(3609,plain,
    aNaturalNumber0(xr),
    inference(cn,[status(thm)],[3608,theory(equality)]) ).

cnf(5510,plain,
    ( sdtpldt0(xp,xr) = xn
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[488,55,theory(equality)]) ).

cnf(5542,plain,
    ( sdtpldt0(xp,xr) = xn
    | $false
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[5510,101,theory(equality)]) ).

cnf(5543,plain,
    ( sdtpldt0(xp,xr) = xn
    | $false
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[5542,105,theory(equality)]) ).

cnf(5544,plain,
    ( sdtpldt0(xp,xr) = xn
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[5543,107,theory(equality)]) ).

cnf(5545,plain,
    sdtpldt0(xp,xr) = xn,
    inference(cn,[status(thm)],[5544,theory(equality)]) ).

cnf(5579,plain,
    ( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xp) ),
    inference(spm,[status(thm)],[140,5545,theory(equality)]) ).

cnf(5620,plain,
    ( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(xp) ),
    inference(rw,[status(thm)],[5579,3609,theory(equality)]) ).

cnf(5621,plain,
    ( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[5620,105,theory(equality)]) ).

cnf(5622,plain,
    ( sdtpldt0(xn,X1) = sdtpldt0(xp,sdtpldt0(xr,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[5621,theory(equality)]) ).

cnf(6350,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[527,201]) ).

cnf(6556,plain,
    ( sdtpldt0(sz00,xn) = xn
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xp) ),
    inference(spm,[status(thm)],[531,5545,theory(equality)]) ).

cnf(6592,plain,
    ( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[6350,531,theory(equality)]) ).

cnf(6597,plain,
    ( sdtpldt0(sz00,xn) = xn
    | $false
    | ~ aNaturalNumber0(xp) ),
    inference(rw,[status(thm)],[6556,3609,theory(equality)]) ).

cnf(6598,plain,
    ( sdtpldt0(sz00,xn) = xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[6597,105,theory(equality)]) ).

cnf(6599,plain,
    sdtpldt0(sz00,xn) = xn,
    inference(cn,[status(thm)],[6598,theory(equality)]) ).

cnf(6656,plain,
    ( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[6592,198,theory(equality)]) ).

cnf(6657,plain,
    ( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[6656,theory(equality)]) ).

cnf(6975,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(csr,[status(thm)],[511,201]) ).

cnf(7019,plain,
    ( sdtpldt0(X1,X2) = X3
    | sdtlseqdt0(sdtpldt0(X4,X3),sdtpldt0(X2,sdtpldt0(X4,X1)))
    | ~ sdtlseqdt0(X3,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X4)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[115,6975,theory(equality)]) ).

cnf(7319,plain,
    ( sz00 = X1
    | sdtpldt0(X3,sdtpldt0(X2,X1)) != sdtpldt0(X2,X3)
    | ~ aNaturalNumber0(sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(spm,[status(thm)],[428,513,theory(equality)]) ).

cnf(7338,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[538,513,theory(equality)]) ).

cnf(7412,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
    | $false
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[7338,105,theory(equality)]) ).

cnf(7413,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
    | $false
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[7412,3609,theory(equality)]) ).

cnf(7414,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[7413,106,theory(equality)]) ).

cnf(7415,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
    inference(cn,[status(thm)],[7414,theory(equality)]) ).

cnf(13381,plain,
    ( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[598,201]) ).

cnf(13410,plain,
    ( sdtmndt0(sdtpldt0(sz00,X1),X1) = sz00
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[13381,6657,theory(equality)]) ).

cnf(13443,plain,
    ( sdtmndt0(sdtpldt0(sz00,X1),X1) = sz00
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[13410,198,theory(equality)]) ).

cnf(13444,plain,
    ( sdtmndt0(sdtpldt0(sz00,X1),X1) = sz00
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[13443,theory(equality)]) ).

cnf(15246,plain,
    ( sdtmndt0(xn,xn) = sz00
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[13444,6599,theory(equality)]) ).

cnf(15272,plain,
    ( sdtmndt0(xn,xn) = sz00
    | $false ),
    inference(rw,[status(thm)],[15246,107,theory(equality)]) ).

cnf(15273,plain,
    sdtmndt0(xn,xn) = sz00,
    inference(cn,[status(thm)],[15272,theory(equality)]) ).

cnf(15321,plain,
    ( sdtpldt0(xn,sz00) = xn
    | ~ sdtlseqdt0(xn,xn)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[488,15273,theory(equality)]) ).

cnf(15332,plain,
    ( sdtpldt0(xn,sz00) = xn
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[15321,1081,theory(equality)]) ).

cnf(15333,plain,
    ( sdtpldt0(xn,sz00) = xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[15332,107,theory(equality)]) ).

cnf(15334,plain,
    sdtpldt0(xn,sz00) = xn,
    inference(cn,[status(thm)],[15333,theory(equality)]) ).

cnf(56014,plain,
    ( sdtpldt0(xp,sdtpldt0(X1,X2)) = sdtpldt0(xn,X2)
    | xr != X1
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[1021,415]) ).

cnf(56049,plain,
    ( sdtpldt0(xp,xn) = sdtpldt0(xn,xp)
    | xr != X1
    | ~ aNaturalNumber0(xp) ),
    inference(spm,[status(thm)],[56014,1401,theory(equality)]) ).

cnf(56268,plain,
    ( sdtpldt0(xp,xn) = sdtpldt0(xn,xp)
    | xr != X1
    | $false ),
    inference(rw,[status(thm)],[56049,105,theory(equality)]) ).

cnf(56269,plain,
    ( sdtpldt0(xp,xn) = sdtpldt0(xn,xp)
    | xr != X1 ),
    inference(cn,[status(thm)],[56268,theory(equality)]) ).

cnf(57056,plain,
    ( X1 = X2
    | sdtlseqdt0(xn,sdtpldt0(xp,X1))
    | xr != X2
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[1023,415]) ).

cnf(57058,plain,
    ( xn = xr
    | sdtlseqdt0(xn,sdtpldt0(xp,xn))
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[57056,151,theory(equality)]) ).

cnf(57175,plain,
    ( xn = xr
    | sdtlseqdt0(xn,sdtpldt0(xp,xn))
    | $false ),
    inference(rw,[status(thm)],[57058,107,theory(equality)]) ).

cnf(57176,plain,
    ( xn = xr
    | sdtlseqdt0(xn,sdtpldt0(xp,xn)) ),
    inference(cn,[status(thm)],[57175,theory(equality)]) ).

cnf(57177,plain,
    sdtlseqdt0(xn,sdtpldt0(xp,xn)),
    inference(sr,[status(thm)],[57176,152,theory(equality)]) ).

cnf(72313,plain,
    sdtpldt0(xn,xp) = sdtpldt0(xp,xn),
    inference(er,[status(thm)],[56269,theory(equality)]) ).

cnf(72335,plain,
    ( sz00 = xp
    | sdtpldt0(xp,xn) != xn
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(spm,[status(thm)],[428,72313,theory(equality)]) ).

cnf(72506,plain,
    ( sz00 = xp
    | sdtpldt0(xp,xn) != xn
    | $false
    | ~ aNaturalNumber0(xp) ),
    inference(rw,[status(thm)],[72335,107,theory(equality)]) ).

cnf(72507,plain,
    ( sz00 = xp
    | sdtpldt0(xp,xn) != xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[72506,105,theory(equality)]) ).

cnf(72508,plain,
    ( sz00 = xp
    | sdtpldt0(xp,xn) != xn ),
    inference(cn,[status(thm)],[72507,theory(equality)]) ).

cnf(72509,plain,
    sdtpldt0(xp,xn) != xn,
    inference(sr,[status(thm)],[72508,236,theory(equality)]) ).

cnf(174671,plain,
    ( sdtpldt0(xp,sdtpldt0(sz00,xr)) = sdtpldt0(xn,sz00)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(xr) ),
    inference(spm,[status(thm)],[5622,6657,theory(equality)]) ).

cnf(174988,plain,
    ( sdtpldt0(xp,sdtpldt0(sz00,xr)) = xn
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(xr) ),
    inference(rw,[status(thm)],[174671,15334,theory(equality)]) ).

cnf(174989,plain,
    ( sdtpldt0(xp,sdtpldt0(sz00,xr)) = xn
    | $false
    | ~ aNaturalNumber0(xr) ),
    inference(rw,[status(thm)],[174988,198,theory(equality)]) ).

cnf(174990,plain,
    ( sdtpldt0(xp,sdtpldt0(sz00,xr)) = xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[174989,3609,theory(equality)]) ).

cnf(174991,plain,
    sdtpldt0(xp,sdtpldt0(sz00,xr)) = xn,
    inference(cn,[status(thm)],[174990,theory(equality)]) ).

cnf(175678,plain,
    ( sdtpldt0(sz00,sdtpldt0(xr,xp)) = xn
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[6975,174991,theory(equality)]) ).

cnf(175918,plain,
    ( sdtpldt0(sz00,sdtpldt0(xr,xp)) = xn
    | $false
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[175678,105,theory(equality)]) ).

cnf(175919,plain,
    ( sdtpldt0(sz00,sdtpldt0(xr,xp)) = xn
    | $false
    | $false
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[175918,3609,theory(equality)]) ).

cnf(175920,plain,
    ( sdtpldt0(sz00,sdtpldt0(xr,xp)) = xn
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[175919,198,theory(equality)]) ).

cnf(175921,plain,
    sdtpldt0(sz00,sdtpldt0(xr,xp)) = xn,
    inference(cn,[status(thm)],[175920,theory(equality)]) ).

cnf(177662,plain,
    ( xn = sdtpldt0(xr,xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xr) ),
    inference(spm,[status(thm)],[531,175921,theory(equality)]) ).

cnf(177891,plain,
    ( xn = sdtpldt0(xr,xp)
    | $false
    | ~ aNaturalNumber0(xr) ),
    inference(rw,[status(thm)],[177662,105,theory(equality)]) ).

cnf(177892,plain,
    ( xn = sdtpldt0(xr,xp)
    | $false
    | $false ),
    inference(rw,[status(thm)],[177891,3609,theory(equality)]) ).

cnf(177893,plain,
    xn = sdtpldt0(xr,xp),
    inference(cn,[status(thm)],[177892,theory(equality)]) ).

cnf(260496,plain,
    ( sdtpldt0(X1,X2) = X3
    | sdtlseqdt0(sdtpldt0(X4,X3),sdtpldt0(X2,sdtpldt0(X4,X1)))
    | ~ sdtlseqdt0(X3,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X4)
    | ~ aNaturalNumber0(X3) ),
    inference(csr,[status(thm)],[7019,201]) ).

cnf(338987,plain,
    ( sz00 = X1
    | sdtpldt0(X3,sdtpldt0(X2,X1)) != sdtpldt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(csr,[status(thm)],[7319,201]) ).

cnf(355077,negated_conjecture,
    ( sdtpldt0(xm,xn) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
    inference(rw,[status(thm)],[7415,177893,theory(equality)]) ).

cnf(355078,negated_conjecture,
    ( sdtpldt0(xm,xn) = sdtpldt0(xn,sdtpldt0(xm,xp))
    | ~ sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
    inference(rw,[status(thm)],[355077,177893,theory(equality)]) ).

cnf(355104,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
    | sdtpldt0(xp,xn) = xn
    | ~ sdtlseqdt0(xn,sdtpldt0(xp,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(spm,[status(thm)],[355078,260496,theory(equality)]) ).

cnf(355154,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
    | sdtpldt0(xp,xn) = xn
    | $false
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(rw,[status(thm)],[355104,57177,theory(equality)]) ).

cnf(355155,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
    | sdtpldt0(xp,xn) = xn
    | $false
    | $false
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(rw,[status(thm)],[355154,106,theory(equality)]) ).

cnf(355156,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
    | sdtpldt0(xp,xn) = xn
    | $false
    | $false
    | $false
    | ~ aNaturalNumber0(xp) ),
    inference(rw,[status(thm)],[355155,107,theory(equality)]) ).

cnf(355157,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
    | sdtpldt0(xp,xn) = xn
    | $false
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[355156,105,theory(equality)]) ).

cnf(355158,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn)
    | sdtpldt0(xp,xn) = xn ),
    inference(cn,[status(thm)],[355157,theory(equality)]) ).

cnf(355159,negated_conjecture,
    sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xm,xn),
    inference(sr,[status(thm)],[355158,72509,theory(equality)]) ).

cnf(355590,negated_conjecture,
    ( sz00 = xp
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[338987,355159,theory(equality)]) ).

cnf(356619,negated_conjecture,
    ( sz00 = xp
    | $false
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[355590,105,theory(equality)]) ).

cnf(356620,negated_conjecture,
    ( sz00 = xp
    | $false
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[356619,106,theory(equality)]) ).

cnf(356621,negated_conjecture,
    ( sz00 = xp
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[356620,107,theory(equality)]) ).

cnf(356622,negated_conjecture,
    sz00 = xp,
    inference(cn,[status(thm)],[356621,theory(equality)]) ).

cnf(356623,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[356622,236,theory(equality)]) ).

cnf(356624,negated_conjecture,
    $false,
    356623,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM494+1 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04  % Command  : Source/sine.py -e eprover -t %d %s
% 0.02/0.23  % Computer : n138.star.cs.uiowa.edu
% 0.02/0.23  % Model    : x86_64 x86_64
% 0.02/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23  % Memory   : 32218.625MB
% 0.02/0.23  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23  % CPULimit : 300
% 0.02/0.23  % DateTime : Fri Jan  5 05:44:00 CST 2018
% 0.02/0.23  % CPUTime  : 
% 0.02/0.27  % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.27  --creating new selector for []
% 7.28/7.52  -running prover on /export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1 with time limit 29
% 7.28/7.52  -running prover with command ['/export/starexec/sandbox/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox/tmp/tmpm2TVOq/sel_theBenchmark.p_1']
% 7.28/7.52  -prover status Theorem
% 7.28/7.52  Problem theBenchmark.p solved in phase 0.
% 7.28/7.52  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.28/7.52  % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.28/7.52  Solved 1 out of 1.
% 7.28/7.52  # Problem is unsatisfiable (or provable), constructing proof object
% 7.28/7.52  # SZS status Theorem
% 7.28/7.52  # SZS output start CNFRefutation.
% See solution above
% 7.28/7.52  # SZS output end CNFRefutation
%------------------------------------------------------------------------------